Conditional expectation estimation through attributable components
Conditional expectation estimation through attributable components
复制标题
通过归因成分进行条件期望估计
DOI：
10.1093/imaiai/iax023
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
G. Trigila
中科院分区：
文献类型：
--
作者：
E. Tabak;G. Trigila
提出了一种用协变量z=(z1，…)解释关注量x的变异性的一般方法。。。，ZL)。它将条件均值x̄(Z)表示为分量之和，其中每个分量表示为通过交替投影过程计算的每个协变量z1的非参数一维函数的乘积。X和zl都可以是实数或分类变量；此外，每个zl的一些或全部值可能是未知的，这为在存在混杂因素的情况下进行多聚类、分类和协变量分配提供了一般框架。该过程可以被视为通过数据驱动的最优传输重心问题来更一般地确定完全条件分布ρ(x|z)的预条件步骤。特别是，只需迭代该过程一次，就会产生ρ(x|z)的二阶结构(即协方差)。通过实例说明了该方法，其中包括对美国大陆地温变异性的解释以及对潜在读者的图书偏好的预测。
A general methodology is proposed for the explanation of variability in a quantity of interest x in terms of covariates z = (z1, . . . ,zL). It provides the conditional mean x̄(z) as a sum of components, where each component is represented as a product of non-parametric one-dimensional functions of each covariate zl that are computed through an alternating projection procedure. Both x and the zl can be real or categorical variables; in addition, some or all values of each zl can be unknown, providing a general framework for multi-clustering, classification and covariate imputation in the presence of confounding factors. The procedure can be considered as a preconditioning step for the more general determination of the full conditional distribution ρ(x|z) through a data-driven optimal-transport barycenter problem. In particular, just iterating the procedure once yields the second order structure (i.e. the covariance) of ρ(x|z). The methodology is illustrated though examples that include the explanation of variability of ground temperature across the continental United States and the prediction of book preference among potential readers.