Transitions in Bayesian model selection problems: Network-based recommender system and symbolic regression

Identifier:  TDX:3296

Handle: https://hdl.handle.net/20.500.11797/TDX3296

Authors:  Fajardo Fontiveros, Oscar

Abstract:
In this thesis we have done a study of the Bayesian inference process applied to model selection problems. These problems consist of a set of models and observed data, looking at which model is the most plausible. Using Bayes theorem in such problems, it allows us not only to value how a model fits in with the data with the likelihood, but also to consider the information that we think can be true a priori thanks to the prior. This makes that the models that we get from these processes can be data based, based in the hypotheses we have (prior), or on both. The aim of this thesis is to see how the different types of models found affect us in the predictions, so we have decided to focus on two problems: the problem of the recommender system and the problem of symbolic regression. The recommender system is a problem with predicting the preferences of a given user who we already know. In this case we have used a Bayesian method and have set as a prior to users with similar attributes having similar tastes. In the case of symbolic regression, the problem consists in finding the best mathematical expression from all the space of mathematical expressions. Here we have used the Bayesian machine scientists that he uses Bayes' theorem where its prior looks for mathematical expressions that are like those in the Wikipedia. As a result, we have seen that in different situations, the prior and data can or cannot help making predictions by giving rise to transitions in accuracy (in the case of the recommender) and detectability (in the case of symbolic regression).