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Se alguma coisa estiver incorreta ou faltando, ou se você tiver alguma informação nova para enviar para o nosso site, envie-a usando o nosso Formulário de Atualizações. - Gerenciamento de Conteúdo RuneHQ - o fornecimento de energia é um meio muito popular para obter a grande quantidade de dados rotulados que requerem métodos modernos de aprendizagem de máquinas. Embora barato e rápido de obter, os rótulos de crowdsourced sofrem de quantidades significativas de erro, degradando assim o desempenho das tarefas de aprendizagem em máquina a jusante. Com o objetivo de melhorar a qualidade dos dados rotulados, buscamos mitigar os muitos erros que ocorrem devido a erros tolos ou erros inadvertidos por trabalhadores do crowdsourcing. Nós propomos uma configuração de dois estágios para crowdsourcing, onde o trabalhador primeiro responde as perguntas, e é permitido alterar suas respostas depois de analisar uma resposta de referência (ruidosa). Formamos matematicamente este processo e desenvolvemos mecanismos para incentivar os trabalhadores a agir adequadamente. Nossas garantias matemáticas mostram que nosso mecanismo incentiva os trabalhadores a responder honestamente em ambos os estágios e se abster de responder aleatoriamente na primeira etapa ou simplesmente copiar no segundo. As experiências numéricas revelam um impulso significativo no desempenho que essa auto-correção 82221 pode fornecer ao usar crowdsourcing para treinar algoritmos de aprendizado de máquina. Existem vários modelos paramétricos para análise de dados de comparação em pares, incluindo os modelos Bradley-Terry-Luce (BTL) e Thurstone, mas a dependência de fortes pressupostos paramétricos é limitante. Neste trabalho, estudamos um modelo flexível para comparações em pares, segundo o qual as probabilidades de resultados são necessárias apenas para satisfazer uma forma natural de transitividade estocástica. Esta classe inclui modelos paramétricos, incluindo os modelos BTL e Thurstone como casos especiais, mas é consideravelmente mais geral. Nós fornecemos vários exemplos de modelos nesta classe estocticamente transitiva mais ampla para a qual os modelos paramétricos clássicos proporcionam ajustes ruins. Apesar desta maior flexibilidade, mostramos que a matriz de probabilidades pode ser estimada na mesma taxa que nos modelos paramétricos padrão. Por outro lado, ao contrário dos modelos BTL e Thurstone, o cálculo do estimador minimax-optimal no modelo estoquentemente transitivo não é trivial, e exploramos várias alternativas computacionalmente atraentes. Mostramos que um simples algoritmo de limiar de valor singular é estatisticamente consistente, mas não atinge a taxa de minimax. Em seguida, propomos e estudamos algoritmos que alcançam a taxa de minimax sobre as sub-classes interessantes da classe transtósticamente transcriptora completa. Nós complementamos nossos resultados teóricos com simulações numéricas detalhadas. Mostramos como qualquer modelo de binário binário pode ser desarraigado para um modelo totalmente simétrico, em que os potenciais singleton originais são transformados em potenciais nas bordas para uma variável adicionada e, em seguida, são rerotados para um novo modelo no número original de variáveis. O novo modelo é essencialmente equivalente ao modelo original, com a mesma função de partição e permitindo a recuperação dos marginais originais ou uma conformação de MAP, mas pode ter propriedades computacionais muito diferentes que permitem uma inferência muito mais eficiente. Esta meta-abordagem aprofunda a nossa compreensão, pode ser aplicada a qualquer algoritmo existente para produzir métodos melhorados na prática, generaliza resultados teóricos anteriores e revela uma interpretação notável do politopo consistente com triplete. Mostramos como métodos de aprendizagem profundos podem ser aplicados no contexto do crowdsourcing e aprendizagem de conjuntos não supervisionados. Primeiro, provamos que o modelo popular de Dawid e Skene, que pressupõe que todos os classificadores são condicionalmente independentes, é a Máquina Boltzmann Restrita (RBM) com um único nó escondido. Assim, sob este modelo, as probabilidades posteriores dos rótulos verdadeiros podem ser estimadas através de um RBM treinado. Em seguida, para abordar o caso mais geral, onde os classificadores podem violar fortemente a suposição de independência condicional, propomos aplicar a rede Neural profunda (DNN) baseada em RBM. Os resultados experimentais