Errors-In-Variables Model Fitting for Partially Unpaired Data Utilizing Mixture Models

TL;DR

This paper presents a flexible errors-in-variables regression framework for partially unpaired data, using mixture models to handle loss of pairing information, demonstrated through simulations and real-world life expectancy data.

Contribution

It introduces a novel mixture model-based approach for regression with partially unpaired data, accommodating various data types and models without ad-hoc loss functions.

Findings

High-quality model fitting achieved with partially unpaired data

Effective for both linear and nonlinear models

Applicable to real-world datasets like life expectancy data

Abstract

We introduce a general framework for regression in the errors-in-variables regime, allowing for full flexibility about the dimensionality of the data, observational error probability density types, the (nonlinear) model type and the avoidance of ad-hoc definitions of loss functions. In this framework, we introduce model fitting for partially unpaired data, i.e. for given data groups the pairing information of input and output is lost (semi-supervised). This is achieved by constructing mixture model densities, which directly model the loss of pairing information allowing inference. In a numerical simulation study linear and nonlinear model fits are illustrated as well as a real data study is presented based on life expectancy data from the world bank utilizing a multiple linear regression model. These results show that high quality model fitting is possible with partially unpaired data, which opens the possibility for new applications with unfortunate or deliberate loss of pairing information in data.