Das durchschnittliche Haus tatsächlich verursacht mehr Luftverschmutzung als das durchschnittliche Auto. Dies liegt daran, dass ein Großteil der Energie, die wir in unseren Häusern verwenden, von Kraftwerken stammt, die fossile Brennstoffe verbrennen, um unsere elektrischen Produkte anzutreiben. Brennende fossile Brennstoffe verursachen Luftverschmutzung und tragen zum Smog, sauren Regen und zur globalen Erwärmung bei. Energie sparen spart auch Geld. Durch den Einsatz energieeffizienter Geräte können Haushalte bis zu 400 pro Jahr auf Stromrechnungen sparen. Durch die effizientere Nutzung unserer vorhandenen Geräte können wir auch die Lebensdauer der Geräte verlängern. Der amerikanische Rat für eine energieeffiziente Wirtschaft schätzt, dass, wenn jeder von uns die Energieeffizienz in unseren Hauptgeräten um 10 - 30 erhöht, freigeben Sie die Nachfrage nach Elektrizität um das Äquivalent von 25 großen Kraftwerken Wie man energieeffiziente Geräte kauft Die Haushaltsgeräte sehen zwar auf der Außenseite ziemlich ähnlich aus, unterscheiden sich aber in Bezug auf Energieeffizienz und Betriebskosten erheblich. Je energieeffizienter ein Gerät ist, desto weniger kostet es zu laufen. Sie können Ihre Stromrechnung senken und helfen, die Umwelt zu schützen. Hier sind ein paar einfache Schritte, um beim Einkaufen für energieeffiziente Geräte folgen: Wählen Sie die Größe und Stil. Messen Sie den Raum, den das Gerät belegt, um sicherzustellen, dass Ihr neuer Kauf passt. Überprüfen Sie, dass es genug Raum, um die Tür oder den Deckel vollständig zu öffnen, und genügend Abstand zur Belüftung. Betrachten Sie sowohl den Kaufpreis als auch den geschätzten Energieverbrauch. Bei der Entscheidung, welche Marke und Modell zu kaufen. In vielen Fällen können Sie Geld sparen, indem Sie das teurere, energieeffizientere Modell kaufen. Fragen Sie nach speziellen energieeffizienten Angeboten. Cash-Rabatte, zinsgünstige Darlehen oder andere Anreizprogramme werden oft angeboten, um Käufer zu ermutigen, energieeffiziente Geräte zu kaufen. Um Rabatte in Ihrer Nähe zu finden, verwenden Sie Energy Stars Rebate Locato r (verknüpft von der Homepage unter Produkte), mit der Sie nach Postleitzahl suchen können. Lesen Sie das Label Energy Guide. Dieses gelbe und schwarze Etikett wird von der FTC gefordert, um an allen neuen Geräten (außer Küchenbereichen, Mikrowellenherden und Wäschetrocknern) befestigt zu werden. Es gibt den geschätzten jährlichen Energieverbrauch des Geräts an. Das Lesen des Energy Guide Labels hilft Ihnen, die Effizienz oder den jährlichen Energieverbrauch von konkurrierenden Marken und ähnlichen Modellen zu vergleichen. Suchen Sie nach dem Energy Star-Logo. Geräte mit diesem Logo sind wesentlich energieeffizienter als das durchschnittliche Vergleichsmodell. Das Energy-Star-Programm wird gemeinsam von der U. S.Department of Energy und der EPA betrieben. Weitere Informationen zu diesem Programm finden Sie weiter unten. Der Kühlschrank ist der größte Verbraucher in den meisten Haushalten. Sind hier einige einfache Weisen, seine Leistungsfähigkeit zu verbessern: Justieren Sie Temperatureinstellungen für verschiedene Jahreszeiten. Überprüfen Sie die Einstellung des Kühlschrankes, indem Sie ein Thermometer in ein Glas Wasser geben und im Kühlschrank über Nacht lassen. Am Morgen sollte die Temperatur 34 bis 40 Grad F lesen. Passen Sie die Einstellungen gegebenenfalls an. Temperatur-Einstellungen müssen in der Regel im Winter reduziert werden. Der Gefrierschrank sollte zwischen 0 und 5 Grad F. Im Winter, Gefrierschrank wird oft unbenutzt. Ihr Kühlschrank verwendet weiterhin Energie, um diesen Raum einzufrieren. Nehmen Sie leere Milchkannen oder andere Kunststoffbehälter und füllen Sie sie mit Wasser. Legen Sie sie draußen, bis sie einfrieren, dann legen Sie sie in Ihrem Gefrierschrank. Dies wird den leeren Raum füllen und die zu kühlende Fläche reduzieren. Manuelle Abtaukühlschränke sind in der Regel effizienter als automatische Abtau-Modelle, aber nur, wenn sie ordnungsgemäß gewartet werden. Der Gefrierschrank sollte aufgetaut werden, wenn Eisaufbau dicker als 14 Zoll ist. Abtauen Lebensmittel, indem Sie es in den Kühlschrank die Nacht, bevor Sie es verwenden möchten. Dies kühlt den Kühlschrank nach unten und reduziert seinen Stromverbrauch. Warten Sie, bis das Essen abgekühlt ist, bevor Sie es in den Kühlschrank stellen. Vakuum die Spulen in der Rückseite Ihres Kühlschranks zweimal im Jahr, um die Effizienz zu maximieren. Überprüfen Sie die Türdichtung gelegentlich, um sicherzustellen, dass die Dichtung nicht durch Schmutz gebrochen oder auf Nahrung verkrustet wird. Der Kühlschrank sollte nicht in der Nähe von Herd, Spülmaschine, Wärmeentlüftung oder direktem Sonnenlicht liegen. Überprüfen Sie, um sicherzustellen, dass Luftstrom um Ihren Kühlschrank nicht behindert wird. Wenn Ihr Kühlschrank einen Energiespar - (Anti-Schweiß-) Schalter hat, sollte er während des Sommers und während des Winters eingeschaltet sein. Führen Sie keine frostfreien Kühlschränke mit Gefrierabteilen in ungeheizten Bereichen mit Lufttemperatur unter 60 Grad F. Ein großer Kühlschrank ist billiger und effizienter zu laufen als zwei kleinere. Loswerden eines alten Kühlschranks ist einer der größten einzelnen Beiträge, die Sie zur Senkung Ihrer elektrischen Rechnungen und zur Erhaltung von Energie und Ressourcen machen können. Erwerb eines neuen Kühlschranks Kühlschränke mit weniger Zubehör sind in der Regel effizienter. Insbesondere: 8226 Eiserzeuger und Wasserspender verwenden übermäßige Energie und sind nicht besonders nützlich. 8226 automatische Abtauung verursacht niedrigeren Gesamtwirkungsgrad, da Wärme verwendet wird, um Abtauung Geschwindigkeit 8226 die effizientesten Kühlschränke sind 16-20cu ft, mit Gefrierschrank auf der Unterseite oder oben statt der Seite. Verwenden Sie den Brenner, der der Topfgröße am nächsten kommt. Hitze ist verloren und Energie wird verschwendet, wenn Brennergröße größer als Topfgröße ist. Verwenden Sie Deckel auf Töpfe und Pfannen, so können Sie bei niedrigeren Einstellungen zu kochen. Tropfwannen unter herkömmlichen Spiralbrennern sauber halten. Dont Line Drip Pfannen mit Aluminiumfolie - sie können zu viel Wärme reflektieren und die Elemente beschädigen. Nur beim Backen vorwärmen. Überprüfen Sie Ihre Ofentemperatur. Verwenden Sie einen separaten Ofen Thermometer, um sicherzustellen, Ihre Backofen-Steuerung ist genau. Stellen Sie sicher, dass die Backofentürdichtung fest sitzt. Vermeiden Sie das Öffnen der Backofentür beim Backen - bei jedem Öffnen der Tür gehen etwa 20 der Innenwärme verloren. Backofen ausschalten ein paar Minuten, bevor das Essen fertig ist, und lassen Ofen Wärme beenden den Job. Gasherde: elektronische Zündung (Piezo) wird etwa 40 weniger Gas als eine Kontrollleuchte verwenden. Pilotlicht und Brennerflamme auf Gasherden sollten blau sein. Wenn die Flamme gelb ist, müssen die Anschlüsse nicht verstopft oder verstellt werden. Anschlüsse können mit Pfeifenreinigern entfernt werden. Verwenden Sie die Mikrowelle. Sie verwenden nur 13 bis 12 so viel Energie wie herkömmliche Öfen. Selbstreinigende Öfen sind effizienter, weil sie besser isoliert sind. Induktionsküchen verwenden 90 der erzeugten Energie im Vergleich zu nur 55 für einen Gasbrenner und 65 für herkömmliche elektrische Bereiche. Mehr Infos Sun (Solar) Öfen sind die energieeffizienteste Kochgerät, da sie keine Brennstoffe jeglicher Art zu kochen brauchen, aber erreichen Temperaturen von 360deg - 400deg. Diese Öfen ließen Sie auch außerhalb des Hauses kochen, das ist ein echter Vorteil während der Sommermonate seit Indoor-Küche erhöht die Innentemperaturen. So Öfen auch unendlich dauern, da es keine beweglichen Teile oder komplexe Technologie zu brechen oder Verschleiß. Vor kurzem wurde der All-American Sun Ofen mit mehr benutzerfreundlichen Funktionen entwickelt. Für ein vollständiges Nahrungsmittelbereitschaftgerät, das Nahrungsmitteldehydratisierungsmerkmale einschließt, sehen Sie den All-Amerikanischen Sonne-Ofen mit Dehydration und Preparedness Paket. Achten Sie darauf, Ihre Kleider sind schmutzig genug, um wirklich brauchen Waschen. Standardwaschmaschinen verwenden 40 Gallonen Wasser pro Ladung. Die einfachste Weise, Wasser und Energie mit Unterlegscheiben zu sparen, ist, sie weniger zu verwenden, also schauen zu Weisen, die Sie Kleidung, Tücher und Leinen zwischen Waschungen wiederverwenden können. Stellen Sie den Wasserstand und die Temperatureinstellungen Ihrer Waschmaschine auf die Größe Ihrer Last ein. Füllen Sie nicht die ganze Wanne für einige Einzelteile. Neuere Maschinen haben automatische Wasserstand-Einstellungen, die auf Lastgröße anpassen. Rufen Sie Ihren Wasser-Dienstprogramm und fragen Sie, wie hart oder weich Ihr Wasser ist. Sie können bis zu sechs Mal so viel Kleidung Waschmittel, wie Sie benötigen. In den Bedienungsanleitungen erfahren Sie, wie viel Sie für Ihren Wassertyp benötigen. So viel wie 90 der Energie von Ihrer Waschmaschine verwendet wird, um das Wasser zu erhitzen. Für die meisten Waschanwendungen sind warmes Waschen und kaltes Spülen genauso effektiv wie heißes Waschen und warmes Spülen. Die Spültemperatur beeinflusst nicht die Qualität der Reinigung. Vermeiden Sie zu viel Spülmittel. Befolgen Sie die Anweisungen auf dem Karton. Oversudsing macht Ihre Maschine härter arbeiten und mehr Energie. Flusensieb nach jedem Gebrauch reinigen. Lint Aufbau stark reduziert die Effizienz. Überlastung des Trockners verlängert die Trockenzeit. Kleidung sollte in 40 Minuten bis eine Stunde trocknen. Wählen Sie einen Abkühlzyklus. In den letzten Minuten wird keine Hitze zugeführt, aber die Trocknung wird fortgesetzt, wenn kühle Luft durch die Taumelkleidung geblasen wird. Halten Sie den Trockner Auspuff an der Außenseite des Hauses sauber. Es sollte klar sein, von Spinnweben und Fusseln. Die beweglichen Rollläden sollten sich leicht bewegen - sie sind so konzipiert, dass keine Kaltluft, Hitze und Insekten in die Lüftung gelangen, wenn der Trockner nicht in Betrieb ist. Trocknen Sie mehrfache Lasten zurück zu Rückseite. Da der Trockner Zeit und Energie braucht, um sich auf die Trocknungstemperatur zu erwärmen, verwendet das Stop-and-Start-Trocknen mehr Energie. Mit einer Wäscheleine, einer versenkbaren Wäscheleine oder einem Innen-Wäscheständer sparen Sie Energie und reduzieren den Stoffverschleiß Ihrer Kleidungsstücke (die Fussel auf dem Flusensieb ist Ihre Kleidung abgebaut). Kauf eines neuen Trockners Suchen Sie nach einem Modell, das mit einem Sensor kommt, der den Trockner automatisch stoppt, wenn die Kleidung trocken ist. Trockner mit Abkühlzeit sparen Energie. Die neueren Frontlader sind viel weniger Wasser, halten größere Lasten und sparen Energie bei reduzierter Wassererwärmung. Trocknerfolien und der Flusenfilter - wie die Brandgefahr zu verringern, die Effizienz zu verbessern Wenn Sie Trocknerbetten verwenden, wenn Sie Ihren Wäschetrockner verwenden, achten Sie darauf, nehmen Sie den Flusenfilter aus und waschen Sie sie mit heißem Seifenwasser und einer alten Zahnbürste mindestens alle sechs Monate . Dies liegt daran, dass die Trocknerfolien den Flusenfilter mit einem unsichtbaren Film beschichten können, der zu einem niedrigeren Trocknerwirkungsgrad, einer ausgebrannten Heizeinheit und sogar zu einem möglichen Brand führen kann. Um zu überprüfen, ob es einen Film auf dem Flusensieb gibt, ziehen Sie einfach den Filter heraus und führen ihn unter heißem Wasser in die Spüle. Wenn das Wasser auf dem Filter aufsammelt, müssen Sie es reinigen. Vermeiden Sie unnötige Vorspülung, bevor Sie Geschirr in die Waschmaschine geben. Moderne Geschirrspülmaschinen sind sehr effizient und entfernen Sie alle, aber die hartnäckigsten Lebensmittelreste. Vorspülen oder einweichen nur die Speisen und Kochgeschirr, die nicht kommen wird sauber in der Spülmaschine. Führen Sie die Waschmaschine nur aus, wenn sie voll ist. Säubern Sie Spülmaschinenabläufe und Filter, um leistungsfähigen Betrieb sicherzustellen. Wenn Sie kaufen eine neue Spülmaschine, kaufen Sie die Größe, die Ihren Bedürfnissen passt. Größere Geschirrspüler verwenden mehr Wasser und Strom und sind teurer. Wählen Sie einen Geschirrspüler mit einem quotenergy-savequot oder Quotch-Waschgang Zyklus, der weniger Wasser verwendet und arbeitet für eine kürzere Zeit. Wählen Sie einen Geschirrspüler mit einem quotair-dryquot Option, die Zirkulationsventilatoren verwendet. Dadurch wird weniger Strom verbraucht als im Modus "quotheat-dryquot". Suchen Sie einen Geschirrspüler mit einem Warmwasserbooster oder internen Wasser-Heizung, die Wassertemperatur in der Spülmaschine erhöht. Installieren Sie einen Deckenventilator im größten Raum Ihres Hauses. Dadurch können Sie die Einstellung auf Ihrer Klimaanlage 3 bis 6 Grad zu senken, die bis zu 25 der Energiekosten der Hauskühlung sparen wird. (Vergewissern Sie sich, dass die Umdrehung des