em vários conjuntos de dados simulados e do mundo real demonstram que nossa abordagem DNN proposta supera os outros métodos de última geração, em particular quando os dados violam a suposição de independência condicional. Revisitando Aprendizagem Semi-Supervisada com Embeddings Gráficos Universidade Zhilin Yang Carnegie Mellon. William Cohen CMU. Ruslan Salakhudinov U. of Toronto Resumo do papel Apresentamos um quadro de aprendizagem semi-supervisionado baseado em incorporações de grafos. Dado um gráfico entre instâncias, treinamos uma incorporação para cada instância para prever conjuntamente o rótulo da classe eo contexto de vizinhança no gráfico. Desenvolvemos variantes transdutivas e indutivas do nosso método. Na variante transdutiva do nosso método, os rótulos de classe são determinados tanto pelo incorporado embeddings quanto por vetores de características de entrada, enquanto que na variante indutiva, os embeddings são definidos como uma função paramétrica dos vetores de características, de modo que as previsões podem ser feitas em instâncias não Visto durante o treinamento. Em um grande e diversificado conjunto de tarefas de benchmark, incluindo classificação de texto, extração de entidade supervisionada remotamente e classificação de entidade, mostramos melhor desempenho em muitos dos modelos existentes. O aprendizado de reforço pode adquirir comportamentos complexos a partir de especificações de alto nível. No entanto, definir uma função de custo que pode ser otimizada efetivamente e codificar a tarefa correta é um desafio na prática. Nós exploramos como o controle otimizado inverso (COI) pode ser usado para aprender comportamentos de demonstrações, com aplicações para controle de torque de sistemas robotizados de alta dimensão. Nosso método aborda dois desafios principais no controle otimizado inverso: primeiro, a necessidade de recursos informativos e regularização efetiva para impor estrutura sobre o custo e, em segundo lugar, a dificuldade de aprender a função de custo sob dinâmica desconhecida para sistemas contínuos de alta dimensão. Para abordar o desafio anterior, apresentamos um algoritmo capaz de aprender funções arbitrárias de custo não-linear, como redes neurais, sem engenharia de recursos meticulosos. Para resolver este último desafio, formulamos uma aproximação eficiente baseada em amostras para o COI MaxEnt. Nós avaliamos nosso método em uma série de tarefas simuladas e problemas de manipulação robótica do mundo real, demonstrando melhorias substanciais em relação aos métodos anteriores, tanto em termos de complexidade da tarefa quanto na eficiência da amostra. Ao aprender modelos de variáveis latentes (LVMs), é importante capturar efetivamente padrões infreqüentes e reduzir o tamanho do modelo sem sacrificar o poder de modelagem. Vários estudos foram feitos para 8220diversify8221 um LVM, que visam aprender um conjunto diversificado de componentes latentes em LVMs. A maioria dos estudos existentes se enquadra em uma estrutura de regularização de estilo freqüentador, onde os componentes são aprendidos através da estimativa de pontos. Neste trabalho, investigamos como 8220diversificamos8221 LVMs no paradigma da aprendizagem bayesiana, que tem vantagens complementares à estimativa pontual, como o alívio da superposição através da média do modelo e quantificação da incerteza. Propomos duas abordagens que possuem vantagens complementares. Um deles é definir os priores angulares mútuos que promovem a diversidade, que atribuem maior densidade aos componentes com ângulos mútuos maiores baseados na rede bayesiana e na distribuição de von Mises-Fisher e usam esses priores para afetar a regra posterior via Bayes. Desenvolvemos dois algoritmos de inferência posterior aproximados e eficientes baseados na inferência variacional e na amostragem de Monte Carlo na cadeia de Markov. A outra abordagem é impor a regularização da promoção da diversidade diretamente sobre a distribuição de componentes pós-dados. Esses dois métodos são aplicados ao modelo Bayesian mix of experts para incentivar o 8220experts8221 a serem diversos e os resultados experimentais demonstram a eficácia e a eficiência de nossos métodos. A regressão não paramétrica de alta dimensão é um problema intrinsecamente difícil, com os limites inferiores conhecidos dependendo exponencialmente da dimensão. Uma estratégia popular para aliviar essa maldição de dimensionalidade tem sido usar modelos aditivos de emph, que modelam a função de regressão como uma soma de funções