Effective dimension of machine learning models

Amira Abbas, David Sutter, Alessio Figalli, Stefan Woerner

Keywords: Generalization, capacity, effective dimension

TL;DR: We introduce a capacity measure called the local effective dimension, which we show has desirable properties and the ability to bound generalization error.

Abstract: Making statements about the performance of trained models on tasks involving new data is one of the primary goals of machine learning, i.e., to understand the generalization power of a model. Various capacity measures try to capture this ability, but usually fall short in explaining important characteristics of models that we observe in practice. In this study, we propose the local effective dimension as a capacity measure which seems to correlate well with generalization error on standard data sets. Importantly, we prove that the local effective dimension bounds the generalization error and discuss the aptness of this capacity measure for machine learning models.

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