Estimating Conditional Covariance between labels for Multilabel Data

TL;DR

This paper compares three statistical models to estimate label dependence in multilabel data, revealing their strengths and limitations in measuring constant and dependent covariances, with implications for multilabel analysis.

Contribution

It introduces a comparative analysis of Multivariate Probit, Multivariate Bernoulli, and Staged Logit models for estimating conditional label covariance in multilabel data.

Findings

All models estimate covariance well depending on strength.

Models falsely detect dependent covariance when only constant covariance is present.

Multivariate Probit has the lowest error rate among the models.

Abstract

Multilabel data should be analysed for label dependence before applying multilabel models. Independence between multilabel data labels cannot be measured directly from the label values due to their dependence on the set of covariates $\vec{x}$, but can be measured by examining the conditional label covariance using a multivariate Probit model. Unfortunately, the multivariate Probit model provides an estimate of its copula covariance, and so might not be reliable in estimating constant covariance and dependent covariance. In this article, we compare three models (Multivariate Probit, Multivariate Bernoulli and Staged Logit) for estimating the constant and dependent multilabel conditional label covariance. We provide an experiment that allows us to observe each model's measurement of conditional covariance. We found that all models measure constant and dependent covariance equally well, depending on the strength of the covariance, but the models all falsely detect that dependent covariance is present for data where constant covariance is present. Of the three models, the Multivariate Probit model had the lowest error rate.