On the Approximation Accuracy of Gaussian Variational Inference
arxiv(2023)
摘要
The main computational challenge in Bayesian inference is to compute
integrals against a high-dimensional posterior distribution. In the past
decades, variational inference (VI) has emerged as a tractable approximation to
these integrals, and a viable alternative to the more established paradigm of
Markov Chain Monte Carlo. However, little is known about the approximation
accuracy of VI. In this work, we bound the TV error and the mean and covariance
approximation error of Gaussian VI in terms of dimension and sample size. Our
error analysis relies on a Hermite series expansion of the log posterior whose
first terms are precisely cancelled out by the first order optimality
conditions associated to the Gaussian VI optimization problem.
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