Pascal Germain, Researcher in Machine Learning

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At first, this master thesis presents a general PAC-Bayes theorem, from which we can easily obtain
some well-known PAC-Bayes bounds. Those bounds allow us to compute a guarantee on the risk of a
classifier from its achievements on the training set. We analyze the behavior of two PAC-Bayes
bounds and we determine peculiar characteristics of classifiers favoured by those bounds. Then, we
present a specialization of those bounds to the linear classifiers family. 

Secondly, we conceive three new machine learning algorithms based on the minimization, by conjugate
gradient descent, of various mathematical expressions of the PAC-Bayes bounds. The last algorithm
uses a part of the training set to capture a priori knowledges. One can use those algorithms to
construct majority vote classifiers as well as linear classifiers implicitly represented by the
kernel trick. Finally, an elaborated empirical study compares the three algorithms and shows that
some versions of those algorithms are competitive with both AdaBoost and SVM. 

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