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Register a new userAutoencoding Variational Inference For Topic Models
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Added by
Akash Srivastava
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
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Topic models are one of the most popular methods for learning representations of text, but a major challenge is that any change to the topic model requires mathematically deriving a new inference algorithm. A promising approach to address this problem is autoencoding variational Bayes (AEVB), but it has proven diffi- cult to apply to topic models in practice. We present what is to our knowledge the first effective AEVB based inference method for latent Dirichlet allocation (LDA), which we call Autoencoded Variational Inference For Topic Model (AVITM). This model tackles the problems caused for AEVB by the Dirichlet prior and by component collapsing. We find that AVITM matches traditional methods in accuracy with much better inference time. Indeed, because of the inference network, we find that it is unnecessary to pay the computational cost of running variational optimization on test data. Because AVITM is black box, it is readily applied to new topic models. As a dramatic illustration of this, we present a new topic model called ProdLDA, that replaces the mixture model in LDA with a product of experts. By changing only one line of code from LDA, we find that ProdLDA yields much more interpretable topics, even if LDA is trained via collapsed Gibbs sampling.
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Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is regarded as a convex combination of a small number of vectors corresponding to `topics or `components. The weights are assumed to have a Dirichlet prior distribution. The standard approach towards approximating the posterior is to use variational inference algorithms, and in particular a mean field approximation. We show that this approach suffers from an instability that can produce misleading conclusions. Namely, for certain regimes of the model parameters, variational inference outputs a non-trivial decomposition into topics. However --for the same parameter values-- the data contain no actual information about the true decomposition, and hence the output of the algorithm is uncorrelated with the true topic decomposition. Among other consequences, the estimated posterior mean is significantly wrong, and estimated Bayesian credible regions do not achieve the nominal coverage. We discuss how this instability is remedied by more accurate mean field approximations.
To train an inference network jointly with a deep generative topic model, making it both scalable to big corpora and fast in out-of-sample prediction, we develop Weibull hybrid autoencoding inference (WHAI) for deep latent Dirichlet allocation, which infers posterior samples via a hybrid of stochastic-gradient MCMC and autoencoding variational Bayes. The generative network of WHAI has a hierarchy of gamma distributions, while the inference network of WHAI is a Weibull upward-downward variational autoencoder, which integrates a deterministic-upward deep neural network, and a stochastic-downward deep generative model based on a hierarchy of Weibull distributions. The Weibull distribution can be used to well approximate a gamma distribution with an analytic Kullback-Leibler divergence, and has a simple reparameterization via the uniform noise, which help efficiently compute the gradients of the evidence lower bound with respect to the parameters of the inference network. The effectiveness and efficiency of WHAI are illustrated with experiments on big corpora.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm for hidden Markov models, in a sequential data setting. Given a collapsed hidden Markov Model, we break its long Markov chain into a set of short subchains. We propose a novel sum-product algorithm to update the posteriors of the subchains, taking into account their boundary transitions due to the sequential dependencies. Our experiments on two discrete datasets show that our collapsed algorithm is scalable to very large datasets, memory efficient and significantly more accurate than the existing uncollapsed algorithm.
To build a flexible and interpretable model for document analysis, we develop deep autoencoding topic model (DATM) that uses a hierarchy of gamma distributions to construct its multi-stochastic-layer generative network. In order to provide scalable posterior inference for the parameters of the generative network, we develop topic-layer-adaptive stochastic gradient Riemannian MCMC that jointly learns simplex-constrained global parameters across all layers and topics, with topic and layer specific learning rates. Given a posterior sample of the global parameters, in order to efficiently infer the local latent representations of a document under DATM across all stochastic layers, we propose a Weibull upward-downward variational encoder that deterministically propagates information upward via a deep neural network, followed by a Weibull distribution based stochastic downward generative model. To jointly model documents and their associated labels, we further propose supervised DATM that enhances the discriminative power of its latent representations. The efficacy and scalability of our models are demonstrated on both unsupervised and supervised learning tasks on big corpora.
We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.
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