Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond
Researchers have developed a new theoretical framework for analyzing the complexity of estimating normalizing constants in probability distributions. This work focuses on annealed importance sampling methods, providing a non-asymptotic analysis with an oracle complexity of \(\\widetilde{O}(\frac{d\beta^2{\mathcal{A}}^2}{\varepsilon^4})\) for achieving a specified relative error. The analysis leverages Girsanov's theorem and optimal transport, avoiding explicit isoperimetric assumptions. Additionally, a novel algorithm using reverse diffusion samplers is proposed to handle large actions and multimodality, with empirical validation. AI
IMPACT Provides a theoretical foundation for improving density estimation techniques in machine learning models.