Corrections extend method of gaps to wider data and models
Corrections to ``The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms''
Information Theory
Summary
A previous method for calculating how well supervised learning algorithms perform had a mistake in one of its key steps. The authors provide an example showing the problem and point out that the original method only worked under a specific assumption about the training data. They then offer a new, improved version that works even when training examples are not independent or identically distributed. This update broadens the situations where the method can be used and applies to more complex learning algorithms.
What this means in practice
- •For machine learning engineers: Improve error estimation techniques for models trained on non-standard or dependent datasets by using a more general method of data-driven gaps.
- •For data scientists: Assess model performance more accurately on complex or correlated data without relying on oversimplified independence assumptions.
Authors
Samir M. Perlaza
Abstract
In this paper, a counterexample to Lemma 5 of the paper referenced in the title is provided. Consequently, the formulation of the method of data-driven gaps presented in the referenced paper relies on an additional assumption, namely, that the conditional distribution of the training dataset given the learned model has identical data-point-specific marginals. To overcome this limitation, a generalized formulation of the method of data-driven gaps that does not rely on Lemma 5 and does not require the training samples to be independent or identically distributed is presented. Through this formulation, the applicability of the method of data-driven gaps is extended to a broader class of data distributions and randomized learning algorithms.