Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors

TL;DR

This paper introduces a scalable Bayesian tensor factorization model for massive binary data using a zero-truncated Poisson likelihood, enabling efficient analysis of large sparse and dense binary tensors with side-information.

Contribution

The paper proposes a novel zero-truncated Poisson likelihood-based Bayesian model that scales to massive binary tensors and incorporates side-information, with simple inference methods and interpretable factors.

Findings

Achieves excellent scalability on large real-world binary tensors.

Effectively leverages side-information such as mode-networks.

Provides interpretable non-negative factor matrices.

Abstract

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale up in the number of \emph{ones} in the tensor, which is especially appealing for massive but sparse binary tensors; (2) side-information in form of binary pairwise relationships (e.g., an adjacency network) between objects in any tensor mode can also be leveraged, which can be especially useful in "cold-start" settings; and (3) the model admits simple Bayesian inference via batch, as well as \emph{online} MCMC; the latter allows scaling up even for \emph{dense} binary data (i.e., when the number of ones in the tensor/network is also massive). In addition, non-negative factor matrices in our model provide easy interpretability, and the tensor rank can be inferred from the data. We evaluate our model on several large-scale real-world binary tensors, achieving excellent computational scalability, and also demonstrate its usefulness in leveraging side-information provided in form of mode-network(s).