Functional Linear Regression of Cumulative Distribution Functions

arXiv:2205.14545v3 Announce Type: replace
Abstract: The estimation of cumulative distribution functions (CDF) is an important learning task with a great variety of downstream applications, such as risk assessments in predictions and decision making. In this paper, we study functional regression of contextual CDFs where each data point is sampled from a linear combination of context dependent CDF basis functions. We propose functional ridge-regression-based estimation methods that estimate CDFs accurately everywhere. In particular, given $n$ samples with $d$ basis functions, we …

abstract applications arxiv combination cs.lg data decision decision making distribution functional functions linear linear regression making math.st paper predictions regression risk stat.th study type