论文标题
部分可观测时空混沌系统的无模型预测
Improved Marginal Unbiased Score Expansion (MUSE) via Implicit Differentiation
论文作者
论文摘要
我们将隐性差异化的技术应用于提高性能，减少数值误差，并删除用于层次结构贝叶斯推论的边际无偏分数扩展（MUSE）算法中所需的用户调整。我们在三个代表性的推理问题上证明了这些改进：1）扩展的尼尔漏斗2）贝叶斯神经网络和3）概率主体成分分析。在我们特定的测试案例中，具有隐式分化的缪斯比哈密顿蒙特卡洛（Hamiltonian Monte Carlo）的速度分别为155、397和5的因素，或者无隐式分化的65、278和1的因素，并产生良好的边际后代。朱莉娅（Julia）和python缪斯包装（Python Muse Package）已更新以使用隐式差异化，并且可以通过手动或使用许多流行的概率编程语言和自动差异化后端来解决问题。
We apply the technique of implicit differentiation to boost performance, reduce numerical error, and remove required user-tuning in the Marginal Unbiased Score Expansion (MUSE) algorithm for hierarchical Bayesian inference. We demonstrate these improvements on three representative inference problems: 1) an extended Neal's funnel 2) Bayesian neural networks, and 3) probabilistic principal component analysis. On our particular test cases, MUSE with implicit differentiation is faster than Hamiltonian Monte Carlo by factors of 155, 397, and 5, respectively, or factors of 65, 278, and 1 without implicit differentiation, and yields good approximate marginal posteriors. The Julia and Python MUSE packages have been updated to use implicit differentiation, and can solve problems defined by hand or with any of a number of popular probabilistic programming languages and automatic differentiation backends.
