# When is the mode functional the Bayes classifier?

## TL;DR

This paper examines the conditions under which the mode of the conditional probability distribution aligns with the Bayes classifier, highlighting its limitations under different cost structures.

## Contribution

It clarifies when the mode functional coincides with the Bayes classifier and demonstrates its failure under non-zero-one loss scenarios.

## Key findings

- Mode equals Bayes classifier under zero-one loss.
- Mode fails to be optimal under other cost structures.
- Provides theoretical insights into classification decision rules.

## Abstract

In classification problems, the mode of the conditional probability distribution, i.e., the most probable category, is the Bayes classifier under zero-one or misclassification loss. Under any other cost structure, the mode fails to persist.