On the Convergence of Black-Box Variational Inference
We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., bounded domain, bounded support, only optimizing for the scale, and such), our setup does not need any such algorithmic modifications. Our results hold for log-smooth posterior densities with and without strong log-concavity and the location-scale variational family. Also, our analysis reveals that certain algorithm design choices commonly employed in practice, particularly, nonlinear parameterizations of the scale of the variational approximation, can result in suboptimal convergence rates. Fortunately, running BBVI with proximal stochastic gradient descent fixes these limitations, and thus achieves the strongest known convergence rate guarantees. We evaluate this theoretical insight by comparing proximal SGD against other standard implementations of BBVI on large-scale Bayesian inference problems.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceVariational InferenceMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Overdispersed Black-Box Variational Inference
We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational …
Variational InferenceProvable convergence guarantees for black-box variational inference
Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs: name…
Stochastic OptimizationVariational InferenceFast Black-box Variational Inference through Stochastic Trust-Region Optimization
We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based o…
Variational InferenceProvable Smoothness Guarantees for Black-Box Variational Inference
Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural prop…
Variational InferenceVariance Control for Black Box Variational Inference Using The James-Stein Estimator
Black Box Variational Inference is a promising framework in a succession of recent efforts to make Variational Inference more ``black box". However, in basic version it either fails to converge due to instability or requ…
Variational Inference