Jean-Francis Roy

Risk upper bounds for general ensemble methods with an application to multiclass classification

This paper generalizes a pivotal result from the PAC-Bayesian literature -the C - bound - primarily designed for binary classification to the general case of ensemble methods of voters with arbitrary outputs. We provide a generic version of the C - bound , an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second statistical moments of the votes margin. On the one hand, this bound may advantageously be applied on more complex outputs than mere binary outputs, such as multiclass labels and multilabel, and on the other hand, it allows us to consider margin relaxations. We provide a specialization of the bound to multiclass classification together with empirical evidence that the presented theoretical result is tightly bound to the risk of the majority vote classifier. We also give insights as to how the proposed bound may be of use to characterize the risk of multilabel predictors.

A pseudo-boolean set covering machine

The Set Covering Machine (SCM) is a machine learning algorithm that constructs a conjunction of Boolean functions. This algorithm is motivated by the minimization of a theoretical bound. However, finding the optimal conjunction according to this bound is a combinatorial problem. The SCM approximates the solution using a greedy approach. Even though SCM seems very efficient in practice, it is unknown how it compares to the optimal solution. To answer this question, we present a novel pseudo-Boolean optimization model that encodes the minimization problem. It is the first time a Constraint Programming approach addresses the combinatorial problem related to this machine learning algorithm. Using that model and recent pseudo-Boolean solvers, we empirically show that the greedy approach is surprisingly close to the optimal.