Lüfters im Winter im Uhrzeigersinn quittiert wird.) Reinigen Sie den Filterbildschirm einmal im Monat. Dies reduziert die Lüfterverbrauch und Strom sparen. Beim Einschalten des Klimageräts vermeiden Sie die kälteste Einstellung. Lassen Sie das Klimagerät für eine Weile warmlaufen, bevor Sie die Temperatureinstellung absenken. Der Raum wird genauso schnell abkühlen. Es isnrsquot empfohlen, dass Sie Ihre Klimaanlage auf verlassen, wenn Sie Ihr Haus verlassen, aber wenn yoursquore gehen, dies zu tun, drehen Sie die Temperatureinrichtung ein paar mehr Grad, während yoursquore gegangen, um 28 ° C (82deg F). Vergessen Sie auch nicht, Ihre Klimaanlage auszuschalten, wenn Ihr Haus weg von Ihrem Haus für mehr als einen Tag sein wird. Halten Sie Blätter und andere Ablagerungen von der Verflüssigungseinheit fern und reinigen Sie vorsichtig Bänder und Staub von kondensierenden Spulen. Vergewissern Sie sich, dass der Luftstrom nicht behindert ist. Wenn Sie ein neues Klimagerät kaufen, wählen Sie ein Modell mit einem Energieeffizienz-Verhältnis (EER) von 10,0 oder höher. Warmwasserbereiter isolieren. Wenn Ihr Wasser-Heizung fühlt sich warm anfühlt, sparen Sie Geld und haben mehr Warmwasser durch zusätzliche Isolierung. Heres, wie unterere Einstellungen auf Wasser-Heizung. Experiment innerhalb der 120-140 Grad Bereich, um die niedrigste Einstellung, die Sie mit ausreichend heißem Wasser liefert zu finden. Der Betrieb eines Wasserkochers bei unnötig hohen Temperaturen erhöht den Energieverbrauch und verkürzt die Tanklebensdauer. Es erhöht auch die Likellihood von Verbrühungen ein besonderes Anliegen für kleine Kinder und Senioren. Als allgemeine Regel sollte sie nicht höher als 120F (49C) sein, aber immer mit dem Behälterhersteller überprüfen oder zuerst im Handbuch sehen. Wrap Wasserleitungen aus dem Wasser-Heizung. Heres, wie Wenn youre bereit für eine neue Wasser-Heizung, betrachten eine tankless Wasser-Heizung. Diese Modelle können so viel wie fünfzig Prozent der Kosten für Heizwasser sparen. Computer und Büroausstattung Schalten Sie den Monitor aus, wenn Ihr Computer nicht in Gebrauch ist. Über die Hälfte der vom Computer verwendeten Energie geht zum Monitor, so dass es ausgeschaltet wird deutlich sparen. Ein einzelner Monitor, der über Nacht eingeschaltet wird, kann die gleiche Energie wie ein Laserdrucker verwenden, der 800 gedruckte Exemplare produziert. Und nicht von einem Bildschirmschoner getäuscht werden der Computer immer noch mit voller Leistung, um diese auszuführen. Schalten Sie das Gerät aus, wenn es nicht benutzt wird (außer Ihrem Faxgerät). Selbst Maschinen im Standby nutzen bis zu 30 Watt Strom. Drucken kann der energieintensivste Schritt sein, also nur Seiten drucken, die Sie benötigen. Bearbeiten Sie Dokumente auf dem Bildschirm, um unnötiges Drucken zu speichern. Wenn Sie eine Auswahl an Druckern haben, vermeiden Sie die Verwendung eines Laserdruckers für Druckausgaben. Papier wiederverwenden. Tintenstrahldrucker können benutztes Papier leicht annehmen, so dass Sie auf der unbenutzten Seite drucken können. Oder halten Sie abgelegte Seiten für Notizen. Kauf eines neuen Computers Überlegen Sie, ob ein Laptop könnte Ihre Bedürfnisse erfüllen. Laptops verwenden etwa die Hälfte des Stromverbrauchs von typischen Desktop-Computern. Wenn Sie einen Laptop kaufen, suchen Sie nach Systemen, die komplett aus 3,3 Volt Komponenten (Prozessor, Speicher und LCD) bestehen. Diese Systeme verwenden 40 bis 50 weniger Energie als 5.0-Volt-Systeme und sind in der Regel mit einer leichteren Batterie ausgestattet. Alternativ suchen Sie nach einem Modell mit einem Energy Star-Rating. Kauf eines neuen Druckers Tintenstrahldrucker haben einen geringen Energieverbrauch, sind preiswert und ermöglichen die Wiederverwendung von Papier, sparen Kosten und reduzieren die Umweltbelastung. Wenn Sie einen Laser-Drucker kaufen, suchen Sie nach einem mit einem Energiespar-Funktion, die Energieverbrauch reduziert, wenn im Leerlauf über 65 Prozent. Selbst im Ruhezustand verbrauchen Laserdrucker zwischen 30 und 35 Prozent ihres Spitzenstrombedarfs. Verlust der Phantomspeisung: Stecken Sie Ihr Fernsehgerät, Ihren DVD-Player, Ihren Videorecorder und Ihre Stereoanlage in eine Stromschiene. Wenn Sie sie ausschalten, schalten Sie die Bar, so dass sie nicht Zeichnung quotphantom powerquot, während Sie nicht mit ihnen. Sie können jede Ihrer home appliancis für versteckten Energieverlust überprüfen, indem Sie einen Elektrizitätsmonitor benutzen. Recycling Ihrer alten Computer: Elektronische Abfälle wird ein ernstes und zunehmendes Problem mit dem hohen Umsatz von Computern. Computer enthalten erhebliche Mengen an Blei und Schwermetallen, die für die Umwelt gefährlich sind. Hier sind mehrere Alternativen zum Senden Ihres Computers auf die Deponie: Pass it on. Die einfachste Lösung zum Recycling Ihres alten Computers. Fragen Sie an einer örtlichen Schule oder einen Hinweis auf eine Community Bulletin Board mit Ihrem Computer kostenlos für die Aufnahme. Viele Menschen ohne Computer werden immer noch mit der Textverarbeitung und grundlegende Programme zu finden. Recyceln. Mehrere Computerhersteller haben Recycling-Programme entwickelt. Für eine kleine Gebühr, können Sie alte Computer-Ausrüstung aufgehoben für das Recycling. Couponpunkte sind von HP für zukünftige Käufe erhältlich. Für weitere Informationen, besuchen Sie: hp. recycle In den USA bietet die National Cristina Foundation (NCF) Computer-Technologie für Menschen mit Behinderungen, Studenten gefährdet und wirtschaftlich benachteiligten Personen. Crowdsourcing ist ein sehr beliebtes Mittel, um die großen Mengen an etikettierten Daten zu erhalten Dass moderne Maschinen lernen Methoden erfordern. Obwohl billig und schnell zu erhalten, leiden Crowdsourcing-Etiketten erhebliche Fehler, wodurch die Leistung der nachgelagerten maschinellen Lernaufgaben verschlechtert wird. Mit dem Ziel, die Qualität der markierten Daten zu verbessern, versuchen wir, die vielen Fehler, die durch dumme Fehler oder unbeabsichtigte Fehler durch Crowdsourcing Arbeiter auftreten zu mildern. Wir schlagen eine zweistufige Einstellung für Crowdsourcing vor, bei der der Arbeiter zuerst die Fragen beantwortet und dann seine Antworten ändern kann, nachdem er eine (verrauschte) Referenzantwort angesehen hat. Wir formulieren diesen Prozess mathematisch und entwickeln Mechanismen, um ArbeiterInnen dazu anzuregen, entsprechend zu handeln. Unsere mathematischen Garantien zeigen, dass unser Mechanismus die Arbeiter anreizt, in beiden Stufen ehrlich zu antworten und in der ersten Phase nicht zufällig zu antworten oder einfach in die zweite zu kopieren. Numerische Experimente zeigen eine signifikante Leistungssteigerung, die diese 8220-Selbstkorrektur8221 bei der Anwendung von Crowdsourcing bereitstellen kann, um maschinelle Lernalgorithmen zu trainieren. Es gibt verschiedene parametrische Modelle für die Analyse von paarweisen Vergleichsdaten, einschließlich der Bradley-Terry-Luce - (BTL) und Thurstone-Modelle, aber ihre Abhängigkeit von starken parametrischen Annahmen ist limitierend. In dieser Arbeit untersuchen wir ein flexibles Modell für paarweise Vergleiche, bei denen die Wahrscheinlichkeiten der Ergebnisse nur erforderlich sind, um eine natürliche Form der stochastischen Transitivität zu befriedigen. Diese Klasse umfasst parametrische Modelle einschließlich der BTL - und Thurstone-Modelle als Spezialfälle, ist aber wesentlich allgemeiner. Wir bieten verschiedene Beispiele für Modelle in dieser breiteren stochastisch transitiven Klasse, für die klassische parametrische Modelle schlechte Anpassungen bieten. Trotz dieser größeren Flexibilität zeigen wir, dass die Matrix der Wahrscheinlichkeiten mit der gleichen Rate geschätzt werden kann wie bei den parametrischen Standardmodellen. Anders als bei den BTL - und Thurstone-Modellen ist die Berechnung des minimaximal-optimalen Schätzers im stochastisch transitiven Modell nicht trivial, und wir erforschen verschiedene rechnerisch lenkbare Alternativen. Wir zeigen, dass ein einfacher singulärer Schwellenwertalgorithmus statistisch konsistent ist, jedoch nicht die minimax-Rate erreicht. Wir schlagen daher Algorithmen vor, die die minimax-Rate über interessante Unterklassen der vollen stochastisch transitiven Klasse erreichen. Wir ergänzen unsere theoretischen Ergebnisse durch gründliche numerische Simulationen. Wir zeigen, wie jedes binäre Paarweise Modell zu einem vollsymmetrischen Modell entwurzelt werden kann, wobei ursprüngliche Singletonpotentiale in Potentiale an Kanten zu einer addierten Variablen transformiert und dann zu einem neuen Modell auf der ursprünglichen Anzahl von Variablen umgeleitet werden. Das neue Modell entspricht im Wesentlichen dem ursprünglichen Modell mit der gleichen Partitionsfunktion und ermöglicht die Wiederherstellung der ursprünglichen Marginale oder eine MAP-Konguration, kann jedoch sehr unterschiedliche Berechnungsmerkmale aufweisen, die eine wesentlich effizientere Schlußfolgerung ermöglichen. Dieser Meta-Ansatz vertieft unser Verständnis, kann auf jeden bestehenden Algorithmus angewendet werden, um verbesserte Methoden in der Praxis zu ergeben, verallgemeinert frühere theoretische Ergebnisse und zeigt eine bemerkenswerte Interpretation des Triplet-konsistenten Polytops. Wir zeigen, wie tiefe Lernmethoden im Kontext von Crowdsourcing und unüberwartetem Ensemble-Lernen angewendet werden können. Zunächst beweisen wir, dass das populäre Modell von Dawid und Skene, das davon ausgeht, dass alle Klassifikatoren bedingt unabhängig sind, auf eine Restricted Boltzmann Machine (RBM) mit einem einzigen verdeckten Knoten. Daher können unter diesem Modell die hinteren Wahrscheinlichkeiten der wahren Markierungen stattdessen über ein trainiertes RBM geschätzt werden. Um dem allgemeineren Fall zu begegnen, wo Klassifikatoren die bedingte Unabhängigkeitsannahme stark verletzen können, schlagen wir vor, RBM-basiertes Deep Neural Net (DNN) anzuwenden. Experimentelle Ergebnisse auf verschiedenen simulierten und realen Datensätzen zeigen, dass unsere vorgeschlagene DNN-Ansatz besser zu anderen state-of-the-art Methoden, insbesondere wenn die Daten gegen die Bedingung der Unabhängigkeit Annahme. Revisiting Semi-überwachte Lernen mit Graph Embeddings Zhilin Yang Carnegie Mellon University. William Cohen CMU. Ruslan Salakhudinov U. von Toronto Papier AbstractWe präsentieren eine semi-überwachte Lern-Framework basierend auf Graph Embeddings. Anhand eines Graphen zwischen Instanzen schulen wir für jede Instanz eine Einbettung, um gemeinsam das Klassenlabel und den Nachbarschaftskontext im Graphen vorhersagen zu können. Wir entwickeln sowohl transduktive als auch induktive Varianten unserer Methode. In der transduktiven Variante unseres Verfahrens werden die Klassenlabels durch sowohl die gelernten Einbettungen als auch die Eingangsmerkmalsvektoren bestimmt, während in der induktiven Variante die Einbettungen als parametrische Funktion der Merkmalsvektoren definiert sind, so dass Vorhersagen für Fälle nicht möglich sind Während des Trainings. Auf einer großen und vielfältigen Reihe von Benchmark-Aufgaben, einschließlich der Textklassifikation, der fernüberwachten Entity-Extraktion und der Entity-Klassifizierung, zeigen wir eine verbesserte Leistung gegenüber vielen der bestehenden Modelle. Das Fortbewegungslernen kann komplexe Verhaltensweisen auf hohem Niveau erlangen. Das Definieren einer Kostenfunktion, die effektiv optimiert werden kann und die richtige Aufgabe kodiert, ist jedoch in der Praxis herausfordernd. Wir untersuchen, wie die inverse optimale Steuerung (IOC) verwendet werden kann, um Verhalten aus Demonstrationen zu erlernen, mit Anwendungen zur Drehmomentsteuerung von hochdimensionalen Robotersystemen. Unsere Methode behandelt zwei wichtige Herausforderungen bei der inversen optimalen Steuerung: zum einen die Notwendigkeit von informativen Merkmalen und eine wirksame Regularisierung, um die Kosten aufzuerlegen, und zum anderen die Schwierigkeit, die Kostenfunktion unter unbekannter Dynamik für hochdimensionale kontinuierliche Systeme zu erlernen. Um der früheren Herausforderung gerecht zu werden, stellen wir einen Algorithmus vor, der in der Lage ist, beliebige nichtlineare Kostenfunktionen, wie neuronale Netze, ohne sorgfältiges Feature Engineering zu erlernen. Um diese Herausforderung anzugehen, formulieren wir eine effiziente samplebasierte Approximation für MaxEnt IOC. Wir evaluieren unsere Methode auf einer Reihe von simulierten Aufgaben und realen Robotermanipulationsproblemen und zeigen eine wesentliche Verbesserung gegenüber früheren Methoden sowohl hinsichtlich der Komplexität der Aufgaben als auch der Effizienz der Proben. Beim Lernen von latenten variablen Modellen (LVMs) ist es wichtig, effektiv unregelmäßige Muster zu erfassen und die Modellgröße zu verkleinern, ohne die Modellierungskraft