Model predictivity assessment: incremental test-set selection and accuracy evaluation

TL;DR

This paper introduces a new method for assessing model predictivity by optimally selecting test points and weighting errors, improving accuracy over traditional methods, and demonstrated on an industrial electricity prediction case.

Contribution

It proposes a novel predictivity criterion combined with incremental test set selection methods, including support points and kernel herding, for more accurate model evaluation.

Findings

Weighted incremental test selection improves prediction error estimates.

Kernel herding and support points outperform traditional test set methods.

Method reduces reliance on costly cross-validation techniques.

Abstract

Unbiased assessment of the predictivity of models learnt by supervised machine-learning methods requires knowledge of the learned function over a reserved test set (not used by the learning algorithm). The quality of the assessment depends, naturally, on the properties of the test set and on the error statistic used to estimate the prediction error. In this work we tackle both issues, proposing a new predictivity criterion that carefully weights the individual observed errors to obtain a global error estimate, and using incremental experimental design methods to "optimally" select the test points on which the criterion is computed. Several incremental constructions are studied, including greedy-packing (coffee-house design), support points and kernel herding techniques. Our results show that the incremental and weighted versions of the latter two, based on Maximum Mean Discrepancy concepts, yield superior performance. An industrial test case provided by the historical French electricity supplier (EDF) illustrates the practical relevance of the methodology, indicating that it is an efficient alternative to expensive cross-validation techniques.