DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework
This work addresses a bottleneck in variational inference for machine learning practitioners by improving approximation efficiency with limited particles, though it is incremental as it builds on existing ParVI methods.
The paper tackled the limitation of fixed-weight particles in Particle-based Variational Inference (ParVI) by proposing a Dynamic-weight Particle-based Variational Inference (DPVI) framework that adjusts particle weights dynamically, leading to faster convergence and superior empirical performance compared to fixed-weight methods.
The recently developed Particle-based Variational Inference (ParVI) methods drive the empirical distribution of a set of \emph{fixed-weight} particles towards a given target distribution $π$ by iteratively updating particles' positions. However, the fixed weight restriction greatly confines the empirical distribution's approximation ability, especially when the particle number is limited. In this paper, we propose to dynamically adjust particles' weights according to a Fisher-Rao reaction flow. We develop a general Dynamic-weight Particle-based Variational Inference (DPVI) framework according to a novel continuous composite flow, which evolves the positions and weights of particles simultaneously. We show that the mean-field limit of our composite flow is actually a Wasserstein-Fisher-Rao gradient flow of certain dissimilarity functional $\mathcal{F}$, which leads to a faster decrease of $\mathcal{F}$ than the Wasserstein gradient flow underlying existing fixed-weight ParVIs. By using different finite-particle approximations in our general framework, we derive several efficient DPVI algorithms. The empirical results demonstrate the superiority of our derived DPVI algorithms over their fixed-weight counterparts.