Heteroscedastic BART via Multiplicative Regression Trees
Heteroscedastic BART via Multiplicative Regression Trees
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DOI：
10.1080/10618600.2019.1677243
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发表时间：
2020-04
影响因子：
2.4
通讯作者：
M. Pratola;H. Chipman;Edward I. George;R. McCulloch
中科院分区：
文献类型：
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作者：
M. Pratola;H. Chipman;Edward I. George;R. McCulloch
摘要贝叶斯加性回归树（BART）作为一种灵活、可扩展的非参数回归方法，在现代应用统计问题中得到越来越广泛的应用。对于处理大型复杂非线性响应面的实践者来说，它的优点包括无矩阵公式和不需要预先指定约束回归基。虽然BART在拟合平均值方面很灵活，但由于依赖于恒定方差误差模型，它受到了限制。为了缓解这一限制，我们提出了BART，这是BART的非参数异方差细化。在BART中，均值函数用树的和建模，每棵树决定了对均值的加性贡献。在HBART中，方差函数进一步用树的乘积建模，每棵树都决定了方差的乘法贡献。与均值模型一样，这种灵活的多维方差模型完全是非参数的，不需要预先指定限制基础。此外，通过这种增强，HBART可以深入了解预测因子与均值和方差的潜在关系。通过二手车价格和发行年份的模拟和真实数据，展示了具有揭示新诊断图的HBART的实际实现。本文的补充材料可在网上获得。
Abstract Bayesian additive regression trees (BART) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces, its advantages include a matrix-free formulation and the lack of a requirement to prespecify a confining regression basis. Although flexible in fitting the mean, BART has been limited by its reliance on a constant variance error model. Alleviating this limitation, we propose HBART, a nonparametric heteroscedastic elaboration of BART. In BART, the mean function is modeled with a sum of trees, each of which determines an additive contribution to the mean. In HBART, the variance function is further modeled with a product of trees, each of which determines a multiplicative contribution to the variance. Like the mean model, this flexible, multidimensional variance model is entirely nonparametric with no need for the prespecification of a confining basis. Moreover, with this enhancement, HBART can provide insights into the potential relationships of the predictors with both the mean and the variance. Practical implementations of HBART with revealing new diagnostic plots are demonstrated with simulated and real data on used car prices and song year of release. Supplementary materials for this article are available online.