Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

2026-06-15 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Research introduces the first unified analysis of variance reduction techniques for sampling from high-dimensional, non-log-concave distributions with unnormalized densities. This addresses a fundamental machine learning challenge where exact gradients are unavailable, leading to high variance in stochastic gradient approximations. The study establishes improved non-asymptotic convergence rates in ε-relative Fisher information and, under a Poincaré inequality assumption, in squared total variation distance, further proving weak convergence to the target distribution. The analysis extends to solving inverse problems using score-based generative priors. Empirical validation demonstrates that techniques like SGD with momentum, STORM, and PAGE consistently improve sample quality in two standard imaging applications, given a fixed budget of gradient computations per iteration.

Key takeaway

For Machine Learning Engineers working with high-dimensional, non-log-concave sampling, you should integrate variance reduction techniques like SGD with momentum, STORM, or PAGE. This approach significantly improves sample quality and convergence rates, especially when exact gradients are unavailable. Consider applying these methods to enhance your solutions for inverse problems, particularly those leveraging score-based generative priors, to achieve more robust and accurate results within fixed computational budgets.

Key insights

Unified analysis shows variance reduction improves sampling from non-log-concave distributions, enhancing convergence and sample quality.

Principles

• Variance reduction improves non-log-concave sampling.
• Stochastic gradients benefit from unified analysis.
• Poincaré inequality aids convergence proofs.

Method

The method involves applying variance reduction techniques (SGD with momentum, STORM, PAGE) to approximate gradients for sampling from non-log-concave distributions, then validating convergence rates.

In practice

• Apply SGD with momentum for sampling.
• Use STORM or PAGE for gradient approximation.
• Enhance inverse problem solutions with priors.

Topics

• Non-Log-Concave Sampling
• Variance Reduction
• Stochastic Gradients
• Inverse Problems
• Generative Priors
• Machine Learning

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.