Related papers: Zero-Truncated Poisson Tensor Factorization for Ma…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
Tensor factorizations (TF) are powerful tools for the efficient representation and analysis of multidimensional data. However, classic TF methods based on maximum likelihood estimation underperform when applied to zero-inflated count data,…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor…
The workhorse model for zero-truncated count data (y = 1, 2, ...) is the zero-truncated negative binomial (ZTNB) model. We find it should seldom be used. Instead, we recommend the one-inflated zero-truncated negative binomial (OIZTNB) model…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…
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…
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables…
We propose a new Bayesian Markov switching regression model for multidimensional arrays (tensors) of binary time series. We assume a zero-inflated logit regression with time-varying parameters and apply it to multilayer temporal networks.…
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on…
We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…
Relational data are usually highly incomplete in practice, which inspires us to leverage side information to improve the performance of community detection and link prediction. This paper presents a Bayesian probabilistic approach that…
While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…
There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…