independentes em cada dimensão. Embora sejam úteis no controle da variação da estimativa, esses modelos são muitas vezes muito restritivos em configurações práticas. Entre os modelos não aditivos que muitas vezes possuem grandes modelos de variância e aditivo de primeira ordem que têm grande polarização, tem sido pouco o trabalho para explorar o trade-off no meio através de modelos aditivos de ordem intermediária. Neste trabalho, propomos a salsa, que faz uma ponte sobre essa lacuna ao permitir interações entre variáveis, mas controla a capacidade do modelo, limitando a ordem das interações. Salsas minimiza a soma residual de quadrados com penalidades de RKHS ao quadrado. Algoritmicamente, pode ser visto como Kernel Ridge Regression com um kernel aditivo. Quando a função de regressão é aditiva, o excesso de risco é apenas de dimensão polinomial. Usando as fórmulas Girard-Newton, nós somamos eficientemente uma quantidade combinatória de termos na expansão aditiva. Através de uma comparação em 15 conjuntos de dados reais, mostramos que nosso método é competitivo contra outras 21 alternativas. Nós propomos uma extensão aos processos de Hawkes tratando os níveis de auto-excitação como uma equação diferencial estocástica. Nosso novo processo de ponto permite uma melhor aproximação em domínios de aplicativos onde eventos e intensidades aceleram-se mutuamente com níveis correlatos de contágio. Nós generalizamos um algoritmo recente para simular tiragens de processos da Hawkes cujos níveis de excitação são processos estocásticos e propomos uma abordagem híbrida de Monte Carlo de cadeia de Monte Carlo para montagem em modelo. Nosso procedimento de amostragem escala linearmente com o número de eventos exigidos e não exige estacionaria do processo de ponto. Um procedimento de inferência modular consistindo em uma combinação entre as etapas de Gibbs e Metropolis Hastings é apresentado. Recuperamos a maximização da expectativa como um caso especial. Nossa abordagem geral é ilustrada para o contágio após o movimento geométrico Browniano e a dinâmica exponencial de Langevin. Os sistemas de agregação de classificação coletam preferências ordinais de indivíduos para produzir um ranking global que representa a preferência social. Para reduzir a complexidade computacional da aprendizagem do ranking global, uma prática comum é usar o ranking. As preferências dos indivíduos são divididas em comparações em pares e depois aplicadas em algoritmos eficientes adaptados para comparações par pares independentes. No entanto, devido às dependências ignoradas, abordagens ingênuas inovadoras podem resultar em estimativas inconsistentes. A idéia-chave para produzir estimativas imparciais e precisas é tratar as comparações resultados comparáveis de forma desigual, dependendo da topologia dos dados coletados. Neste artigo, fornecemos o melhor estimador de classificação, que não só alcança consistência, mas também atinge o melhor erro vinculado. Isso nos permite caracterizar o tradeoff fundamental entre precisão e complexidade em alguns cenários canônicos. Além disso, identificamos como a precisão depende da diferença espectral de um gráfico de comparação correspondente. Destilação de saída Samuel Rota Bul FBK. Lorenzo Porzi FBK. Peter Kontschieder Microsoft Research Cambridge Paper AbstractDropout é uma técnica de regularização estocástica popular para redes neurais profundas que funciona de forma aleatória (ou seja, zerando) unidades da rede durante o treinamento. Este processo de randomização permite treinar implicitamente um conjunto de várias redes exponencialmente compartilhando a mesma parametrização, que deve ser calculada em média no tempo de teste para entregar a previsão final. Uma solução típica para esta operação de média intratável consiste em dimensionar as camadas em fase de randomização. Esta regra simples, chamada de abandono padrão 8217 padrão, é eficiente, mas pode degradar a precisão da previsão. Neste trabalho, introduzimos uma abordagem inovadora, inventada em 8216, a partir da destilação 8217, que nos permite treinar um preditor de forma a melhor aproximar o processo intratável, mas preferível, em média, mantendo sob controle sua eficiência computacional. Consequentemente, somos capazes de construir modelos tão eficientes quanto o abandono padrão, ou ainda mais eficientes, sendo mais precisos. As experiências em conjuntos de dados padrão de referência demonstram a validade do nosso método, proporcionando melhorias consistentes em relação ao abandono