The Tractability Landscape of Sampling with Inexact Scores

2026-07-21

AI Summary

This work investigates the feasibility boundary for achieving asymptotically unbiased sampling under inexact score functions. Focusing on standard families of target distributions, it characterizes sampling bias via total variation distance and models errors in the score function. Leveraging tools from probability theory and computational complexity, the analysis generalizes existing results to an algorithm-agnostic framework and extends them to broader error assumptions. The central contribution establishes sub-Gaussian error as the tight condition for asymptotically unbiased sampling: this requirement is both sufficient and necessary, and any relaxation to weaker-than-sub-Gaussian error assumptions renders the problem unsolvable.

Abstract

We provide a simple and tight characterization of the types of inexact score oracle access that permit sampling with vanishing total variation bias, for a standard, well-behaved target family. Our main result shows that any weaker error than the sub-Gaussian assumption used by [YW26] rules out the tractability of unbiased sampling. This strengthens the conclusion of [CCSW26] to be algorithm-agnostic, and to hold for a wider range of error assumptions.

Problem

• inexact scores
• sampling
• total variation bias
• tractability
• score oracle

Innovation

• inexact score oracle
• unbiased sampling
• sub-Gaussian error
• total variation bias
• tractability