Importance Sampling via Score-based Generative Models

2025-02-07

AI Summary

This work addresses the inefficiency of retraining models for each importance-weighting function in multi-task biased sampling. We propose a **training-free importance sampling framework**, leveraging a pre-trained score-based generative model (SGM). By combining its score function with an arbitrary importance weight function, we formulate importance sampling as a **controllable reverse diffusion process**, requiring neither fine-tuning nor retraining. Our key contribution is the first fully training-free importance sampling method, featuring an explicitly derived weight-adaptive reverse stochastic differential equation (SDE) grounded in the score function. Extensive experiments on industrial and natural image datasets demonstrate high scalability and effectiveness: the approach significantly reduces computational and training overhead in multi-task settings while enabling flexible adaptation of a single base distribution to diverse bias objectives.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Proposes training-free importance sampling using SGMs.
• Implements sampling as a backward diffusion process.
• Scalable across diverse datasets and tasks.

Innovation

• Training-free importance sampling framework
• Utilizes score-based generative models
• Implements backward diffusion process