Related papers: Bayesian Extensive-Rank Matrix Factorization with …

We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

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…

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging…

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…

Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the…

In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…

Analyzing demographic data collected across multiple populations, time periods, and age groups is challenging due to the interplay of high dimensionality, demographic heterogeneity among groups, and stochastic variability within smaller…

We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime, where the rank of the signal matrix to infer $M$ scales with its size $N$ as $M=\mathrm{o}(\sqrt{\ln N})$.…

Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…