zu opfern. Verschiedene Studien wurden durchgeführt, um 8220diversify8221 eine LVM, die darauf abzielen, eine Vielzahl von latenten Komponenten in LVMs zu lernen. Die meisten existierenden Studien fallen in einen regelmäßigen Regularisierungsrahmen, in dem die Komponenten mittels Punktschätzung erlernt werden. In diesem Beitrag wird untersucht, wie sich 8220diversify8221-LVMs im Paradigma des Bayes'schen Lernens ergänzen, was die Punktschätzung ergänzt, wie etwa die Minderung der Übermodellierung durch Modell-Mittelwertbildung und die Quantifizierung der Unsicherheit. Wir schlagen zwei Ansätze vor, die komplementäre Vorteile haben. Eines ist die Definition von Vielfalt fördernden gegenseitigen Winkelprioritäten, die Komponenten mit größeren gegenseitigen Winkeln basierend auf dem Bayesschen Netzwerk und der von Mises-Fisher-Verteilung eine grßere Dichte verleihen und diese Vorurteile zur Beeinflussung der posterioren über die Bayes-Regel verwenden. Wir entwickeln zwei effiziente approximative hintere Schlußfolgerungsalgorithmen basierend auf Variationsinferenz und Markov-Kette Monte-Carlo-Sampling. Der andere Ansatz besteht darin, eine Diversity-förderliche Regularisierung direkt über die Post-Datenverteilung von Komponenten zu verhängen. Diese beiden Methoden werden auf die Bayes'sche Mischung von Expertenmodellen angewendet, um die 8220experts8221 zu ermutigen, verschieden zu sein, und experimentelle Ergebnisse zeigen die Wirksamkeit und Effizienz unserer Methoden. Eine hochdimensionale nichtparametrische Regression ist ein inhärent schwieriges Problem mit bekannten unteren Schranken, die exponentiell in der Dimension sind. Eine populäre Strategie, um diesen Fluch der Dimensionalität zu lindern, besteht darin, additive Modelle von emph zu verwenden, die die Regressionsfunktion als eine Summe von unabhängigen Funktionen auf jeder Dimension modellieren. Obwohl es nützlich ist, die Varianz der Schätzung zu steuern, sind solche Modelle in der Praxis oft zu restriktiv. Zwischen nicht additiven Modellen, die oft große Varianz - und Additivmodelle erster Ordnung aufweisen, die eine große Vorspannung aufweisen, gab es wenig Arbeit, um den Kompromiß in der Mitte über additive Modelle der Zwischenordnung auszunutzen. In dieser Arbeit schlagen wir Salsa vor, die diese Lücke überbrückt, indem sie Interaktionen zwischen Variablen erlaubt, aber die Modellkapazität durch Begrenzung der Reihenfolge der Interaktionen steuert. Salsas minimiert die restliche Summe von Quadraten mit quadrierten RKHS-Normstrafen. Algorithmisch kann es als Kernel Ridge Regression mit einem additiven Kernel angesehen werden. Wenn die Regressionsfunktion additiv ist, ist das überschüssige Risiko nur in der Dimension polynomial. Unter Verwendung der Girard-Newton-Formeln summieren wir effizient eine kombinatorische Anzahl von Termen in der additiven Expansion. Über einen Vergleich an 15 realen Datensätzen zeigen wir, dass unsere Methode gegenüber 21 Alternativen wettbewerbsfähig ist. Wir schlagen eine Erweiterung der Hawkes-Prozesse vor, indem wir die Ebenen der Selbsterregung als stochastische Differentialgleichung behandeln. Unser neues Punktverfahren ermöglicht eine bessere Annäherung in Anwendungsdomänen, in denen Ereignisse und Intensitäten sich gegenseitig mit korrelierten Ansteckungsgraden beschleunigen. Wir verallgemeinern einen neueren Algorithmus für die Simulation von Auszügen aus Hawkes-Prozessen, deren Erregungsstufen stochastische Prozesse sind, und schlagen einen hybriden Markov-Ketten-Monte-Carlo-Ansatz für die Modellanpassung vor. Unser Probenahmeverfahren skaliert linear mit der Anzahl der erforderlichen Ereignisse und benötigt keine Stationarität des Punktprozesses. Ein modulares Inferenzverfahren, bestehend aus einer Kombination zwischen Gibbs und Metropolis Hastings Schritte wird vorgebracht. Als Spezialfall erholen wir die Erwartungsmaximierung. Unser allgemeiner Ansatz ist für die Ansteckung nach geometrischer Brownsche Bewegung und exponentieller Langevin-Dynamik dargestellt. Rank-Aggregationssysteme sammeln Ordinalpräferenzen von Individuen, um ein globales Ranking zu erzeugen, das die soziale Präferenz darstellt. Um die rechnerische Komplexität des Lernens der globalen Rangliste zu reduzieren, ist es eine gängige Praxis, den Rang zu brechen. Individuelle Präferenzen werden in paarweise Vergleiche gebrochen und dann auf effiziente Algorithmen angewendet, die für unabhängige paarweise Vergleiche zugeschnitten sind. Allerdings können aufgrund der ignorierten Abhängigkeiten naive Rank-Breaking-Ansätze zu inkonsistenten Schätzungen führen. Die zentrale Idee, objektive und genaue Schätzungen zu erstellen, besteht darin, die Ergebnisse der paarweisen Vergleiche in Abhängigkeit von der Topologie der gesammelten Daten ungleich zu behandeln. In dieser Arbeit stellen wir den optimalen Rank-Breaking-Schätzer zur Verfügung, der nicht nur Konsistenz erreicht, sondern auch die beste Fehlergrenze erreicht. Dies ermöglicht es uns, den grundlegenden Kompromiss zwischen Genauigkeit und Komplexität in einigen kanonischen Szenarien zu charakterisieren. Weiterhin wird festgestellt, wie die Genauigkeit von der spektralen Lücke eines entsprechenden Vergleichsgraphen abhängt. Ausscheidungsdestillation Samuel Rota Bul FBK. Lorenzo Porzi FBK. Peter Kontschieder Microsoft-Forschung Cambridge-Papier AbstractDropout ist eine populäre stochastische Regularisierungstechnik für tiefe neuronale Netze, die durch zufälliges Fallenlassen (d. H. Nullen) von Einheiten aus dem Netzwerk während des Trainings arbeitet. Dieses Randomisierungsverfahren ermöglicht es, implizit ein Ensemble von exponentiell vielen Netzwerken zu trainieren, die dieselbe Parametrisierung teilen, die zum Testzeitpunkt gemittelt werden sollte, um die endgültige Vorhersage zu liefern. Eine typische Problemumgehung für diesen nicht beherrschbaren Mittelungsbetrieb besteht in der Skalierung der Schichten, die einer Dropout-Randomisierung unterliegen. Diese einfache Regel namens 8216 standard dropout8217 ist effizient, könnte aber die Genauigkeit der Vorhersage verschlechtern. In dieser Arbeit stellen wir einen neuartigen Ansatz vor, der eine gezielte Destillation8217 gelingt, die es uns ermöglicht, einen Prädiktor so zu trainieren, dass er dem nicht beherrschbaren, aber vorzuziehenden Mittelungsprozess besser gerecht wird, während er seine rechnerische Effizienz unter Kontrolle hält. Wir sind so in der Lage, Modelle, die so effizient wie Standard-Dropout, oder sogar effizienter, während sie genauer zu konstruieren. Experimente an Standard-Benchmark-Datensätzen zeigen die Gültigkeit unserer Methode und liefern konsequente Verbesserungen gegenüber herkömmlichen Dropouts. Metadatenbewusste anonyme Nachrichtenübermittlung Giulia Fanti UIUC. Peter Kairouz UIUC. Sewoong Oh UIUC. Kannan Ramchandran UC Berkeley. Pramod Viswanath UIUC Paper AbstractAnonymous Messaging-Plattformen wie Whisper und Yik Yak ermöglichen es Benutzern, Nachrichten über ein Netzwerk (z. B. ein soziales Netzwerk) zu verbreiten, ohne Nachricht Autorenschaft für andere Benutzer. Die Verbreitung von Nachrichten auf diesen Plattformen kann durch einen Diffusionsprozess über einen Graphen modelliert werden. Jüngste Fortschritte in der Netzwerkanalyse haben gezeigt, dass solche Diffusionsprozesse anfällig für Autordeanonymisierung durch Gegner mit Zugriff auf Metadaten sind, wie z. B. Timing-Informationen. In dieser Arbeit stellen wir die grundlegende Frage, wie sich anonyme Botschaften über einen Graphen verbreiten, um es den Gegnern schwer machen, auf die Quelle zu schließen. Insbesondere untersuchen wir die Leistungsfähigkeit eines Meldungsfortpflanzungsprotokolls, das als adaptive Diffusion bezeichnet wird (Fanti et al., 2015). Wir beweisen, dass die adaptive Diffusion, wenn der Gegner Zugriff auf Metadaten bei einem Bruchteil von verdorbenen Graphenknoten hat, eine asymptotisch optimale Quellenverbergung erreicht und die Standarddiffusion deutlich übertrifft. Wir zeigen weiterhin empirisch, dass adaptive Diffusion die Quelle effektiv auf realen sozialen Netzwerken verbirgt. Die Lehrdimension der Linearen Lernenden Ji Liu University of Rochester. Xiaojin Zhu Universität von Wisconsin. Hrag Ohannessian Universität Wisconsin-Madison Papier AbstractTeaching Dimension ist eine Lerntheorie Menge, die die minimale Trainingsgröße festgelegt, um ein Ziel-Modell für einen Lernenden zu lehren. Frühere Studien zur Lehrdimension konzentrierten sich auf Versionsraum-Lernende, die alle Hypothesen konsistent mit den Trainingsdaten beibehalten und können nicht auf moderne Maschinenlernen angewandt werden, die eine spezifische Hypothese durch Optimierung auswählen. Dieses Papier präsentiert die erste bekannte Lehre Dimension für Kante Regression, Support-Vektor-Maschinen und logistische Regression. Wir weisen auch optimale Trainingseinheiten auf, die diesen Unterrichtsmaßen entsprechen. Unser Ansatz verallgemeinert sich für andere lineare Lerner. Wahrhaftig Univariate Schätzer Ioannis Caragiannis Universität von Patras. Ariel Procaccia Carnegie Mellon Universität. Nisarg Shah Carnegie Mellon University Paper AbstractWe revisit das klassische Problem der Schätzung der Bevölkerung Mittel einer unbekannten eindimensionalen Verteilung aus Proben, wobei eine spiel-theoretische Sicht. In unserem Rahmen werden Proben von strategischen Agenten, die die Schätzung so nah wie möglich an ihren eigenen Wert ziehen möchten geliefert. In dieser Einstellung führt das Stichprobenmittel zu Manipulationsmöglichkeiten, während der Probenmedian nicht. Unsere zentrale Frage ist, ob die Stichprobe Median ist die beste (in Bezug auf die durchschnittliche quadratische Fehler) wahrheitsgemäßen Schätzer der Bevölkerung bedeutet. Wir zeigen, dass, wenn die zugrunde liegende Verteilung symmetrisch ist, es wahrheitsgemäße Schätzer gibt, die den Median dominieren. Our main result is a characterization of worst-case optimal truthful estimators, which provably outperform the median, for possibly asymmetric distributions with bounded support. Why Regularized Auto-Encoders learn Sparse Representation Devansh Arpit SUNY Buffalo . Yingbo Zhou SUNY Buffalo . Hung Ngo SUNY Buffalo . Venu Govindaraju SUNY Buffalo Paper AbstractSparse distributed representation is the key to learning useful features in deep learning algorithms, because not only it is an efficient mode of data representation, but also 8212 more importantly 8212 it captures the generation process of most real world data. While a number of regularized auto-encoders (AE) enforce sparsity explicitly in their learned representation and others don8217t, there has been little formal analysis on what encourages sparsity in these models in general. Our objective is to formally study this general problem for regularized auto-encoders. We provide sufficient conditions on both regularization and activation functions that encourage sparsity. We show that multiple popular models (de-noising and contractive auto encoders, e. g.) and activations (rectified linear and sigmoid, e. g.) satisfy these conditions thus, our conditions help explain sparsity in their learned representation. Thus our theoretical and empirical analysis together shed light on the properties of regularizationactivation that are conductive to sparsity and unify a number of existing auto-encoder models and activation functions under the same analytical framework. k-variates: more pluses in the k-means Richard Nock Nicta 038 ANU . Raphael Canyasse Ecole Polytechnique and The Technion . Roksana Boreli Data61 . Frank Nielsen Ecole Polytechnique and Sony CS Labs Inc. Paper Abstractk-means seeding has become a de facto standard for hard clustering algorithms. In this paper, our first contribution is a two-way generalisation of this seeding, k-variates, that includes the sampling of general densities rather than just a discrete set of Dirac densities anchored at the point locations, textit a generalisation of the well known Arthur-Vassilvitskii (AV) approximation guarantee, in the form of a textit approximation bound of the textit optimum. This approximation exhibits a reduced dependency on the 8220noise8221 component with respect to the optimal potential 8212 actually approaching the statistical lower bound. We show that k-variates textit to efficient (biased seeding) clustering algorithms tailored to specific frameworks these include distributed, streaming and on-line clustering, with textit approximation results for these algorithms. Finally, we present a novel application of k-variates to differential privacy. For either the specific frameworks considered here, or for the differential privacy setting, there is little to no prior results on the direct application of k-means and its approximation bounds 8212 state of the art contenders appear to be significantly more complex and or display less favorable (approximation) properties. We stress that our algorithms can still be run in cases where there is textit closed form solution for the population minimizer. We demonstrate the applicability of our analysis via experimental evaluation on several domains and settings, displaying competitive performances vs state of the art. Multi-Player Bandits 8212 a Musical Chairs Approach Jonathan Rosenski Weizmann Institute of Science . Ohad Shamir Weizmann Institute of Science . Liran Szlak Weizmann Institute of Science Paper AbstractWe consider a variant of the stochastic multi-armed bandit problem, where multiple players simultaneously choose from the same set of arms and may collide, receiving no reward. This setting has been motivated by problems arising in cognitive radio networks, and is especially challenging under the realistic assumption that communication between players is limited. We provide a communication-free algorithm (Musical Chairs) which attains constant regret with high probability, as well as a sublinear-regret, communication-free algorithm (Dynamic Musical Chairs) for the more difficult setting of players dynamically entering and leaving throughout the game. Moreover, both algorithms do not require prior knowledge of the number of players. To the best of our knowledge, these are the first communication-free algorithms with these types of formal guarantees. The Information Sieve Greg Ver Steeg Information Sciences Institute . Aram Galstyan Information Sciences Institute Paper AbstractWe introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data. Deep Speech 2. End-to-End Speech Recognition in English and Mandarin Dario Amodei . Rishita Anubhai . Eric Battenberg . Carl Case . Jared Casper . Bryan Catanzaro . JingDong Chen . Mike Chrzanowski Baidu USA, Inc. . Adam Coates . Greg Diamos Baidu USA, Inc. . Erich Elsen Baidu USA, Inc. . Jesse Engel . Linxi Fan . Christopher Fougner . Awni Hannun Baidu USA, Inc. . Billy Jun . Tony Han . Patrick LeGresley . Xiangang Li Baidu . Libby Lin . Sharan Narang . Andrew Ng . Sherjil Ozair . Ryan Prenger . Sheng Qian Baidu . Jonathan Raiman . Sanjeev Satheesh Baidu SVAIL . David Seetapun . Shubho Sengupta . Chong Wang . Yi Wang . Zhiqian Wang . Bo Xiao . Yan Xie Baidu . Dani Yogatama . Jun Zhan . zhenyao Zhu Paper AbstractWe show that an end-to-end deep learning approach can be used to recognize either English or Mandarin Chinese speechtwo vastly different languages. Because it replaces entire pipelines of hand-engineered components with neural networks, end-to-end learning allows us to handle a diverse variety of speech including noisy environments, accents and different languages. Key to our approach is our application of HPC techniques, enabling experiments that previously took weeks to now run in days. This allows us to iterate more quickly to identify superior architectures and algorithms. As a result, in several cases, our system is competitive with the transcription of human workers when benchmarked on standard datasets. Finally, using a technique called Batch Dispatch with GPUs in the data center, we show that our system can be inexpensively deployed in an online setting, delivering low latency when serving users at scale. An important question in feature selection is whether a selection strategy recovers the 8220true8221 set of features, given enough data. We study this question in the context of the popular Least Absolute Shrinkage and Selection Operator (Lasso) feature selection strategy. In particular, we consider the scenario when the model is misspecified so that the learned model is linear while the underlying real target is nonlinear. Surprisingly, we prove that under certain conditions, Lasso is still able to recover the correct features in this case. We also carry out numerical studies to empirically verify the theoretical results and explore the necessity of the conditions under which the proof holds. We propose minimum regret search (MRS), a novel acquisition function for Bayesian optimization. MRS bears similarities with information-theoretic approaches such as entropy search (ES). However, while ES aims in each query at maximizing the information gain with respect to the global maximum, MRS aims at minimizing the expected simple regret of its ultimate recommendation for the optimum. While empirically ES and MRS perform similar in most of the cases, MRS produces fewer outliers with high simple regret than ES. We provide empirical results both for a synthetic single-task optimization problem as well as for a simulated multi-task robotic control problem. CryptoNets: Applying Neural Networks to Encrypted Data with High Throughput and Accuracy Ran Gilad-Bachrach Microsoft Research . Nathan Dowlin Princeton . Kim Laine Microsoft Research . Kristin Lauter Microsoft Research . Michael Naehrig Microsoft Research . John Wernsing Microsoft Research Paper AbstractApplying machine learning to a problem which involves medical, financial, or other types of sensitive data, not only requires accurate predictions but also careful attention to maintaining data privacy and security. Legal and ethical requirements may prevent the use of cloud-based machine learning solutions for such tasks. In this work, we will present a method to convert learned neural networks to CryptoNets, neural networks that can be applied to encrypted data. This allows a data owner to send their data in an encrypted form to a cloud service that hosts the network. The encryption ensures that the data remains confidential since the cloud does not have access to the keys needed to decrypt it. Nevertheless, we will show that the cloud service is capable of applying the neural network to the encrypted data to make encrypted predictions, and also return them in encrypted form. These encrypted predictions can be sent back to the owner of the secret key who can decrypt them. Therefore, the cloud service does not gain any information about the raw data nor about the prediction it made. We demonstrate CryptoNets on the MNIST optical character recognition tasks. CryptoNets achieve 99 accuracy and can make around 59000 predictions per hour on a single PC. Therefore, they allow high throughput, accurate, and private predictions. Spectral methods for dimensionality reduction and clustering require solving an eigenproblem defined by a sparse affinity matrix. When this matrix is large, one seeks an approximate solution. The standard way to do this is the Nystrom method, which first solves a small eigenproblem considering only a subset of landmark points, and then applies an out-of-sample formula to extrapolate the solution to the entire dataset. We show that by constraining the original problem to satisfy the Nystrom formula, we obtain an approximation that is computationally simple and efficient, but achieves a lower approximation error using fewer landmarks and less runtime. We also study the role of normalization in the computational cost and quality of the resulting solution. As a widely used non-linear activation, Rectified Linear Unit (ReLU) separates noise and signal in a feature map by learning a threshold or bias. However, we argue that the classification of noise and signal not only depends on the magnitude of responses, but also the context of how the feature responses would be used to detect more abstract patterns in higher layers. In order to output multiple response maps with magnitude in different ranges for a particular visual pattern, existing networks employing ReLU and its variants have to learn a large number of redundant filters. In this paper, we propose a multi-bias non-linear activation (MBA) layer to explore the information hidden in the magnitudes of responses. It is placed after the convolution layer to decouple the responses to a convolution kernel into multiple maps by multi-thresholding magnitudes, thus generating more patterns in the feature space at a low computational cost. It provides great flexibility of selecting responses to different visual patterns in different magnitude ranges to form rich representations in higher layers. Such a simple and yet effective scheme achieves the state-of-the-art performance on several benchmarks. We propose a novel multi-task learning method that can minimize the effect of negative transfer by allowing asymmetric transfer between the tasks based on task relatedness as well as the amount of individual task losses, which we refer to as Asymmetric Multi-task Learning (AMTL). To tackle this problem, we couple multiple tasks via a sparse, directed regularization graph, that enforces each task parameter to be reconstructed as a sparse combination of other tasks, which are selected based on the task-wise loss. We present two different algorithms to solve this joint learning of the task predictors and the regularization graph. The first algorithm solves for the original learning objective using alternative optimization, and the second algorithm solves an approximation of it using curriculum learning strategy, that learns one task at a time. We perform experiments on multiple datasets for classification and regression, on which we obtain significant improvements in performance over the single task learning and symmetric multitask learning baselines. This paper illustrates a novel approach to the estimation of generalization error of decision tree classifiers. We set out the study of decision tree errors in the context of consistency analysis theory, which proved that the Bayes error can be achieved only if when the number of data samples thrown into each leaf node goes to infinity. For the more challenging and practical case where the sample size is finite or small, a novel sampling error term is introduced in this paper to cope with the small sample problem effectively and efficiently. Extensive experimental results show that the proposed error estimate is superior to the well known K-fold cross validation methods in terms of robustness and accuracy. Moreover it is orders of magnitudes more efficient than cross validation methods. We study the convergence properties of the VR-PCA algorithm introduced by cite for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the algorithm, and convergence from random initialization. We also make a few observations of independent interest, such as how pre-initializing with just a single exact power iteration can significantly improve the analysis, and what are the convexity and non-convexity properties of the underlying optimization problem. We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i. i.d. data points in realsd. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in cite . Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap. Dealbreaker: A Nonlinear Latent Variable Model for Educational Data Andrew Lan Rice University . Tom Goldstein University of Maryland . Richard Baraniuk Rice University . Christoph Studer Cornell University Paper AbstractStatistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a students success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretablethey provide key insights into which concepts are critical (i. e. the dealbreaker) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model. We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein8217s identity and the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-of-fit tests that are widely applicable for complex and high dimensional distributions, even for those with computationally intractable normalization constants. Both theoretical and empirical properties of our methods are studied thoroughly. Variable Elimination in the Fourier Domain Yexiang Xue Cornell University . Stefano Ermon . Ronan Le Bras Cornell University . Carla . Bart Paper AbstractThe ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements. Low-rank matrix approximation has been widely adopted in machine learning applications with sparse data, such as recommender systems. However, the sparsity of the data, incomplete and noisy, introduces challenges to the algorithm stability 8212 small changes in the training data may significantly change the models. As a result, existing low-rank matrix approximation solutions yield low generalization performance, exhibiting high error variance on the training dataset, and minimizing the training error may not guarantee error reduction on the testing dataset. In this paper, we investigate the algorithm stability problem of low-rank matrix approximations. We present a new algorithm design framework, which (1) introduces new optimization objectives to guide stable matrix approximation algorithm design, and (2) solves the optimization problem to obtain stable low-rank approximation solutions with good generalization performance. Experimental results on real-world datasets demonstrate that the proposed work can achieve better prediction