Semi-supervised distribution learning
成果类型：
Article
署名作者：
Wen, Mengtao; Jia, Yinxu; Ren, Haojie; Wang, Zhaojun; Zou, Changliang
署名单位：
Nankai University; Shanghai Jiao Tong University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asae056
发表日期：
2024
关键词：
摘要：
This study addresses the challenge of distribution estimation and inference in a semi-supervised setting. In contrast to prior research focusing on parameter inference, this work explores the complexities of semi-supervised distribution estimation, particularly the uniformity problem inherent in functional processes. To tackle this issue, we introduce a versatile framework designed to extract valuable information from unlabelled data by approximating a conditional distribution on covariates. The proposed estimator is derived using K-fold cross-fitting, and exhibits both consistency and asymptotic Gaussian process properties. Under mild conditions, the proposed estimator outperforms the empirical cumulative distribution function in terms of asymptotic efficiency. Several applications of the methodology are given, including parameter inference and goodness-of-fit tests.