Importance Sampling via Score-based Generative Models

• URL: http://arxiv.org/abs/2502.04646v1
• Date: Fri, 07 Feb 2025 04:09:03 GMT
• Title: Importance Sampling via Score-based Generative Models
• Authors: Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo de Veciana,
• Abstract summary: Importance sampling involves sampling from a probability density function proportional to the product of an importance weight function and a base PDF. We propose an entirely training-free Importance sampling framework that relies solely on an SGM for the base PDF. We conduct a thorough analysis demonstrating the method's scalability and effectiveness across diverse datasets and tasks.
• Score: 12.32722207200796
• License:
• Abstract: Importance sampling, which involves sampling from a probability density function (PDF) proportional to the product of an importance weight function and a base PDF, is a powerful technique with applications in variance reduction, biased or customized sampling, data augmentation, and beyond. Inspired by the growing availability of score-based generative models (SGMs), we propose an entirely training-free Importance sampling framework that relies solely on an SGM for the base PDF. Our key innovation is realizing the importance sampling process as a backward diffusion process, expressed in terms of the score function of the base PDF and the specified importance weight function--both readily available--eliminating the need for any additional training. We conduct a thorough analysis demonstrating the method's scalability and effectiveness across diverse datasets and tasks, including importance sampling for industrial and natural images with neural importance weight functions. The training-free aspect of our method is particularly compelling in real-world scenarios where a single base distribution underlies multiple biased sampling tasks, each requiring a different importance weight function. To the best of our knowledge our approach is the first importance sampling framework to achieve this.

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