Understanding Stochastic Natural Gradient Variational Inference

• URL: http://arxiv.org/abs/2406.01870v1
• Date: Tue, 4 Jun 2024 00:45:37 GMT
• Title: Understanding Stochastic Natural Gradient Variational Inference
• Authors: Kaiwen Wu, Jacob R. Gardner,
• Abstract summary: We show a global convergence rate of $mathcalO(frac1)$ implicitly a non-asymptotic convergence rate of NGVI. The rate is no worse than descent (aka black-box variational inference) and has better constant dependency.
• Score: 12.800664845601197
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic natural gradient variational inference (NGVI) is a popular posterior inference method with applications in various probabilistic models. Despite its wide usage, little is known about the non-asymptotic convergence rate in the \emph{stochastic} setting. We aim to lessen this gap and provide a better understanding. For conjugate likelihoods, we prove the first $\mathcal{O}(\frac{1}{T})$ non-asymptotic convergence rate of stochastic NGVI. The complexity is no worse than stochastic gradient descent (\aka black-box variational inference) and the rate likely has better constant dependency that leads to faster convergence in practice. For non-conjugate likelihoods, we show that stochastic NGVI with the canonical parameterization implicitly optimizes a non-convex objective. Thus, a global convergence rate of $\mathcal{O}(\frac{1}{T})$ is unlikely without some significant new understanding of optimizing the ELBO using natural gradients.

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