convencional. Mensagens anônimas conscientes de metadata Giulia Fanti UIUC. Peter Kairouz UIUC. Sewoong Oh UIUC. Kannan Ramchandran UC Berkeley. Pramod Viswanath UIUC Paper AbstractManotecas de mensagens anônimas como Whisper e Yik Yak permitem aos usuários espalhar mensagens através de uma rede (por exemplo, uma rede social) sem revelar a autoria de mensagens para outros usuários. A propagação de mensagens nessas plataformas pode ser modelada por um processo de difusão sobre um gráfico. Avanços recentes na análise da rede revelaram que esses processos de difusão são vulneráveis à desanonização do autor por adversários com acesso a metadados, como informações de temporização. Neste trabalho, perguntamos a questão fundamental de como propagar mensagens anônimas sobre um gráfico para dificultar a inferência da origem. Em particular, estudamos o desempenho de um protocolo de propagação de mensagens chamado difusão adaptativa introduzida (Fanti et al., 2015). Provamos que quando o adversário tem acesso a metadados em uma fração de nós corrompidos, a difusão adaptativa atinge o esconderijo de origem otimamente assintoticamente e supera significativamente a difusão padrão. Demonstremos ainda empiricamente que a difusão adaptativa esconde a fonte de forma eficaz em redes sociais reais. A Dimensão de Ensino de Alunos Lineares Ji Liu University of Rochester. Xiaojin Zhu University of Wisconsin. Hrag Ohannessian University of Wisconsin-Madison Paper AbstractTeaching dimension é uma quantidade teórica de aprendizagem que especifica o tamanho mínimo do treinamento para ensinar um modelo-alvo a um aluno. Estudos anteriores sobre dimensões de ensino voltados para aprendizes do espaço de versão que mantêm todas as hipóteses consistentes com os dados de treinamento e não podem ser aplicados aos aprendentes modernos de máquinas que selecionam uma hipótese específica através da otimização. Este artigo apresenta a primeira dimensão de ensino conhecida para regressão de cume, máquinas de vetor de suporte e regressão logística. Também exibimos conjuntos de treinamento ótimos que combinam essas dimensões de ensino. Nossa abordagem generaliza para outros alunos lineares. Estimadores Univariantes Verdadeiros Ioannis Caragiannis University of Patras. Ariel Procaccia Carnegie Mellon University. Nisarg Shah Carnegie Mellon University Paper Resumo Revisamos o problema clássico de estimar a média da população de uma distribuição única-dimensional desconhecida a partir de amostras, tomando um ponto de vista teórico-teórico. Em nossa configuração, as amostras são fornecidas por agentes estratégicos, que desejam obter a estimativa o mais próximo possível do seu próprio valor. Nesta configuração, a média da amostra dá origem a oportunidades de manipulação, enquanto que a mediana da amostra não. Nossa principal questão é saber se a mediana da amostra é o melhor (em termos de erro quadrático médio) estimador verdadeiro da média da população. Mostramos que quando a distribuição subjacente é simétrica, existem estimadores verdadeiros que dominam a mediana. Nosso resultado principal é uma caracterização de estimadores óptimos ótimos do pior caso, o que provávelmente supera a mediana, para distribuições possivelmente assimétricas com suporte limitado. Por que os encoders automáticos regularizados aprendem Representação Dispersa Devansh Arpit SUNY Buffalo. Yingbo Zhou SUNY Buffalo. Hung Ngo SUNY Buffalo. Venu Govindaraju SUNY Buffalo Paper AbstractSparse a representação distribuída é a chave para aprender recursos úteis em algoritmos de aprendizagem profunda, porque não só é um modo eficiente de representação de dados, mas também 8212, mais importante, que captura o processo de geração da maioria dos dados do mundo real. Embora uma série de auto-encoders regulares (AE) apliquem explicitamente a dispersão em sua representação aprendida e outros don8217t, houve pouca análise formal sobre o que encoraja a dispersão nesses modelos em geral. Nosso objetivo é estudar formalmente este problema geral para auto-encoders regularizados. Nós fornecemos condições suficientes para as funções de regularização e ativação que estimulam a sparsity. Mostramos que vários modelos populares (codificadores automáticos de desinfecção e contração, por exemplo) e ativações (rectificado linear e sigmoide, por exemplo) satisfazem estas condições, assim, nossas condições ajudam a explicar a escassez em sua representação aprendida. Assim, nossa análise teórica e empírica em conjunto lança luz sobre as