Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling update equations, they are natural candidates for nonparametric Bayesian priors over count matrices. A key aspect of our analysis is the recognition that, although the random count matrices within the family are defined by a row-wise construction, their columns can be shown to be i.i.d. This fact is used to derive explicit formulas for drawing all the columns at once. Moreover, by analyzing these matrices' combinatorial structure, we describe how to sequentially construct a column-i.i.d. random count matrix one row at a time, and derive the predictive distribution of a new row count vector with previously unseen features. We describe the similarities and differences between the three priors, and argue that the greater flexibility of the gamma- and beta- negative binomial processes, especially their ability to model over-dispersed, heavy-tailed count data, makes these well suited to a wide variety of real-world applications. As an example of our framework, we construct a naive-Bayes text classifier to categorize a count vector to one of several existing random count matrices of different categories. The classifier supports an unbounded number of features, and unlike most existing methods, it does not require a predefined finite vocabulary to be shared by all the categories, and needs neither feature selection nor parameter tuning. Both the gamma- and beta- negative binomial processes are shown to significantly outperform the gamma-Poisson process for document categorization, with comparable performance to other state-of-the-art supervised text classification algorithms.Comment: To appear in Journal of the American Statistical Association (Theory and Methods). 31 pages + 11 page supplement, 5 figure

Document Informed Neural Autoregressive Topic Models with Distributional Prior

We address two challenges in topic models: (1) Context information around words helps in determining their actual meaning, e.g., "networks" used in the contexts "artificial neural networks" vs. "biological neuron networks". Generative topic models infer topic-word distributions, taking no or only little context into account. Here, we extend a neural autoregressive topic model to exploit the full context information around words in a document in a language modeling fashion. The proposed model is named as iDocNADE. (2) Due to the small number of word occurrences (i.e., lack of context) in short text and data sparsity in a corpus of few documents, the application of topic models is challenging on such texts. Therefore, we propose a simple and efficient way of incorporating external knowledge into neural autoregressive topic models: we use embeddings as a distributional prior. The proposed variants are named as DocNADEe and iDocNADEe. We present novel neural autoregressive topic model variants that consistently outperform state-of-the-art generative topic models in terms of generalization, interpretability (topic coherence) and applicability (retrieval and classification) over 7 long-text and 8 short-text datasets from diverse domains.Comment: AAAI2019. arXiv admin note: substantial text overlap with arXiv:1808.0379

Bivariate Beta-LSTM

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.Comment: AAAI 202