Related papers: Bayesian Robust Tensor Factorization for Incomplet…

We propose a unified probabilistic framework for sparse count tensors with excess zeros, motivated by single-cell Hi-C data. The observed data are naturally represented as a three-way tensor indexed by genomic loci pairs and cells,…

We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be…

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics.…

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…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

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…

In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…

Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…

We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both…

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…