Related papers: The trace norm constrained matrix-variate Gaussian…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities…
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
Gaussian processes (GP) are a versatile tool in machine learning and computational science. We here consider the case of multi-output Gaussian processes (MOGP) and present low-rank approaches for efficiently computing the posterior mean of…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
Multi-task/Multi-output learning seeks to exploit correlation among tasks to enhance performance over learning or solving each task independently. In this paper, we investigate this problem in the context of Gaussian Processes (GPs) and…
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…
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family…