accuracy compared with both state-of-the-art low-rank matrix approximation methods and ensemble methods in recommendation task. Given samples from two densities p and q, density ratio estimation (DRE) is the problem of estimating the ratio pq. Two popular discriminative approaches to DRE are KL importance estimation (KLIEP), and least squares importance fitting (LSIF). In this paper, we show that KLIEP and LSIF both employ class-probability estimation (CPE) losses. Motivated by this, we formally relate DRE and CPE, and demonstrate the viability of using existing losses from one problem for the other. For the DRE problem, we show that essentially any CPE loss (eg logistic, exponential) can be used, as this equivalently minimises a Bregman divergence to the true density ratio. We show how different losses focus on accurately modelling different ranges of the density ratio, and use this to design new CPE losses for DRE. For the CPE problem, we argue that the LSIF loss is useful in the regime where one wishes to rank instances with maximal accuracy at the head of the ranking. In the course of our analysis, we establish a Bregman divergence identity that may be of independent interest. We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD) but their theoretical analysis almost exclusively assumes convexity. In contrast, we prove non-asymptotic rates of convergence (to stationary points) of SVRG for nonconvex optimization, and show that it is provably faster than SGD and gradient descent. We also analyze a subclass of nonconvex problems on which SVRG attains linear convergence to the global optimum. We extend our analysis to mini-batch variants of SVRG, showing (theoretical) linear speedup due to minibatching in parallel settings. Hierarchical Variational Models Rajesh Ranganath . Dustin Tran Columbia University . Blei David Columbia Paper AbstractBlack box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM, and has the same computational efficiency as the original approximation. We study HVMs on a variety of deep discrete latent variable models. HVMs generalize other expressive variational distributions and maintains higher fidelity to the posterior. The field of mobile health (mHealth) has the potential to yield new insights into health and behavior through the analysis of continuously recorded data from wearable health and activity sensors. In this paper, we present a hierarchical span-based conditional random field model for the key problem of jointly detecting discrete events in such sensor data streams and segmenting these events into high-level activity sessions. Our model includes higher-order cardinality factors and inter-event duration factors to capture domain-specific structure in the label space. We show that our model supports exact MAP inference in quadratic time via dynamic programming, which we leverage to perform learning in the structured support vector machine framework. We apply the model to the problems of smoking and eating detection using four real data sets. Our results show statistically significant improvements in segmentation performance relative to a hierarchical pairwise CRF. Binary embeddings with structured hashed projections Anna Choromanska Courant Institute, NYU . Krzysztof Choromanski Google Research NYC . Mariusz Bojarski NVIDIA . Tony Jebara Columbia . Sanjiv Kumar . Yann Paper AbstractWe consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudorandom projection is described by a matrix, where not all entries are independent random variables but instead a fixed budget of randomness is distributed across the matrix. Such matrices can be efficiently stored in sub-quadratic or even linear space, provide reduction in randomness usage (i. e. number of required random values), and very often lead to computational speed ups. We prove several theoretical results showing that projections via various structured matrices followed by nonlinear mappings accurately preserve the angular distance between input high-dimensional vectors. To the best of our knowledge, these results are the first that give theoretical ground for the use of general structured matrices in the nonlinear setting. In particular, they generalize previous extensions of the Johnson - Lindenstrauss lemma and prove the plausibility of the approach that was so far only heuristically confirmed for some special structured matrices. Consequently, we show that many structured matrices can be used as an efficient information compression mechanism. Our findings build a better understanding of certain deep architectures, which contain randomly weighted and untrained layers, and yet achieve high performance on different learning tasks. We empirically verify our theoretical findings and show the dependence of learning via structured hashed projections on the performance of neural network as well as nearest neighbor classifier. A Variational Analysis of Stochastic Gradient Algorithms Stephan Mandt Columbia University . Matthew Hoffman Adobe Research . Blei David Columbia Paper AbstractStochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show that SGD with constant rates can be effectively used as an approximate posterior inference algorithm for probabilistic modeling. Specifically, we show how to adjust the tuning parameters of SGD such as to match the resulting stationary distribution to the posterior. This analysis rests on interpreting SGD as a continuous-time stochastic process and then minimizing the Kullback-Leibler divergence between its stationary distribution and the target posterior. (This is in the spirit of variational inference.) In more detail, we model SGD as a multivariate Ornstein-Uhlenbeck process and then use properties of this process to derive the optimal parameters. This theoretical framework also connects SGD to modern scalable inference algorithms we analyze the recently proposed stochastic gradient Fisher scoring under this perspective. We demonstrate that SGD with properly chosen constant rates gives a new way to optimize hyperparameters in probabilistic models. This paper proposes a new mechanism for sampling training instances for stochastic gradient descent (SGD) methods by exploiting any side-information associated with the instances (for e. g. class-labels) to improve convergence. Previous methods have either relied on sampling from a distribution defined over training instances or from a static distribution that fixed before training. This results in two problems a) any distribution that is set apriori is independent of how the optimization progresses and b) maintaining a distribution over individual instances could be infeasible in large-scale scenarios. In this paper, we exploit the side information associated with the instances to tackle both problems. More specifically, we maintain a distribution over classes (instead of individual instances) that is adaptively estimated during the course of optimization to give the maximum reduction in the variance of the gradient. Intuitively, we sample more from those regions in space that have a textit gradient contribution. Our experiments on highly multiclass datasets show that our proposal converge significantly faster than existing techniques. Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iterations. The memory requirement grows linearly with the size of the problem. We demonstrate superior empirical performance on both multi-linear multi-task learning and spatio-temporal applications. This paper presents a novel distributed variational inference framework that unifies many parallel sparse Gaussian process regression (SGPR) models for scalable hyperparameter learning with big data. To achieve this, our framework exploits a structure of correlated noise process model that represents the observation noises as a finite realization of a high-order Gaussian Markov random process. By varying the Markov order and covariance function for the noise process model, different variational SGPR models result. This consequently allows the correlation structure of the noise process model to be characterized for which a particular variational SGPR model is optimal. We empirically evaluate the predictive performance and scalability of the distributed variational SGPR models unified by our framework on two real-world datasets. Online Stochastic Linear Optimization under One-bit Feedback Lijun Zhang Nanjing University . Tianbao Yang University of Iowa . Rong Jin Alibaba Group . Yichi Xiao Nanjing University . Zhi-hua Zhou Paper AbstractIn this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement and online recommendation. We assume the binary feedback is a random variable generated from the logit model, and aim to minimize the regret defined by the unknown linear function. Although the existing method for generalized linear bandit can be applied to our problem, the high computational cost makes it impractical for real-world applications. To address this challenge, we develop an efficient online learning algorithm by exploiting particular structures of the observation model. Specifically, we adopt online Newton step to estimate the unknown parameter and derive a tight confidence region based on the exponential concavity of the logistic loss. Our analysis shows that the proposed algorithm achieves a regret bound of O(dsqrt ), which matches the optimal result of stochastic linear bandits. We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints, which are constraints that need to be satisfied when accumulated over a finite number of rounds T, but can be violated in intermediate rounds. For some user-defined trade-off parameter beta in (0, 1), the proposed algorithm achieves cumulative regret bounds of O(Tmax ) and O(T ), respectively for the loss and the constraint violations. Our results hold for convex losses, can handle arbitrary convex constraints and rely on a single computationally efficient algorithm. Our contributions improve over the best known cumulative regret bounds of Mahdavi et al. (2012), which are respectively O(T12) and O(T34) for general convex domains, and respectively O(T23) and O(T23) when the domain is further restricted to be a polyhedral set. We supplement the analysis with experiments validating the performance of our algorithm in practice. Motivated by an application of eliciting users8217 preferences, we investigate the problem of learning hemimetrics, i. e. pairwise distances among a set of n items that satisfy triangle inequalities and non-negativity constraints. In our application, the (asymmetric) distances quantify private costs a user incurs when substituting one item by another. We aim to learn these distances (costs) by asking the users whether they are willing to switch from one item to another for a given incentive offer. Without exploiting structural constraints of the hemimetric polytope, learning the distances between each pair of items requires Theta(n2) queries. We propose an active learning algorithm that substantially reduces this sample complexity by exploiting the structural constraints on the version space of hemimetrics. Our proposed algorithm achieves provably-optimal sample complexity for various instances of the task. For example, when the items are embedded into K tight clusters, the sample complexity of our algorithm reduces to O(n K). Extensive experiments on a restaurant recommendation data set support the conclusions of our theoretical analysis. We present an approach for learning simple algorithms such as copying, multi-digit addition and single digit multiplication directly from examples. Our framework consists of a set of interfaces, accessed by a controller. Typical interfaces are 1-D tapes or 2-D grids that hold the input and output data. For the controller, we explore a range of neural network-based models which vary in their ability to abstract the underlying algorithm from training instances and generalize to test examples with many thousands of digits. The controller is trained using Q-learning with several enhancements and we show that the bottleneck is in the capabilities of the controller rather than in the search incurred by Q-learning. Learning Physical Intuition of Block Towers by Example Adam Lerer Facebook AI Research . Sam Gross Facebook AI Research . Rob Fergus Facebook AI Research Paper AbstractWooden blocks are a common toy for infants, allowing them to develop motor skills and gain intuition about the physical behavior of the world. In this paper, we explore the ability of deep feed-forward models to learn such intuitive physics. Using a 3D game engine, we create small towers of wooden blocks whose stability is randomized and render them collapsing (or remaining upright). This data allows us to train large convolutional network models which can accurately predict the outcome, as well as estimating the trajectories