Goal-Oriented Sensitivity Analysis of Hyperparameters in Deep Learning

TL;DR

This paper introduces a goal-oriented sensitivity analysis method using HSIC to understand and optimize hyperparameters in neural networks, improving interpretability and efficiency across various datasets and scientific applications.

Contribution

The paper develops a robust HSIC-based sensitivity analysis framework for hyperparameters, addressing complex interactions and dependencies, and proposes an optimization algorithm for neural network tuning.

Findings

HSIC-based analysis quantifies hyperparameter impact effectively.

The method improves hyperparameter optimization interpretability.

Neural networks optimized with this approach perform competitively on multiple datasets.

Abstract

Tackling new machine learning problems with neural networks always means optimizing numerous hyperparameters that define their structure and strongly impact their performances. In this work, we study the use of goal-oriented sensitivity analysis, based on the Hilbert-Schmidt Independence Criterion (HSIC), for hyperparameter analysis and optimization. Hyperparameters live in spaces that are often complex and awkward. They can be of different natures (categorical, discrete, boolean, continuous), interact, and have inter-dependencies. All this makes it non-trivial to perform classical sensitivity analysis. We alleviate these difficulties to obtain a robust analysis index that is able to quantify hyperparameters' relative impact on a neural network's final error. This valuable tool allows us to better understand hyperparameters and to make hyperparameter optimization more interpretable. We illustrate the benefits of this knowledge in the context of hyperparameter optimization and derive an HSIC-based optimization algorithm that we apply on MNIST and Cifar, classical machine learning data sets, but also on the approximation of Runge function and Bateman equations solution, of interest for scientific machine learning. This method yields neural networks that are both competitive and cost-effective.