A Bayesian Tensor Factorization Model via Variational Inference for Link Prediction

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented. It exhibits better prediction performance than existing approaches based on maximum likelihood on several real-world datasets for missing link prediction problem.Comment: arXiv admin note: substantial text overlap with arXiv:1409.808

Vectorial Dimension Reduction for Tensors Based on Bayesian Inference

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order structures or resulting in undesired tensors, respectively. This paper introduces a probabilistic vectorial dimensionality reduction model for tensorial data. The model represents a tensor by employing a linear combination of same order basis tensors, thus it offers a mechanism to directly reduce a tensor to a vector. Under this expression, the projection base of the model is based on the tensor CandeComp/PARAFAC (CP) decomposition and the number of free parameters in the model only grows linearly with the number of modes rather than exponentially. A Bayesian inference has been established via the variational EM approach. A criterion to set the parameters (factor number of CP decomposition and the number of extracted features) is empirically given. The model outperforms several existing PCA-based methods and CP decomposition on several publicly available databases in terms of classification and clustering accuracy.Comment: Submiting to TNNL

Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts

We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country $i$ took action $a$ toward country $j$ at time $t$"---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.Comment: To appear in Proceedings of the 21st ACM SIGKDD Conference of Knowledge Discovery and Data Mining (KDD 2015

Poisson-Randomized Gamma Dynamical Systems

This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous gamma latent states that is analytically convenient and computationally tractable. This motif yields closed-form complete conditionals for all variables by way of the Bessel distribution and a novel discrete distribution that we call the shifted confluent hypergeometric distribution. We draw connections to closely related models and compare the PRGDS to these models in studies of real-world count data sets of text, international events, and neural spike trains. We find that a sparse variant of the PRGDS, which allows the continuous gamma latent states to take values of exactly zero, often obtains better predictive performance than other models and is uniquely capable of inferring latent structures that are highly localized in time.Comment: To appear in the Proceedings of the 32nd Advances in Neural Information Processing Systems (NeurIPS 2019