Semi-Implicit Functional Gradient Flow for Efficient Sampling

2024-10-23

AI Summary

Particle-based variational inference (ParVI) suffers from limited exploration capability, low sampling efficiency, and high computational cost across repeated runs. To address these issues, we propose Semi-Implicit Function Gradient Flow (SIFG): a method that models the target distribution via a particle ensemble perturbed by Gaussian noise and estimates the gradient flow direction using denoising score matching. SIFG is the first to embed Gaussian perturbation into the function gradient flow framework, thereby enhancing the smoothness of the approximating family and improving theoretical convergence guarantees. We further introduce an adaptive noise scheduling mechanism to dynamically balance exploration breadth and approximation accuracy. Parameterized by neural networks, SIFG generates high-quality, diverse samples in a single run without reinitialization. Experiments on synthetic and real-world datasets demonstrate that SIFG significantly improves distribution approximation accuracy and sampling efficiency while accelerating convergence, validating its effectiveness and practicality.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Particle-based variational inference methods (ParVIs) use nonparametric variational families represented by particles to approximate the target distribution according to the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. Although functional gradient flows have been introduced to expand the kernel space for better flexibility, the deterministic updating mechanism may limit exploration and require expensive repetitive runs for new samples. In this paper, we propose Semi-Implicit Functional Gradient flow (SIFG), a functional gradient ParVI method that uses perturbed particles with Gaussian noise as the approximation family. We show that the corresponding functional gradient flow, which can be estimated via denoising score matching with neural networks, exhibits strong theoretical convergence guarantees due to a higher-order smoothness brought to the approximation family via Gaussian perturbation. In addition, we present an adaptive version of our method that automatically selects the appropriate noise magnitude during sampling, striking a good balance between exploration efficiency and approximation accuracy. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness and efficiency of the proposed framework.

Problem

• Improving particle-based variational inference via flexible functional gradient flows
• Enhancing sampling exploration with Gaussian noise perturbation
• Automating noise magnitude selection for efficient accurate approximation

Innovation

• Semi-Implicit Functional Gradient flow with Gaussian noise
• Denoising score matching via neural networks
• Adaptive noise magnitude selection for sampling