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贝叶斯非参数准似然AI 解读

A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a data generating mechanism. This article focuses on a Bayesian nonparametric extension of Wedderburn’s quasi-likelihood, using Bayesian additive regression trees to model the mean function. Here, the analyst posits only a structural relationship between the mean and variance of the outcome. We show that this approach…

用贝叶斯决策树集成估计异质性因果中介效应AI 解读

The causal inference literature has increasingly recognized that targeting treatment effect heterogeneity can lead to improved scientific understanding and policy recommendations. Similarly, studying the causal pathway connecting the treatment to the outcome can be useful. We address these problems in the context of causal mediation analysis . We introduce a varying coefficient model based on Bayesian additive regression trees to estimate and regularize heterogeneous causal…

广义贝叶斯加性回归树：突破条件共轭限制AI 解读

Bayesian additive regression trees have seen increased interest in recent years due to their ability to combine machine learning techniques with principled uncertainty quantification. The Bayesian backfitting algorithm used to fit BART models, however, limits their application to a small class of models for which conditional conjugacy exists. In this article, we greatly expand the domain of applicability of BART to arbitrary generalized BART models by introducing a very…

非参数与高维模型中的贝叶斯可忽略性是一种信息性先验AI 解读

In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process, which generates the response, and the missing data mechanism, which determines the data we observe. Under the ignorability condition of Rubin, however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the former needs to be estimated; partially because of this simplification, ignorability is…

基于贝叶斯决策树集成的自适应条件分布估计AI 解读

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Like other BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in our BART model, we introduce an approach to targeted smoothing of BART models which is of…

适应平滑度与稀疏性的贝叶斯回归树集成AI 解读

Summary Ensembles of decision trees are a useful tool for obtaining flexible estimates of regression functions. Examples of these methods include gradient-boosted decision trees, random forests and Bayesian classification and regression trees. Two potential shortcomings of tree ensembles are their lack of smoothness and their vulnerability to the curse of dimensionality. We show that these issues can be overcome by instead considering sparsity inducing soft decision trees in…

用于高维预测与变量选择的贝叶斯回归树AI 解读

Decision tree ensembles are an extremely popular tool for obtaining high-quality predictions in nonparametric regression problems. Unmodified, however, many commonly used decision tree ensemble methods do not adapt to sparsity in the regime in which the number of predictors is larger than the number of observations. A recent stream of research concerns the construction of decision tree ensembles that are motivated by a generative probabilistic model, the most influential…

非可忽略单调缺失纵向数据的灵活贝叶斯方法及精神分裂症试验应用AI 解读

We develop a Bayesian nonparametric model for a longitudinal response in the presence of nonignorable missing data. Our general approach is to first specify a working model that flexibly models the missingness and full outcome processes jointly. We specify a Dirichlet process mixture of missing at random (MAR) models as a prior on the joint distribution of the working model. This aspect of the model governs the fit of the observed data by modeling the observed data…