A statistical physics approach for the analysis of machine learning algorithms on real data
We combine the replica approach of statistical physics with a variational technique to make it applicable for the analysis of machine learning algorithms on real data. The method is applied to Gaussian process models and their relative, the support vector machine. We discuss the quality of our theoretical results in comparison to experiments. As a key result, we apply our theory on real world benchmark data and show its potential for practical applications by deriving approximate expressions for data averaged performance measures which hold for general data distributions and allow us to optimize the performance of the learning algorithm.