Statistical machine learning and combinatorial optimization

In this work we apply statistical learning methods in the context of combinatorial optimization, which is understood as finding a binary string minimizing a given cost function. We first consider probability densities over binary strings and we define two different statistical criteria. Then we recast the initial problem as the problem of finding a density minimizing one of the two criteria. We restrict ourselves to densities described by a small number of parameters and solve the new problem by means of gradient techniques. This results in stochastic algorithms which iteratively update density parameters. We apply these algorithms to two families of densities, the Bernoulli model and the Gaussian model. The algorithms have been implemented and some experiments are reported.