propriedades de ativação de regularização que são condutoras para sparsity e unificam vários modelos de auto-encoder existentes e funções de ativação sob a mesma estrutura analítica. K-variates: mais vantajosos no k-means Richard Nock Nicta 038 ANU. Raphael Canyasse Ecole Polytechnique e The Technion. Roksana Boreli Data61. Frank Nielsen Ecole Polytechnique e Sony CS Labs Inc. Paper Abstractk significa amadurecimento tornou-se um padrão de fato para algoritmos de cluster duro. Neste artigo, nossa primeira contribuição é uma generalização em duas direções dessa semeadura, k-variates, que inclui a amostragem de densidades gerais em vez de apenas um conjunto discreto de densidades de Dirac ancoradas nos locais dos pontos, uma generalização do bem conhecido Garantia de aproximação de Arthur-Vassilvitskii (AV), na forma de um limite de aproximação textu do textit optimum. Essa aproximação exibe uma dependência reduzida do componente 8220noise8221 em relação ao potencial ótimo 8212 que se aproxima do limite inferior estatístico. Mostramos que k-variates textit para algoritmos de agrupamento eficiente (agrupamento tendencioso), adaptados a estruturas específicas, que incluem distribuição, transmissão e agrupamento on-line, com resultados de aproximação de textit para esses algoritmos. Finalmente, apresentamos uma nova aplicação de k-variates para privacidade diferencial. Para os enquadramentos específicos considerados aqui, ou para a configuração de privacidade diferencial, há pouco ou nenhum resultado prévio na aplicação direta de k-means e seus limites de aproximação 8212 os concorrentes do estado da arte parecem ser significativamente mais complexos e exibir menos Propriedades favoráveis (aproximação). Nós enfatizamos que nossos algoritmos ainda podem ser executados nos casos em que existe uma solução de texto fechada textit para o minimizador de população. Demonstramos a aplicabilidade de nossa análise através de avaliação experimental em vários domínios e configurações, exibindo performances competitivas versus estado da arte. Multiplayer Bandits 8212 uma abordagem de cadeiras musicais Jonathan Rosenski Weizmann Institute of Science. Ohad Shamir Weizmann Institute of Science. Liran Szlak Weizmann Institute of Science Paper Resumo Consideramos uma variante do problema estocástico de bandidos multi-armados, onde vários jogadores escolhem simultaneamente do mesmo conjunto de braços e podem colidir, sem receber recompensa. Esta configuração foi motivada por problemas que surgem nas redes de rádio cognitivas e é especialmente desafiadora sob o pressuposto realista de que a comunicação entre os jogadores é limitada. Nós fornecemos um algoritmo sem comunicação (cadeiras musicais) que atinge o arrependimento constante com alta probabilidade, bem como um algoritmo de lembrete sublinear, livre de comunicação (Cadeiras musicais dinâmicas) para a configuração mais difícil de jogadores que entram e saem dinamicamente ao longo do jogo . Além disso, ambos os algoritmos não requerem conhecimento prévio do número de jogadores. No nosso melhor conhecimento, estes são os primeiros algoritmos sem comunicação com esses tipos de garantias formais. The Information Sieve Greg Ver Steeg Information Sciences Institute. Aram Galstyan Information Sciences Institute Paper AbstractWe introduzir uma nova estrutura para o aprendizado sem supervisão de representações com base em uma nova decomposição hierárquica de informação. Intuitivamente, os dados são passados através de uma série de peneiras progressivamente de grão fino. Cada camada da peneira recupera um único fator latente que é altamente informativo sobre a dependência multivariada nos dados. Os dados são transformados após cada passagem para que a informação inexplicada restante caia até a próxima camada. Em última análise, ficamos com um conjunto de fatores latentes que explicam toda a dependência nos dados originais e informações do restante consistindo em ruído independente. Apresentamos uma implementação prática deste quadro para variáveis discretas e aplicamos a uma variedade de tarefas fundamentais na aprendizagem sem supervisão, incluindo análise independente de componentes, compressão com perdas e sem perdas e previsão de valores faltantes em dados. Discurso profundo 2. Reconhecimento de voz de ponta a ponta em inglês e mandarim 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. Wang Zhiqian. Bo Xiao. Yan Xie Baidu. Dani Yogatama. Jun Zhan. Zhenyao Zhu Paper AbstractWe mostram que uma abordagem de aprendizagem