Kernel Conditional Exponential Family

TL;DR

This paper introduces a nonparametric family of conditional distributions using RKHS, providing an algorithm for learning and demonstrating superior performance over existing methods in complex datasets.

Contribution

It generalizes conditional exponential families with functional parameters in RKHS and offers a consistent estimator with practical algorithms.

Findings

Outperforms competing approaches with guarantees of consistency

Effective on datasets with abrupt transitions and heteroscedasticity

Competitive with deep conditional density models

Abstract

A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter, and consistency of the estimator is established in the well specified case. In experiments, the new method generally outperforms a competing approach with consistency guarantees, and is competitive with a deep conditional density model on datasets that exhibit abrupt transitions and heteroscedasticity.