A relation between log-likelihood and cross-validation log-scores

TL;DR

This paper establishes a theoretical link between the log-likelihood of a model and its cross-validation log-scores, showing they are equivalent under certain conditions, which enhances understanding of model evaluation methods.

Contribution

It introduces a novel theoretical relationship connecting log-likelihood with leave-one-out and k-fold cross-validation scores, unifying these evaluation metrics.

Findings

Log-likelihood equals the average of leave-one-out cross-validation scores.

The relation generalizes to any k-fold cross-validation log-score.

Provides a theoretical foundation for comparing model evaluation metrics.

Abstract

It is shown that the log-likelihood of a hypothesis or model given some data is equivalent to an average of all leave-one-out cross-validation log-scores that can be calculated from all subsets of the data. This relation can be generalized to any $k$-fold cross-validation log-scores.