Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete mixture models, we consider a continuous latent variable model in general covariate spaces, which we call DR-BART. The prior mapping the latent variable to the observed data is constructed via a novel application of Bayesian Additive Regression Trees (BART). We prove that the posterior induced by our model concentrates quickly around true generative functions that are sufficiently smooth. We also analyze the performance of DR-BART on a set of challenging simulated examples, where it outperforms various other methods for Bayesian density regression. Lastly, we apply DR-BART to two real datasets from educational testing and economics, to study student growth and predict returns to education. Our proposed sampler is efficient and allows one to take advantage of BART's flexibility in many applied settings where the entire distribution of the response is of primary interest. Furthermore, our scheme for splitting on latent variables within BART facilitates its future application to other classes of models that can be described via latent variables, such as those involving hierarchical or time series data.
翻译:以共变式构建整个密度变化的方式, 共变式的全密度变化是一个重要但具有挑战性的普通平均值和四分回归的典型。 虽然现有的密度回归方法主要是由共变的离离散混合模型构成的, 但我们在一般的共变空间中考虑一个连续的潜伏变量模型, 我们称之为 DR- BART。 先前绘制观测数据的潜变量的图示前, 是通过Bayesian Additive Recresresres回树( BART) 的新应用来构建的。 我们证明, 我们模型引出的外表象迅速围绕足够平稳的真正的基因功能, 迅速围绕足够平稳的真正基因功能展开具有挑战性的概括。 我们还分析DR-BART在一组具有挑战性的模拟例子中的表现, 这套方法优于Bayesian 密度回归的其他方法。 最后, 我们将DR-BART应用于两个来自教育测试和经济学的真正数据集, 研究学生成长和预测教育的回报。 我们提议的采样器是高效的, 并允许人们利用BART的灵活性在许多应用环境中应用的、 反应的整体分布最为感兴趣的应用环境环境。 此外, 我们关于D-BART级变变变变的系统或变变变变的模型, 通过这些变的模型, 用于其他等级变等的变的变的变的变的模型,如BART的变的变的变的变的变的变的变的变的变, 或变的变等的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变的变,