The paper introduces a Bayesian approach to matrix completion that uses a nuclear norm-based prior and addresses the challenge of unknown noise variance by placing a prior on it. It presents the first sampler for this model, providing a non‑asymptotic polynomial‑time guarantee in terms of matrix dimensions and desired accuracy. The method discretizes the noise precision and employs thermodynamic integration to construct a categorical posterior, offering a feasibility result for Bayesian sampling in non‑log‑concave settings.
arXiv:2609.08873v1 Announce Type: cross Abstract: Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over th...
arXiv:2606. 29203v1 Announce Type: new Abstract: We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation.
arXiv:2606. 27269v1 Announce Type: cross Abstract: Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models.
arXiv:2603. 12037v2 Announce Type: replace Abstract: Foundation models based on prior-data fitted networks (PFNs) have shown strong empirical performance in causal inference by framing the task as an in-context learning problem.
Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv:2109. 11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights.
arXiv:2607. 07735v1 Announce Type: cross Abstract: Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data.
arXiv:2606. 04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty.
arXiv:2609.13586v1 Announce Type: cross Abstract: We develop a causal framework for matrix completion under missing not at random (MNAR) data. Drawing on synthetic controls from the econometric panel...
arXiv:2608. 20183v1 Announce Type: new Abstract: Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selection in settings such as deep learning.
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.