Semi-Implicit Functional Gradient Flow

Particle-based variational inference methods (ParVIs) use non-parametric variational families represented by particles to approximate the target distribution according to the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. Recent works introduce functional gradient flows to substitute the kernel for better flexibility. However, the deterministic updating mechanism may suffer from limited 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 as the approximation family. The corresponding functional gradient flow, which can be estimated via denoising score matching, exhibits strong theoretical convergence guarantee. We also present an adaptive version of our method to automatically choose the suitable noise magnitude. Extensive experiments demonstrate the effectiveness and efficiency of the proposed framework on both simulated and real data problems.