Evolutionary computation in hierarchical model discovery

Abstract

Despite its continuous growth, probabilistic programming is still a great unknown among scientists, specially those whose research areas involve sampling dis- tributions, statistical modeling or statistical inference. This Master Thesis provides, on one hand, a novel procedure to learn and construct probabilistic programs that serve to model and sample probabilistic distributions. These probabilistic programs are based on grammatical rules through the potential given by evolutionary algorithms, concretely, the genetic programming approach. This technique provides a reliable back- end methodology that has served us to evolve a wide variety of program specifications and leading us, in a final step, to an optimal set of operations between distributions. These are visualized as a hierarchy, able to represent accurately any 1-dimensional ten- sor. On the other hand, the implemented framework offers the possibility of improving these models by calculating the best set of parameters for these learned models, with numerical optimization or distribution approximation methods, such as Markov Chain Monte Carlo techniques.