mlsanityData to 14 Oct 2026

How many measurements are enough? Bayesian recovery in inverse problems with general distributions

arXiv 2505.10630 ↗First posted 15 May 2025cs.LG math.ST stat.THcited by 2

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Abstract (arXiv)

We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior P, and establish sufficient conditions for stable and accurate recovery with high probability. Our main result is a non-asymptotic bound that shows that the sample complexity depends on (i) the intrinsic complexity of P, quantified by its so-called approximate covering number, and (ii) concentration bounds for the forward operator and noise distributions. As a key application, we specialize to generative priors, where P is the pushforward of a latent distribution via a Deep Neural Network (DNN). We show that the sample complexity scales log-linearly with the latent dimension k, thus establishing the efficacy of DNN-based priors. Generalizing existing results on deterministic (i.e., non-Bayesian) recovery for the important problem of random sampling with an orthogonal matrix U, we show how the sample complexity is determined by the coherence of U with respect to the support of P. Hence, we establish that coherence plays a fundamental role in Bayesian recovery as well. Overall, our framework unifies and extends prior work, providing rigorous guarantees for the sample complexity of solving Bayesian inverse problems with arbitrary distributions.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 43 of its 80 references that are in the map. First posted on arXiv 15 May 2025.

Builds on

43 of 80 references.

References · 43

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  2. 2026Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributionscited by 0