Incorporating the natural document-sentence-word structure into hierarchical Bayesian modeling, we propose convolutional Poisson gamma dynamical systems (PGDS) that introduce not only word-level probabilistic convolutions, but also sentence-level stochastic temporal transitions. With word-level convolutions capturing phrase-level topics and sentence-level transitions capturing how the topic usages evolve over consecutive sentences, we aggregate the topic proportions of all sentences of a document as its feature representation. To consider not only forward but also backward sentence-level information transmissions, we further develop a bidirectional convolutional PGDS to incorporate the full contextual information to represent each sentence. For efficient inference, we construct a convolutional-recurrent inference network, which provides both sentence-level and document-level representations, and introduce a hybrid Bayesian inference scheme combining stochastic-gradient MCMC and amortized variational inference. Experimental results on a variety of document corpora demonstrate that the proposed models can extract expressive multi-level latent representations, including interpretable phrase-level topics and sentence-level temporal transitions as well as discriminative document-level features, achieving state-of-the-art document categorization performance while being memory and computation efficient.

Summary and Contributions: The paper presents a new hierarchical Bayesian model -- convolutional Poisson-Gamma Dynamical Systems (conv-PGDS) -- for generating the observed words in a document corpus. Globally, the model assumes there are K "topic filters", D_1, ... D_K, which are distributions over 3-grams from a finite size vocabulary (size V). Each "topic" (indexed by k) has an appearance probability weight v_k 0 for appearing in a document, and we define transition probability vectors \pi_k Given this global structure, the model generates each document iid. To generate a document j, we use a Gamma dynamical system (with transitions \pi) to obtain a sequence of un-normalized membership "weight embeddings", w_j1 ... w_jT, one for each sentence (indexed by t). Each weight embedding vector w_jt indicates the relative weight of topic k across all words in the sentence t.

Incorporating the natural document-sentence-word structure into hierarchical Bayesian modeling, we propose convolutional Poisson gamma dynamical systems (PGDS) that introduce not only word-level probabilistic convolutions, but also sentence-level stochastic temporal transitions. With word-level convolutions capturing phrase-level topics and sentence-level transitions capturing how the topic usages evolve over consecutive sentences, we aggregate the topic proportions of all sentences of a document as its feature representation. To consider not only forward but also backward sentence-level information transmissions, we further develop a bidirectional convolutional PGDS to incorporate the full contextual information to represent each sentence. For efficient inference, we construct a convolutional-recurrent inference network, which provides both sentence-level and document-level representations, and introduce a hybrid Bayesian inference scheme combining stochastic-gradient MCMC and amortized variational inference. Experimental results on a variety of document corpora demonstrate that the proposed models can extract expressive multi-level latent representations, including interpretable phrase-level topics and sentence-level temporal transitions as well as discriminative document-level features, achieving state-of-the-art document categorization performance while being memory and computation efficient.