A Consistency Result for Bayes Classifiers with Censored Response Data

TL;DR

This paper establishes the strong consistency of a maximum collective conditional likelihood estimator for naive Bayes classifiers trained on right censored response data, extending their applicability to censored data scenarios.

Contribution

It introduces a new estimator for naive Bayes classifiers with censored responses and proves its strong consistency under standard conditions.

Findings

The estimator is strongly consistent.

Applicability to censored data in prediction problems.

Theoretical validation under identifiability conditions.

Abstract

Naive Bayes classifiers have proven to be useful in many prediction problems with complete training data. Here we consider the situation where a naive Bayes classifier is trained with data where the response is right censored. Such prediction problems are for instance encountered in profiling systems used at National Employment Agencies. In this paper we propose the maximum collective conditional likelihood estimator for the prediction and show that it is strongly consistent under the usual identifiability condition.