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arXiv Machine Learning

Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing

The paper investigates compressed sensing using a family of tunable linear generative priors linked through their singular value decompositions. It proves that in noiseless Gaussian compressed sensing, the full-dimensional linear prior yields the lowest expected reconstruction error across the entire family, meaning lower-complexity priors do not improve performance in this idealized setting. This contrasts with denoising, where lower complexity priors can reduce error due to bias‑variance tradeoffs, suggesting that the experimental gains seen with neural network priors stem from their nonlinearities.

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Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing

The paper investigates the sample complexity of noisy one‑bit compressed sensing for signals drawn from a prior distribution. By linking the prior’s effective distributional complexity to its approximate covering number, the authors prove that posterior sampling can recover signals accurately when the number of measurements scales with the logarithm of this covering number, modulo a one‑bit separation gap. They also show that the method remains reliable under learned prior mismatch measured in Wasserstein distance, provide a matching lower bound, and demonstrate practical performance using a diffusion‑based plug‑and‑play algorithm on FFHQ and ImageNet.

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arXiv AI
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Energy-based Transport for Amortized Bayesian Inference

arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.

By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
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arXiv AI
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Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

arXiv:2606. 16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration.

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