Regression with Variable Dimension Covariates

TL;DR

This paper reviews recent methods for regression problems where the covariate dimension varies, addressing a gap in the literature for such models which are common in practice.

Contribution

It highlights the lack of established methods for variable dimension covariate regression and reviews recent approaches using random partitions.

Findings

Identifies a gap in regression methodology for varying covariate dimensions.

Reviews recent proposals employing random partitions for variable dimension regression.

Emphasizes the need for further development of methods in this area.

Abstract

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the ubiquitous nature of regression problems and the abundance of related methods and results there is a surprising gap in the literature. There are no well established methods for regression with a varying dimension covariate vectors, despite the common occurrence of such problems. In this paper we review some recent related papers proposing varying dimension regression by way of random partitions.