Automatic selection of hyper-parameters via the use of softened profile likelihood

TL;DR

This paper introduces a softened profile likelihood method for automatic multi-hyper-parameter selection, demonstrated on various models, improving the efficiency of model tuning.

Contribution

It extends existing heuristic methods to enable simultaneous automatic selection of multiple hyper-parameters using a novel softened profile likelihood approach.

Findings

Successfully applied to elastic nets, SVMs, and neural networks.

Demonstrated ability to select multiple hyper-parameters automatically.

Investigated robustness to assumption violations through simulation.

Abstract

We extend a heuristic method for automatic dimensionality selection, which maximizes a profile likelihood to identify "elbows" in scree plots. Our extension enables researchers to make automatic choices of multiple hyper-parameters simultaneously. To facilitate our extension to multi-dimensions, we propose a "softened" profile likelihood. We present two distinct parameterizations of our solution and demonstrate our approach on elastic nets, support vector machines, and neural networks. We also report a small simulation study to investigate violations to an assumption we make, and briefly discuss applications of our method to other data-analytic tasks than hyper-parameter selection.