Benchmarking The Performance Of Bayesian Optimization Across Multiple Experimental Materials Science Domains PDF Download

In this thesis, we consider the analysis and extension of Bayesian hyperparameter optimization methodology to various problems related to supervised machine learning. The contributions of the thesis are attached to 1) the overestimation of the generalization accuracy of hyperparameters and models resulting from Bayesian optimization, 2) an application of Bayesian optimization to ensemble learning, and 3) the optimization of spaces with a conditional structure such as found in automatic machine learning (AutoML) problems. Generally, machine learning algorithms have some free parameters, called hyperparameters, allowing to regulate or modify these algorithms' behaviour. For the longest time, hyperparameters were tuned by hand or with exhaustive search algorithms. Recent work highlighted the conceptual advantages in optimizing hyperparameters with more rational methods, such as Bayesian optimization. Bayesian optimization is a very versatile framework for the optimization of unknown and non-derivable functions, grounded strongly in probabilistic modelling and uncertainty estimation, and we adopt it for the work in this thesis. We first briefly introduce Bayesian optimization with Gaussian processes (GP) and describe its application to hyperparameter optimization. Next, original contributions are presented on the dangers of overfitting during hyperparameter optimization, where the optimization ends up learning the validation folds. We show that there is indeed overfitting during the optimization of hyperparameters, even with cross-validation strategies, and that it can be reduced by methods such as a reshuffling of the training and validation splits at every iteration of the optimization. Another promising method is demonstrated in the use of a GP's posterior mean for the selection of final hyperparameters, rather than directly returning the model with the minimal crossvalidation error. Both suggested approaches are demonstrated to deliver significant improvements in the generalization accuracy of the final selected model on a benchmark of 118 datasets. The next contributions are provided by an application of Bayesian hyperparameter optimization for ensemble learning. Stacking methods have been exploited for some time to combine multiple classifiers in a meta classifier system. Those can be applied to the end result of a Bayesian hyperparameter optimization pipeline by keeping the best classifiers and combining them at the end. Our Bayesian ensemble optimization method consists in a modification of the Bayesian optimization pipeline to search for the best hyperparameters to use for an ensemble, which is different from optimizing hyperparameters for the performance of a single model. The approach has the advantage of not requiring the training of more models than a regular Bayesian hyperparameter optimization. Experiments show the potential of the suggested approach on three different search spaces and many datasets. The last contributions are related to the optimization of more complex hyperparameter spaces, namely spaces that contain a structure of conditionality. Conditions arise naturally in hyperparameter optimization when one defines a model with multiple components - certain hyperparameters then only need to be specified if their parent component is activated. One example of such a space is the combined algorithm selection and hyperparameter optimization, now better known as AutoML, where the objective is to choose the base model and optimize its hyperparameters. We thus highlight techniques and propose new kernels for GPs that handle structure in such spaces in a principled way. Contributions are also supported by experimental evaluation on many datasets. Overall, the thesis regroups several works directly related to Bayesian hyperparameter optimization. The thesis showcases novel ways to apply Bayesian optimization for ensemble learning, as well as methodologies to reduce overfitting or optimize more complex spaces.