arXiv Machine Learning September 25, 2026 By Calvin Tolbert

Nuclear Norm-Regularized Bayesian Matrix Completion

Read the original on arXiv Machine Learning →

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.

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