of the blocks. The models are also able to generalize in two important ways: (i) to new physical scenarios, e. g. towers with an additional block and (ii) to images of real wooden blocks, where it obtains a performance comparable to human subjects. Structure Learning of Partitioned Markov Networks Song Liu The Inst. of Stats. Mathe. . Taiji Suzuki . Masashi Sugiyama University of Tokyo . Kenji Fukumizu The Institute of Statistical Mathematics Paper AbstractWe learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable option. We introduce a novel concept called the emph whose factorization directly associates with the Markovian properties of random variables across two groups. A simple one-shot convex optimization procedure is proposed for learning the emph factorizations of the partitioned ratio and it is theoretically guaranteed to recover the correct inter-group structure under mild conditions. The performance of the proposed method is experimentally compared with the state of the art MN structure learning methods using ROC curves. Real applications on analyzing bipartisanship in US congress and pairwise DNAtime-series alignments are also reported. This work focuses on dynamic regret of online convex optimization that compares the performance of online learning to a clairvoyant who knows the sequence of loss functions in advance and hence selects the minimizer of the loss function at each step. By assuming that the clairvoyant moves slowly (i. e. the minimizers change slowly), we present several improved variation-based upper bounds of the dynamic regret under the true and noisy gradient feedback, which are in light of the presented lower bounds. The key to our analysis is to explore a regularity metric that measures the temporal changes in the clairvoyant8217s minimizers, to which we refer as path variation. Firstly, we present a general lower bound in terms of the path variation, and then show that under full information or gradient feedback we are able to achieve an optimal dynamic regret. Secondly, we present a lower bound with noisy gradient feedback and then show that we can achieve optimal dynamic regrets under a stochastic gradient feedback and two-point bandit feedback. Moreover, for a sequence of smooth loss functions that admit a small variation in the gradients, our dynamic regret under the two-point bandit feedback matches that is achieved with full information. Beyond CCA: Moment Matching for Multi-View Models Anastasia Podosinnikova INRIA 8211 ENS . Francis Bach Inria . Simon Lacoste-Julien INRIA Paper AbstractWe introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis (DICA), we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices, which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diagonalization techniques for matching the cumulants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets. We present two computationally inexpensive techniques for estimating the numerical rank of a matrix, combining powerful tools from computational linear algebra. These techniques exploit three key ingredients. The first is to approximate the projector on the non-null invariant subspace of the matrix by using a polynomial filter. Two types of filters are discussed, one based on Hermite interpolation and the other based on Chebyshev expansions. The second ingredient employs stochastic trace estimators to compute the rank of this wanted eigen-projector, which yields the desired rank of the matrix. In order to obtain a good filter, it is necessary to detect a gap between the eigenvalues that correspond to noise and the relevant eigenvalues that correspond to the non-null invariant subspace. The third ingredient of the proposed approaches exploits the idea of spectral density, popular in physics, and the Lanczos spectroscopic method to locate this gap. Unsupervised Deep Embedding for Clustering Analysis Junyuan Xie University of Washington . Ross Girshick Facebook . Ali Farhadi University of Washington Paper AbstractClustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods. Dimensionality reduction is a popular approach for dealing with high dimensional data that leads to substantial computational savings. Random projections are a simple and effective method for universal dimensionality reduction with rigorous theoretical guarantees. In this paper, we theoretically study the problem of differentially private empirical risk minimization in the projected subspace (compressed domain). Empirical risk minimization (ERM) is a fundamental technique in statistical machine learning that forms the basis for various learning algorithms. Starting from the results of Chaudhuri et al. (NIPS 2009, JMLR 2011), there is a long line of work in designing differentially private algorithms for empirical risk minimization problems that operate in the original data space. We ask: is it possible to design differentially private algorithms with small excess risk given access to only projected data In this paper, we answer this question in affirmative, by showing that for the class of generalized linear functions, we can obtain excess risk bounds of O(w(Theta) n ) under eps-differential privacy, and O((w(Theta)n) ) under (eps, delta)-differential privacy, given only the projected data and the projection matrix. Here n is the sample size and w(Theta) is the Gaussian width of the parameter space that we optimize over. Our strategy is based on adding noise for privacy in the projected subspace and then lifting the solution to original space by using high-dimensional estimation techniques. A simple consequence of these results is that, for a large class of ERM problems, in the traditional setting (i. e. with access to the original data), under eps-differential privacy, we improve the worst-case risk bounds of Bassily et al. (FOCS 2014). We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e. g. when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets. Large-Margin Softmax Loss for Convolutional Neural Networks Weiyang Liu Peking University . Yandong Wen South China University of Technology . Zhiding Yu Carnegie Mellon University . Meng Yang Shenzhen University Paper AbstractCross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly encourage discriminative learning of features. In this paper, we propose a generalized large-margin softmax (L-Softmax) loss which explicitly encourages intra-class compactness and inter-class separability between learned features. Moreover, L-Softmax not only can adjust the desired margin but also can avoid overfitting. We also show that the L-Softmax loss can be optimized by typical stochastic gradient descent. Extensive experiments on four benchmark datasets demonstrate that the deeply-learned features with L-softmax loss become more discriminative, hence significantly boosting the performance on a variety of visual classification and verification tasks. A Random Matrix Approach to Echo-State Neural Networks Romain Couillet CentraleSupelec . Gilles Wainrib ENS Ulm, Paris, France . Hafiz Tiomoko Ali CentraleSupelec, Gif-sur-Yvette, France . Harry Sevi ENS Lyon, Lyon, Paris Paper AbstractRecurrent neural networks, especially in their linear version, have provided many qualitative insights on their performance under different configurations. This article provides, through a novel random matrix framework, the quantitative counterpart of these performance results, specifically in the case of echo-state networks. Beyond mere insights, our approach conveys a deeper understanding on the core mechanism under play for both training and testing. One-hot CNN (convolutional neural network) has been shown to be effective for text categorization (Johnson 038 Zhang, 2015). We view it as a special case of a general framework which jointly trains a linear model with a non-linear feature generator consisting of text region embedding pooling8217. Under this framework, we explore a more sophisticated region embedding method using Long Short-Term Memory (LSTM). LSTM can embed text regions of variable (and possibly large) sizes, whereas the region size needs to be fixed in a CNN. We seek effective and efficient use of LSTM for this purpose in the supervised and semi-supervised settings. The best results were obtained by combining region embeddings in the form of LSTM and convolution layers trained on unlabeled data. The results indicate that on this task, embeddings of text regions, which can convey complex concepts, are more useful than embeddings of single words in isolation. We report performances exceeding the previous best results on four benchmark datasets. Crowdsourcing systems are popular for solving large-scale labelling tasks with low-paid (or even non-paid) workers. We study the problem of recovering the true labels from noisy crowdsourced labels under the popular Dawid-Skene model. To address this inference problem, several algorithms have recently been proposed, but the best known guarantee is still significantly larger than the fundamental limit. We close this gap under a simple but canonical scenario where each worker is assigned at most two tasks. In particular, we introduce a tighter lower bound on the fundamental limit and prove that Belief Propagation (BP) exactly matches this lower bound. The guaranteed optimality of BP is the strongest in the sense that it is information-theoretically impossible for any other algorithm to correctly la - bel a larger fraction of the tasks. In the general setting, when more than two tasks are assigned to each worker, we establish the dominance result on BP that it outperforms other existing algorithms with known provable guarantees. Experimental results suggest that BP is close to optimal for all regimes considered, while existing state-of-the-art algorithms exhibit suboptimal performances. Learning control has become an appealing alternative to the derivation of control laws based on classic control theory. However, a major shortcoming of learning control is the lack of performance guarantees which prevents its application in many real-world scenarios. As a step in this direction, we provide a stability analysis tool for controllers acting on dynamics represented by Gaussian processes (GPs). We consider arbitrary Markovian control policies and system dynamics given as (i) the mean of a GP, and (ii) the full GP distribution. For the first case, our tool finds a state space region, where the closed-loop system is provably stable. In the second case, it is well known that infinite horizon stability guarantees cannot exist. Instead, our tool analyzes finite time stability. Empirical evaluations on simulated benchmark problems support our theoretical results. Learning a classifier from private data distributed across multiple parties is an important problem that has many potential applications. How can we build an accurate and differentially private global classifier by combining locally-trained classifiers from different parties, without access to any partys private data We propose to transfer the knowledge of the local classifier ensemble by first creating labeled data from auxiliary unlabeled data, and then train a global differentially private classifier. We show that majority voting is too sensitive and therefore propose a new risk weighted by class probabilities estimated from the ensemble. Relative to a non-private solution, our private solution has a generalization error bounded by O(epsilon M ). This allows strong privacy without performance loss when the number of participating parties M is large, such as in crowdsensing applications. We demonstrate the performance of our framework with realistic tasks of activity recognition, network intrusion detection, and malicious URL detection. Network Morphism Tao Wei University at Buffalo . Changhu Wang Microsoft Research . Yong Rui Microsoft Research . Chang Wen Chen Paper AbstractWe present a systematic study on how to morph a well-trained neural network to a new one so that its network function can be completely preserved. We define this as network morphism in this research. After morphing a parent network, the child network is expected to inherit the knowledge from its parent network and also has the potential to continue growing into a more powerful one with much shortened training time. The first requirement for this network morphism is its ability to handle diverse morphing types of networks, including changes of depth, width, kernel size, and even subnet. To meet this requirement, we first introduce the network morphism equations, and then develop novel morphing algorithms for all these morphing types for both classic and convolutional neural networks. The second requirement is its ability to deal with non-linearity in a network. We propose a family of parametric-activation functions to facilitate the morphing of any continuous non-linear activation neurons. Experimental results on benchmark datasets and typical neural networks demonstrate the effectiveness of the proposed network morphism scheme. Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive iterative procedure or make crude approximations to the curvature. We present Kronecker Factors for Convolution (KFC), a tractable approximation to the Fisher matrix for convolutional networks based on a structured probabilistic model for the distribution over backpropagated derivatives. Similarly to the recently proposed Kronecker-Factored Approximate Curvature (K-FAC), each block of the approximate Fisher matrix decomposes as the Kronecker product of small matrices, allowing for efficient inversion. KFC captures important curvature information while still yielding comparably efficient updates to stochastic gradient descent (SGD). We show that the updates are invariant to commonly used reparameterizations, such as centering of the activations. In our experiments, approximate natural gradient descent with KFC was able to train convolutional networks several times faster than carefully tuned SGD. Furthermore, it was able to train the networks in 10-20 times fewer iterations than SGD, suggesting its potential applicability in a distributed setting. Budget constrained optimal design of experiments is a classical problem in statistics. Although the optimal design literature is very mature, few efficient strategies are available when these design problems appear in the context of sparse linear models commonly encountered in high dimensional machine learning and statistics. In this work, we study experimental design for the setting where the underlying regression model is characterized by a ell1-regularized linear function. We propose two novel strategies: the first is motivated geometrically whereas the second is algebraic in nature. We obtain tractable algorithms for this problem and also hold for a more general class of sparse linear models. We perform an extensive set of experiments, on benchmarks and a large multi-site neuroscience study, showing that the proposed models are effective in practice. The latter experiment suggests that these ideas may play a small role in informing enrollment strategies for similar scientific studies in the short-to-medium term future. Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs Anton Osokin . Jean-Baptiste Alayrac ENS . Isabella Lukasewitz INRIA . Puneet Dokania INRIA and Ecole Centrale Paris . Simon Lacoste-Julien INRIA Paper AbstractIn this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our improvements is that the estimates of block gaps maintained by BCFW reveal the block suboptimality that can be used as an adaptive criterion. First, we sample objects at each iteration of BCFW in an adaptive non-uniform way via gap-based sampling. Second, we incorporate pairwise and away-step variants of Frank-Wolfe into the block-coordinate setting. Third, we cache oracle calls with a cache-hit criterion based on the block gaps. Fourth, we provide the first method to compute an approximate regularization path for SSVM. Finally, we provide an exhaustive empirical evaluation of all our methods on four structured prediction datasets. Exact Exponent in Optimal Rates for Crowdsourcing Chao Gao Yale University . Yu Lu Yale University . Dengyong Zhou Microsoft Research Paper AbstractCrowdsourcing has become a popular tool for labeling large datasets. This paper studies the optimal error rate for aggregating crowdsourced labels provided by a collection of amateur workers. Under the Dawid-Skene probabilistic model, we establish matching upper and lower bounds with an exact exponent mI(pi), where m is the number of workers and I(pi) is the average Chernoff information that characterizes the workers8217 collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement m ge frac logfrac in order to achieve an epsilon misclassification error. In addition, our results imply optimality of various forms of EM algorithms given accurate initializers of the model parameters. Unsupervised learning and supervised learning are key research topics in deep learning. However, as high-capacity supervised neural networks trained with a large amount of labels have achieved remarkable success in many computer vision tasks, the availability of large-scale labeled images reduced the significance of unsupervised learning. Inspired by the recent trend toward revisiting the importance of unsupervised learning, we investigate joint supervised and unsupervised learning in a large-scale setting by augmenting existing neural networks with decoding pathways for reconstruction. First, we demonstrate that the intermediate activations of pretrained large-scale classification networks preserve almost all the information of input images except a portion of local spatial details. Then, by end-to-end training of the entire augmented architecture with the reconstructive objective, we show improvement of the network performance for supervised tasks. We evaluate several variants of autoencoders, including the recently proposed 8220what-where8221 autoencoder that uses the encoder pooling switches, to study the importance of the architecture design. Taking the 16-layer VGGNet trained under the ImageNet ILSVRC 2012 protocol as a strong baseline for image classification, our methods improve the validation-set accuracy by a noticeable margin. (LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is also known that solving LRR is challenging in terms of time complexity and memory footprint, in that the size of the nuclear norm regularized matrix is n-by-n (where n is the number of samples). In this paper, we thereby develop a novel online implementation of LRR that reduces the memory cost from O(n2) to O(pd), with p being the ambient dimension and d being some estimated rank (d 20 reduction in the model size without any loss in accuracy on CIFAR-10 benchmark. We also demonstrate that fine-tuning can further enhance the accuracy of fixed point DCNs beyond that of the original floating point model. In doing so, we report a new state-of-the-art fixed point performance of 6.78 error-rate on CIFAR-10 benchmark. Provable Algorithms for Inference in Topic Models Sanjeev Arora Princeton University . Rong Ge . Frederic Koehler Princeton University . Tengyu Ma Princeton University . Ankur Moitra Paper AbstractRecently, there has been considerable progress on designing algorithms with provable guarantees 8212typically using linear algebraic methods8212for parameter learning in latent variable models. Designing provable algorithms for inference has proved more difficult. Here we take a first step towards provable inference in topic models. We leverage a property of topic models that enables us to construct simple linear estimators for the unknown topic proportions that have small variance, and consequently can work with short documents. Our estimators also correspond to finding an estimate around which the posterior is well-concentrated. We show lower bounds that for shorter documents it can be information theoretically impossible to find the hidden topics. Finally, we give empirical results that demonstrate that our algorithm works on realistic topic models. It yields good solutions on synthetic data and runs in time comparable to a single iteration of Gibbs sampling. This paper develops an approach for efficiently solving general convex optimization problems specified as disciplined convex programs (DCP), a common general-purpose modeling framework. Specifically we develop an algorithm based upon fast epigraph projections, projections onto the epigraph of a convex function, an approach closely linked to proximal operator methods. We show that by using these operators, we can solve any disciplined convex program without transforming the problem to a standard cone form, as is done by current DCP libraries. We then develop a large library of efficient epigraph projection operators, mirroring and extending work on fast proximal algorithms, for many common convex functions. Finally, we evaluate the performance of the algorithm, and show it often achieves order of magnitude speedups over existing general-purpose optimization solvers. We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function f, we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear time algorithms for the problem that 8211 while not being minimax optimal 8211 achieve a significantly better sample-time tradeoff on large datasets compared to the DP approach. Our experimental evaluation shows that, compared with the DP approach, our algorithms provide a convergence rate that is only off by a factor of 2 to 4, while achieving speedups of three orders of magnitude. Energetic Natural Gradient Descent Philip Thomas CMU . Bruno Castro da Silva . Christoph Dann Carnegie Mellon University . Emma Paper AbstractWe propose a new class of algorithms for minimizing or maximizing functions of parametric probabilistic models. These new algorithms are natural gradient algorithms that leverage more information than prior methods by using a new metric tensor in place of the commonly used Fisher information matrix. This new metric tensor is derived by computing directions of steepest ascent where the distance between distributions is measured using an approximation of energy distance (as opposed to Kullback-Leibler divergence, which produces the Fisher information matrix), and so we refer to our new ascent direction as the energetic natural gradient. Partition Functions from Rao-Blackwellized Tempered Sampling David Carlson Columbia University . Patrick Stinson Columbia University . Ari Pakman Columbia University . Liam Paper AbstractPartition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM) moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost. In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any kgeq 2, the mixture of k Plackett-Luce models for no more than 2k-1 alternatives is non-identifiable and this bound is tight for k2. For generic identifiability, we prove that the mixture of k Plackett-Luce models over m alternatives is if kleqlfloorfrac 2rfloor. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley 038 Murphy (2008), while achieving competitive statistical efficiency. The combinatorial explosion that plagues planning and reinforcement learning (RL) algorithms can be moderated using state abstraction. Prohibitively large task representations can be condensed such that essential information is preserved, and consequently, solutions are tractably computable. However, exact abstractions, which treat only fully-identical situations as equivalent, fail to present opportunities for abstraction in environments where no two situations are exactly alike. In this work, we investigate approximate state abstractions, which treat nearly-identical situations as equivalent. We present theoretical guarantees of the quality of behaviors derived from four types of approximate abstractions. Additionally, we empirically demonstrate that approximate abstractions lead to reduction in task complexity and bounded loss of optimality of behavior in a variety of environments. Power of Ordered Hypothesis Testing Lihua Lei Lihua . William Fithian UC Berkeley, Department of Statistics Paper AbstractOrdered testing procedures are multiple testing procedures that exploit a pre-specified ordering of the null hypotheses, from most to least promising. We analyze and compare the power of several recent proposals using the asymptotic framework of Li 038 Barber (2015). While accumulation tests including ForwardStop can be quite powerful when the ordering is very informative, they are asymptotically powerless when the ordering is weaker. By contrast, Selective SeqStep, proposed by Barber 038 Candes (2015), is much less sensitive to the quality of the ordering. We compare the power of these procedures in different regimes, concluding that Selective SeqStep dominates accumulation tests if either the ordering is weak or non-null hypotheses are sparse or weak. Motivated by our asymptotic analysis, we derive an improved version of Selective SeqStep which we call Adaptive SeqStep, analogous to Storeys improvement on the Benjamini-Hochberg proce - dure. We compare these methods using the GEO-Query data set analyzed by (Li 038 Barber, 2015) and find Adaptive SeqStep has favorable performance for both good and bad prior orderings. PHOG: Probabilistic Model for Code Pavol Bielik ETH Zurich . Veselin Raychev ETH Zurich . Martin Vechev ETH Zurich Paper AbstractWe introduce a new generative model for code called probabilistic higher order grammar (PHOG). PHOG generalizes probabilistic context free grammars (PCFGs) by allowing conditioning of a production rule beyond the parent non-terminal, thus capturing rich contexts