Nonparametric Prediction Distribution from Resolution-Wise Regression with Heterogeneous Data
提出一种非参数分辨率回归方法，通过分解响应和预测变量的信息，用惩罚逻辑回归建模分辨率与模式的关系，最终给出条件响应的直方图分布，适用于异质数据场景。
Modeling and inference for heterogeneous data have gained great interest recently due to rapid developments in personalized marketing. Most existing regression approaches are based on the conditional mean and may require additional cluster information to accommodate data heterogeneity. In this paper, we propose a novel nonparametric resolution-wise regression procedure to provide an estimated distribution of the response instead of one single value. We achieve this by decomposing the information of the response and the predictors into resolutions and patterns respectively based on marginal binary expansions. The relationships between resolutions and patterns are modeled by penalized logistic regressions. Combining the resolution-wise prediction, we deliver a histogram of the conditional response to approximate the distribution. Moreover, we show a sure independence screening property and the consistency of the proposed method for growing dimensions. Simulations and a real estate valuation dataset further illustrate the effectiveness of the proposed method.