Learning Graphical Models for Parameter Tuning

The information provided is the sole responsibility of the authors and does not necessarily reflect the opinion of the members of IRIDIA. The authors take full responsibility for any copyright breaches that may result from publication of this paper in the IRIDIA – Technical Report Series. IRIDIA is not responsible for any use that might be made of data appearing in this publication. Abstract We introduce a new method for deciding the values of categorical and numerical parameters of algorithms for optimization. The method is based on graphical models and Bayesian learning. Each parameter is modelled by a node of the network and parameter dependencies by arcs. Nodes have associated a local probability distribution. Both discrete and continuous variables can be treated, assuming Gaussian linear regression for the latter. Learning can be achieved by a combination of importance sampling techniques and Bayesian calculus. We describe the method and review the main elements of the theory underlying its components. We then present its application on simple cases and compare its performance with methods from the literature. The results show that the method achieves comparable results to the state-of-the-art while being perhaps more principled and having interesting features. Among them the flexibility to handle different tuning scenarios, the possibility to include prior knowledge and the output of relevant information. We make available in form of an R package an implementation of the method that works also in parallel environments.