profunda de ponta a ponta pode ser usada para reconhecer a linguagem inglesa ou chinesa mandariana em línguas muito diferentes. Como substitui pipelines inteiros de componentes manipulados a mão com redes neurais, o aprendizado de ponta a ponta nos permite lidar com uma variedade diversificada de fala, incluindo ambientes ruidosos, acentos e diferentes idiomas. A chave para nossa abordagem é a nossa aplicação de técnicas HPC, permitindo experimentos que anteriormente demoravam semanas até agora em dias. Isso nos permite iterar mais rapidamente para identificar arquiteturas e algoritmos superiores. Como resultado, em vários casos, nosso sistema é competitivo com a transcrição de trabalhadores humanos quando comparados em conjuntos de dados padrão. Finalmente, usando uma técnica chamada Batch Dispatch com GPUs no centro de dados, mostramos que nosso sistema pode ser implantado de forma econômica em uma configuração on-line, oferecendo baixa latência ao atender usuários em escala. Uma questão importante na seleção de recursos é se uma estratégia de seleção recupera o conjunto de recursos 8220true8221, com dados suficientes. Nós estudamos essa questão no contexto da estratégia de seleção de recursos do Least Absolute Shrinkage and Selection Operator (Lasso) popular. Em particular, consideramos o cenário quando o modelo é especificado, de modo que o modelo aprendido é linear enquanto o alvo real subjacente não é linear. Surpreendentemente, provamos que sob certas condições, Lasso ainda é capaz de recuperar as características corretas neste caso. Também realizamos estudos numéricos para verificar empiricamente os resultados teóricos e explorar a necessidade das condições em que a prova é válida. Propomos uma busca mínima pelo arrependimento (MRS), uma nova função de aquisição para otimização bayesiana. A MRS tem semelhanças com abordagens teóricas de informação, como pesquisa de entropia (ES). No entanto, enquanto o ES visa em cada consulta ao maximizar o ganho de informação em relação ao máximo global, o MRS visa minimizar o simples arrependimento esperado de sua melhor recomendação para o melhor. Enquanto empiricamente ES e MRS executam semelhante na maioria dos casos, a MRS produz menos valores atípicos com grande arrependimento simples do que ES. Nós fornecemos resultados empíricos tanto para um problema sintético de otimização de tarefa única quanto para um problema de controle robotizado multitópico simulado. CryptoNets: aplicação de redes neurais a dados criptografados com alto rendimento e precisão 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 máquina aprendendo para um problema que envolve dados médicos, financeiros ou outros tipos de dados sensíveis, não só exige previsões precisas, mas também uma atenção cuidadosa para manter a privacidade e a segurança dos dados. Os requisitos legais e éticos podem impedir o uso de soluções de aprendizagem de máquinas baseadas em nuvem para tais tarefas. Neste trabalho, apresentaremos um método para converter redes neurais aprendidas em CryptoNets, redes neurais que podem ser aplicadas em dados criptografados. Isso permite que um proprietário de dados envie seus dados em uma forma criptografada para um serviço na nuvem que hospeda a rede. A criptografia garante que os dados permaneçam confidenciais uma vez que a nuvem não tem acesso às chaves necessárias para descriptografá-lo. No entanto, mostraremos que o serviço em nuvem é capaz de aplicar a rede neural aos dados criptografados para fazer previsões criptografadas e também devolvê-las em forma criptografada. Essas previsões criptografadas podem ser enviadas de volta ao proprietário da chave secreta que pode descriptografá-las. Portanto, o serviço da nuvem não ganha nenhuma informação sobre os dados brutos nem sobre a previsão que fez. Demonstimos CryptoNets nas tarefas de reconhecimento de caracteres ópticos MNIST. CryptoNets atinge 99 precisões e pode produzir cerca de 59000 previsões por hora em um único PC. Portanto, eles permitem previsões de alto rendimento, precisas e particulares. Métodos espectrales para a redução da dimensionalidade e agrupamento requerem a resolução de um eigenproblem definido por uma matriz de afinidade esparsa. Quando esta matriz é grande, procura-se uma solução aproximada. A maneira padrão para fazer isso é o método Nystrom, que primeiro resolve um pequeno eigenproblema considerando apenas um subconjunto de pontos de referência e, em seguida, aplica uma fórmula fora da amostra para extrapolar a solução para