Goal-Oriented Sensitivity Analysis of Hyperparameters in Deep Learning
This work addresses the challenge of interpretable hyperparameter optimization for machine learning practitioners, but it is incremental as it builds on existing sensitivity analysis techniques.
The authors tackled the problem of hyperparameter optimization in deep learning by applying goal-oriented sensitivity analysis based on the Hilbert-Schmidt Independence Criterion (HSIC) to quantify hyperparameters' impact on neural network error, resulting in a method that yields competitive and cost-effective networks on datasets like MNIST and Cifar.
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.