Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing

Key points

• By characterizing the effective distributional complexity of the prior via its approximate covering number, we prove that posterior sampling achieves accurate recovery with high probability when the number of measurements scales with the logarithm of the approximate covering number, up to a one-bit separation gap factor.1
• This upper bound is robust to learned prior mismatch.1
• Specifically, we show that posterior sampling with an approximate prior remains reliable, provided that the learned prior distribution is sufficiently close to the true signal distribution in Wasserstein distance.1
• To approximate the ideal posterior sampling process for real world scenarios, we instantiate posterior sampling through a plug-and-play algorithm with diffusion priors.1

Sources (1)

• [1]Recovery Guarantees for Posterior Sampling of One-Bit Compressed Sensing
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 12:27 PM

  We study the sample complexity of noisy one-bit compressed sensing for signals drawn from a prior distribution.

  By characterizing the effective distributional complexity of the prior via its approximate covering number, we prove that posterior sampling achieves accurate recovery with high probability when the number of measurements scales with the logarithm of the approximate covering number, up to a one-bit separation gap factor.

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