论文标题
部分可观测时空混沌系统的无模型预测
A Mixing Time Lower Bound for a Simplified Version of BART
论文作者
论文摘要
贝叶斯添加剂回归树（BART）是一种流行的贝叶斯非参数回归算法。后部是对决策树总和的分布，并且通过平均后部的样本进行预测。 强大的预测性能和提供不确定性度量的能力的结合使BART通常用于社会科学，生物统计学和因果推断。 Bart使用Markov Chain Monte Carlo（MCMC）在树木之和的参数化空间上获得近似的后样品，但经常观察到链的混合速度很慢。 在本文中，我们在混合时间上为BART提供了第一个下限，其中将总和减少到一棵树，并将可能的移动子集用于MCMC提案分布。我们在混合时间的下限随着数据点数的数量呈指数增长。 受到混合时间和数据点数量之间的新连接的启发，我们对BART进行了严格的模拟。我们定性地表明，巴特的混合时间随数据点的数量而增加。 简化的巴特的缓慢混合时间表明，简化的巴特算法的不同运行之间存在很大的变化，而文献中巴特已知类似的大变化。这种较大的变化可能导致从BART MCMC样品获得的模型，预测和后间隔缺乏稳定性。 我们的下限和模拟表明，随着数据点的数量增加了链的数量。
Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression algorithm. The posterior is a distribution over sums of decision trees, and predictions are made by averaging approximate samples from the posterior. The combination of strong predictive performance and the ability to provide uncertainty measures has led BART to be commonly used in the social sciences, biostatistics, and causal inference. BART uses Markov Chain Monte Carlo (MCMC) to obtain approximate posterior samples over a parameterized space of sums of trees, but it has often been observed that the chains are slow to mix. In this paper, we provide the first lower bound on the mixing time for a simplified version of BART in which we reduce the sum to a single tree and use a subset of the possible moves for the MCMC proposal distribution. Our lower bound for the mixing time grows exponentially with the number of data points. Inspired by this new connection between the mixing time and the number of data points, we perform rigorous simulations on BART. We show qualitatively that BART's mixing time increases with the number of data points. The slow mixing time of the simplified BART suggests a large variation between different runs of the simplified BART algorithm and a similar large variation is known for BART in the literature. This large variation could result in a lack of stability in the models, predictions, and posterior intervals obtained from the BART MCMC samples. Our lower bound and simulations suggest increasing the number of chains with the number of data points.
