Variational inference via Wasserstein gradient flows
Variational inference via Wasserstein gradient flows
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DOI：
10.48550/arxiv.2205.15902
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Marc Lambert;Sinho Chewi;F. Bach;S. Bonnabel;P. Rigollet
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文献类型：
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作者：
Marc Lambert;Sinho Chewi;F. Bach;S. Bonnabel;P. Rigollet
沿着马尔可夫链蒙特卡罗（MCMC）方法，变分推理（VI）已经成为大规模贝叶斯推理的中心计算方法。而不是从真实的后验$\pi$采样，VI的目的是产生一个简单但有效的近似$\hat \pi$到$\pi$，其汇总统计量很容易计算。然而，与经过充分研究的MCMC方法不同，VI的算法保证仍然相对不那么好理解。在这项工作中，我们提出了原则性的方法VI，其中$\hat \pi$被认为是高斯或高斯的混合物，这取决于理论上的梯度流的Bures-Wasserstein空间的高斯措施。类似于MCMC，当$\pi$是对数凹时，它具有强有力的理论保证。
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.