relevant to programs. Even though PHOG is more powerful than a PCFG, it can be learned from data just as efficiently. We trained a PHOG model on a large JavaScript code corpus and show that it is more precise than existing models, while similarly fast. As a result, PHOG can immediately benefit existing programming tools based on probabilistic models of code. We consider the problem of online prediction in changing environments. In this framework the performance of a predictor is evaluated as the loss relative to an arbitrarily changing predictor, whose individual components come from a base class of predictors. Typical results in the literature consider different base classes (experts, linear predictors on the simplex, etc.) separately. Introducing an arbitrary mapping inside the mirror decent algorithm, we provide a framework that unifies and extends existing results. As an example, we prove new shifting regret bounds for matrix prediction problems. Hyperparameter selection generally relies on running multiple full training trials, with selection based on validation set performance. We propose a gradient-based approach for locally adjusting hyperparameters during training of the model. Hyperparameters are adjusted so as to make the model parameter gradients, and hence updates, more advantageous for the validation cost. We explore the approach for tuning regularization hyperparameters and find that in experiments on MNIST, SVHN and CIFAR-10, the resulting regularization levels are within the optimal regions. The additional computational cost depends on how frequently the hyperparameters are trained, but the tested scheme adds only 30 computational overhead regardless of the model size. Since the method is significantly less computationally demanding compared to similar gradient-based approaches to hyperparameter optimization, and consistently finds good hyperparameter values, it can be a useful tool for training neural network models. Many of the recent Trajectory Optimization algorithms alternate between local approximation of the dynamics and conservative policy update. However, linearly approximating the dynamics in order to derive the new policy can bias the update and prevent convergence to the optimal policy. In this article, we propose a new model-free algorithm that backpropagates a local quadratic time-dependent Q-Function, allowing the derivation of the policy update in closed form. Our policy update ensures exact KL-constraint satisfaction without simplifying assumptions on the system dynamics demonstrating improved performance in comparison to related Trajectory Optimization algorithms linearizing the dynamics. Due to its numerous applications, rank aggregation has become a problem of major interest across many fields of the computer science literature. In the vast majority of situations, Kemeny consensus(es) are considered as the ideal solutions. It is however well known that their computation is NP-hard. Many contributions have thus established various results to apprehend this complexity. In this paper we introduce a practical method to predict, for a ranking and a dataset, how close the Kemeny consensus(es) are to this ranking. A major strength of this method is its generality: it does not require any assumption on the dataset nor the ranking. Furthermore, it relies on a new geometric interpretation of Kemeny aggregation that, we believe, could lead to many other results. Horizontally Scalable Submodular Maximization Mario Lucic ETH Zurich . Olivier Bachem ETH Zurich . Morteza Zadimoghaddam Google Research . Andreas Krause Paper AbstractA variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity 8211 number of instances that can fit in memory 8211 must grow with the data set size. In practice, while one can provision many machines, the capacity of each machine is limited by physical constraints. We propose a truly scalable approach for distributed submodular maximization under fixed capacity. The proposed framework applies to a broad class of algorithms and constraints and provides theoretical guarantees on the approximation factor for any available capacity. We empirically evaluate the proposed algorithm on a variety of data sets and demonstrate that it achieves performance competitive with the centralized greedy solution. Group Equivariant Convolutional Networks Taco Cohen University of Amsterdam . Max Welling University of Amsterdam CIFAR Paper AbstractWe introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST. The partition function is fundamental for probabilistic graphical models8212it is required for inference, parameter estimation, and model selection. Evaluating this function corresponds to discrete integration, namely a weighted sum over an exponentially large set. This task quickly becomes intractable as the dimensionality of the problem increases. We propose an approximation scheme that, for any discrete graphical model whose parameter vector has bounded norm, estimates the partition function with arbitrarily small error. Our algorithm relies on a near minimax optimal polynomial approximation to the potential function and a Clenshaw-Curtis style quadrature. Furthermore, we show that this algorithm can be randomized to split the computation into a high-complexity part and a low-complexity part, where the latter may be carried out on small computational devices. Experiments confirm that the new randomized algorithm is highly accurate if the parameter norm is small, and is otherwise comparable to methods with unbounded error. Correcting Forecasts with Multifactor Neural Attention Matthew Riemer IBM . Aditya Vempaty IBM . Flavio Calmon IBM . Fenno Heath IBM . Richard Hull IBM . Elham Khabiri IBM Paper AbstractAutomatic forecasting of time series data is a challenging problem in many industries. Current forecast models adopted by businesses do not provide adequate means for including data representing external factors that may have a significant impact on the time series, such as weather, national events, local events, social media trends, promotions, etc. This paper introduces a novel neural network attention mechanism that naturally incorporates data from multiple external sources without the feature engineering needed to get other techniques to work. We demonstrate empirically that the proposed model achieves superior performance for predicting the demand of 20 commodities across 107 stores of one of America8217s largest retailers when compared to other baseline models, including neural networks, linear models, certain kernel methods, Bayesian regression, and decision trees. Our method ultimately accounts for a 23.9 relative improvement as a result of the incorporation of external data sources, and provides an unprecedented level of descriptive ability for a neural network forecasting model. Observational studies are rising in importance due to the widespread accumulation of data in fields such as healthcare, education, employment and ecology. We consider the task of answering counterfactual questions such as, 8220Would this patient have lower blood sugar had she received a different medication8221. We propose a new algorithmic framework for counterfactual inference which brings together ideas from domain adaptation and representation learning. In addition to a theoretical justification, we perform an empirical comparison with previous approaches to causal inference from observational data. Our deep learning algorithm significantly outperforms the previous state-of-the-art. Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with a composite covariance kernel function. Unfortunately, learning a composite covariance kernel with a single time-series data set often results in less informative kernel that may not give qualitative, distinctive descriptions of data. We address this challenge by proposing two relational kernel learning methods which can model multiple time-series data sets by finding common, shared causes of changes. We show that the relational kernel learning methods find more accurate models for regression problems on several real-world data sets US stock data, US house price index data and currency exchange rate data. We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We describe a procedure for constructing and learning a structured neural network which represents an inverse factorization of the graphical model, resulting in a conditional density estimator that takes as input particular values of the observed random variables, and returns an approximation to the distribution of the latent variables. This recognition model can be learned offline, independent from any particular dataset, prior to performing inference. The output of these networks can be used as automatically-learned high-quality proposal distributions to accelerate sequential Monte Carlo across a diverse range of problem settings. Slice Sampling on Hamiltonian Trajectories Benjamin Bloem-Reddy Columbia University . John Cunningham Columbia University Paper AbstractHamiltonian Monte Carlo and slice sampling are amongst the most widely used and studied classes of Markov Chain Monte Carlo samplers. We connect these two methods and present Hamiltonian slice sampling, which allows slice sampling to be carried out along Hamiltonian trajectories, or transformations thereof. Hamiltonian slice sampling clarifies a class of model priors that induce closed-form slice samplers. More pragmatically, inheriting properties of slice samplers, it offers advantages over Hamiltonian Monte Carlo, in that it has fewer tunable hyperparameters and does not require gradient information. We demonstrate the utility of Hamiltonian slice sampling out of the box on problems ranging from Gaussian process regression to Pitman-Yor based mixture models. Noisy Activation Functions Caglar Glehre . Marcin Moczulski . Misha Denil . Yoshua Bengio U. of Montreal Paper AbstractCommon nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order gradients only). Gating mechanisms that use softly saturating activation functions to emulate the discrete switching of digital logic circuits are good examples of this. We propose to exploit the injection of appropriate noise so that the gradients may flow easily, even if the noiseless application of the activation function would yield zero gradients. Large noise will dominate the noise-free gradient and allow stochastic gradient descent to explore more. By adding noise only to the problematic parts of the activation function, we allow the optimization procedure to explore the boundary between the degenerate saturating) and the well-behaved parts of the activation function. We also establish connections to simulated annealing, when the amount of noise is annealed down, making it easier to optimize hard objective functions. We find experimentally that replacing such saturating activation functions by noisy variants helps optimization in many contexts, yielding state-of-the-art or competitive results on different datasets and task, especially when training seems to be the most difficult, e. g. when curriculum learning is necessary to obtain good results. PD-Sparse. A Primal and Dual Sparse Approach to Extreme Multiclass and Multilabel Classification Ian En-Hsu Yen University of Texas at Austin . Xiangru Huang UTaustin . Pradeep Ravikumar UT Austin . Kai Zhong ICES department, University of Texas at Austin . Inderjit Paper AbstractWe consider Multiclass and Multilabel classification with extremely large number of classes, of which only few are labeled to each instance. In such setting, standard methods that have training, prediction cost linear to the number of classes become intractable. State-of-the-art methods thus aim to reduce the complexity by exploiting correlation between labels under assumption that the similarity between labels can be captured by structures such as low-rank matrix or balanced tree. However, as the diversity of labels increases in the feature space, structural assumption can be easily violated, which leads to degrade in the testing performance. In this work, we show that a margin-maximizing loss with l1 penalty, in case of Extreme Classification, yields extremely sparse solution both in primal and in dual without sacrificing the expressive power of predictor. We thus propose a Fully-Corrective Block-Coordinate Frank-Wolfe (FC-BCFW) algorithm that exploits both primal and dual sparsity to achieve a complexity sublinear to the number of primal and dual variables. A bi-stochastic search method is proposed to further improve the efficiency. In our experiments on both Multiclass and Multilabel problems, the proposed method achieves significant higher accuracy than existing approaches of Extreme Classification with very competitive training and prediction time.
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