论文标题
部分可观测时空混沌系统的无模型预测
Variational inference via Wasserstein gradient flows
论文作者
论文摘要
与马尔可夫链蒙特卡洛（MCMC）方法一起，变异推理（VI）已成为大规模贝叶斯推断的中央计算方法。 VI不是从真正的后部$π$取样，而是旨在生产一个简单但有效的近似值$ \hatπ$到$π$，对于摘要统计数据，易于计算。但是，与经过良好研究的MCMC方法论不同，VI的算法保证仍然相对较少地理解。在这项工作中，我们提出了VI的原则方法，其中$ \hatπ$被视为高斯或高斯人的混合物，它基于bures bures on Bures的梯度流理论 - 高斯措施的空间。类似于MCMC，当$π$是log-concave时，它具有强大的理论保证。
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 $π$, VI aims at producing a simple but effective approximation $\hat π$ to $π$ 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 $\hat π$ 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 $π$ is log-concave.
