论文检索

GS-BART：采用图分裂决策规则的贝叶斯加性回归树AI 解读

Ensemble decision tree methods such as XGBoost, Random Forest, and Bayesian Additive Regression Trees (BART) have gained enormous popularity in data science for their superior performance in machine learning regression and classification tasks. In this paper, we introduce a new Bayesian graph-split additive decision tree method, GS-BART, designed to enhance the performance of axis-parallel split-based BART for dependent data with graph structures. The proposed approach…

不依赖评分等价性的基于排序的结构学习AI 解读

Summary We propose an empirical Bayes formulation of the structure learning problem, where the prior specification assumes that all node variables have the same error variance, an assumption known to ensure the identifiability of the underlying causal directed acyclic graph. To facilitate efficient posterior computation, we approximate the posterior probability of each ordering by that of a best directed acyclic graph model, which naturally leads to an order-based Markov…

高维有向无环图模型及其等价类的贝叶斯学习复杂度AI 解读

Structure learning via MCMC sampling is known to be very challenging because of the enormous search space and the existence of Markov equivalent DAGs. Theoretical results on the mixing behavior are lacking. In this work, we prove the rapid mixing of a random walk Metropolis–Hastings algorithm, which reveals that the complexity of Bayesian learning of sparse equivalence classes grows only polynomially in n and p, under some high-dimensional assumptions. A series of…

高维贝叶斯变量选择中不依赖维度的混合时间AI 解读

Abstract Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves a much faster mixing time that is independent of the number of covariates, under the assumptions of Yang et al. To the best of our knowledge, this is the first high-dimensional…

线性回归中贝叶斯因子的零假设分布AI 解读

We show that under the null, the 2 log(Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide…