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• W2912073643 abstract "We study the asymptotic consistency properties of $alpha$-Renyi approximate posteriors, a class of variational Bayesian methods that approximate an intractable Bayesian posterior with a member of a tractable family of distributions, the member chosen to minimize the $alpha$-Renyi divergence from the true posterior. Unique to our work is that we consider settings with $alpha > 1$, resulting in approximations that upperbound the log-likelihood, and consequently have wider spread than traditional variational approaches that minimize the Kullback-Liebler (KL) divergence from the posterior. Our primary result identifies sufficient conditions under which consistency holds, centering around the existence of a 'good' sequence of distributions in the approximating family that possesses, among other properties, the right rate of convergence to a limit distribution. We further characterize the good sequence by demonstrating that a sequence of distributions that converges too quickly cannot be a good sequence. We also extend our analysis to the setting where $alpha$ equals one, corresponding to the minimizer of the reverse KL divergence, and to models with local latent variables. We also illustrate the existence of good sequence with a number of examples. Our results complement a growing body of work focused on the frequentist properties of variational Bayesian methods." @default.
• W2912073643 created "2019-02-21" @default.
• W2912073643 creator A5018713742 @default.
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• W2912073643 date "2019-02-05" @default.
• W2912073643 modified "2023-09-27" @default.
• W2912073643 title "Asymptotic Consistency of $alpha-$R'enyi-Approximate Posteriors" @default.
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