Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a simple but effective approximation $\hat \pi$ to $\pi$ for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which $\hat \pi$ is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when $\pi$ is log-concave.
翻译:与Markov连锁公司Monte Carlo(MCMC)方法一起,变式推论(VI)已成为大规模巴伊西亚推论的一种中央计算方法。与其从真正的后方美元取样,VI的目的不是要产生一个简单而有效的近似美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=元=美元=美元=美元=美元=美元=元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=美元=六的有原则性方法,而与经过仔细研究的MC方法不同,当$=美元是日汇时,它具有很强的理论保证。