Sum-Product Network in the context of missing data
Abstract: In recent years, the interest in new Deep Learning methods has increased considerably due to their robustness and applications in many fields. However, the lack of interpretability of these models and the lack of theoretical knowledge about them raises many issues. It is in this context that sum product network models have emerged. From a mathematical point of view, SPNs can be described as Directed Acyclic Graphs. In practice, they can be seen as deep mixture models and as a consequence they can be used to represent very rich collections of distributions. The objective of this master thesis was threefold. First we formalized the concept of SPNs with proper mathematical notations, using the concept of Directed Acyclic Graphs and Bayesian Networks theory. Then we developed a new method for learning the structure of a SPN, based on K-means and Mutual Information Theory. Finally we proposed a new method for the estimation of parameters in a fixed SPN, in the context of incomplete data. Our estimation method is based on maximum likelihood methods with the EM algorithm.
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