This thesis examines Bayesian inference in neural networks with Markov chain Monte Carlo sampling for performing regression and classification, and how this is different from using non-Bayesian feedforward neural networks. Initially basic machine learning theory for supervised learning algorithms is outlined. This theory is subsequently used for examining how neural networks work, and how they can be trained and regularized. This provides the fundamentals for introducing Bayesian inference and how it can be used for neural networks. The Markov chain Monte Carlo based Bayesian neural networks will be the focal point for this analysis, and we examine the most popular sampling methods for these, while only covering the fundamentals on the choice of prior distributions. Through implementation of different neural networks and Bayesian neural networks we illustrate and evaluate how these perform when predicting house prices using regression and predicting probabilities for default of credit card clients for binary classification.
|Uddannelser||Cand.merc.mat Erhvervsøkonomi og Matematik, (Kandidatuddannelse) Afsluttende afhandling|