todo o conjunto de dados. Mostramos que, ao restringir o problema original para satisfazer a fórmula de Nystrom, obtemos uma aproximação que é computacionalmente simples e eficiente, mas consegue um menor erro de aproximação usando menos marcos e menos tempo de execução. Também estudamos o papel da normalização no custo computacional e na qualidade da solução resultante. Como uma ativação não linear amplamente utilizada, a Unidade Linear Rectificada (ReLU) separa o ruído e o sinal em um mapa de recursos, aprendendo um limite ou viés. No entanto, argumentamos que a classificação de ruído e sinal não depende apenas da magnitude das respostas, mas também do contexto de como as respostas das características seriam usadas para detectar padrões mais abstratos em camadas mais altas. Para exibir múltiplos mapas de resposta com magnitude em intervalos diferentes para um padrão visual específico, as redes existentes que utilizam ReLU e suas variantes devem aprender um grande número de filtros redundantes. Neste artigo, propomos uma camada de ativação não-linear multi-bias (MBA) para explorar a informação escondida nas magnitudes das respostas. É colocado após a camada de convolução para desacoplar as respostas a um núcleo de convolução em múltiplos mapas por magnitudes de vários limiares, gerando assim mais padrões no espaço de recursos com baixo custo computacional. Fornece grande flexibilidade de seleção de respostas a padrões visuais diferentes em diferentes faixas de magnitude para formar representações ricas em camadas mais altas. Um esquema tão simples e eficaz efetivamente atinge o desempenho de ponta em vários benchmarks. Nós propomos um novo método de aprendizagem multitarefa que pode minimizar o efeito da transferência negativa, permitindo a transferência assimétrica entre as tarefas com base na relação de tarefa, bem como a quantidade de perdas de tarefas individuais, que chamamos de Aprendizagem Multi-tarefa assimétrica (AMTL ). Para enfrentar esse problema, juntamos múltiplas tarefas por meio de um gráfico de regularização escasso e direcionado, que impõe cada parâmetro de tarefa a ser reconstruído como uma combinação esparsa de outras tarefas, que são selecionadas com base na perda de tarefa. Apresentamos dois algoritmos diferentes para resolver esta aprendizagem conjunta dos preditores da tarefa e do gráfico de regularização. O primeiro algoritmo resolve o objetivo de aprendizagem original usando a otimização alternativa e o segundo algoritmo resolve uma aproximação usando a estratégia de aprendizagem curricular, que aprende uma tarefa de cada vez. Realizamos experimentos em conjuntos de dados múltiplos para classificação e regressão, nos quais obtemos melhorias significativas no desempenho ao longo da aprendizagem única e das linhas de base simétricas de aprendizado multitarefa. Este artigo ilustra uma nova abordagem para a estimação do erro de generalização dos classificadores de árvores de decisão. Nós estabelecemos o estudo de erros de árvore de decisão no contexto da teoria da análise de consistência, o que provou que o erro de Bayes pode ser alcançado apenas quando o número de amostras de dados lançadas em cada nó da folha passa para o infinito. Para o caso mais desafiador e prático em que o tamanho da amostra é finito ou pequeno, um novo termo de erro de amostragem é introduzido neste documento para lidar com o pequeno problema de amostra de forma eficaz e eficiente. Vários resultados experimentais mostram que a estimativa de erro proposta é superior aos conhecidos métodos de validação cruzada de dobra em termos de robustez e precisão. Além disso, são ordens de magnitudes mais eficientes que os métodos de validação cruzada. Estudamos as propriedades de convergência do algoritmo VR-PCA introduzido por citar para a computação rápida de vetores líderes de singularidade. Provamos vários novos resultados, incluindo uma análise formal de uma versão em bloco do algoritmo e a convergência da inicialização aleatória. Também fazemos algumas observações de interesse independente, como por exemplo, como a pré-inicialização com apenas uma única iteração de poder exato pode melhorar significativamente a análise e quais são as propriedades de convexidade e não convexidade do problema de otimização subjacente. 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. Matemática. . 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 tak e 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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