Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models
多项 Logistic 与计数回归的对数线性贝叶斯加性回归树AI 解读 ↓
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多项 Logistic 与计数回归的对数线性贝叶斯加性回归树
- 研究问题
- 如何把主要依托高斯似然计算的贝叶斯加性回归树推广到多项 Logistic 和计数模型，同时处理零膨胀与过度离散？
- 方法与思路
- 作者针对对数线性模型设计数据增广策略及经过校准的先验，使树模型保持灵活性，并能在非高斯模型中实施 MCMC。
- 材料陈述的贡献
- 摘要称新先验与增广方案支持非高斯模型的高效后验采样，并通过示例及既有数据应用展示多项和计数回归用途。
- 阅读关注点
- 应核对各模型的数据增广表示、先验校准与过拟合控制方式，以及多类别参数约束、零膨胀识别和采样效率证据。
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- 仅据稿件版本未注明的 OpenAlex 索引摘要；摘要未给出具体先验、增广公式或数值比较，不能据此判断其普遍计算或预测优势。
原文摘要
We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been mostly limited to models for Gaussian “data,” either observed or latent. This is primarily because efficient MCMC algorithms are available for Gaussian likelihoods. But while many useful models are naturally cast in terms of latent Gaussian variables, many others are not—including models considered in this article. We develop new data augmentation strategies and carefully specified prior distributions for these new models. Like the original BART prior, the new prior distributions are carefully constructed and calibrated to be flexible while guarding against overfitting. Together the new priors and data augmentation schemes allow us to implement an efficient MCMC sampler outside the context of Gaussian models. The utility of these new methods is illustrated with examples and an application to a previously published dataset. Supplementary materials for this article are available online.