Related papers: Bayesian Learning for Low-Rank matrix reconstructi…
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank…
The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into…
Large Language Models usually put more emphasis on accuracy and therefore, will guess even when not certain about the prediction, which is especially severe when fine-tuned on small datasets due to the inherent tendency toward…
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done…
Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…
Established methods for unsupervised representation learning such as variational autoencoders produce none or poorly calibrated uncertainty estimates making it difficult to evaluate if learned representations are stable and reliable. In…
Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
In this paper we study the problem of reconstruction of a low-rank matrix observed with additive Gaussian noise. First we show that under mild assumptions (about the prior distribution of the signal matrix) we can restrict our attention to…
This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…