Gaussian Sum-Product Networks Learning in the Presence of Interval Censored Data

Abstract

Sum-Product Networks (SPNs) can be seen as deep mixture models that have demonstrated efficient and tractable inference properties. In this context, graph and parameters learning have been deeply studied but the standard approaches do not apply to interval censored data. In this paper, we derive an approach for learning SPN parameters based on maximum likelihood using Expectation-Maximization (EM) in the context of interval censored data. Assuming the graph structure known, our algorithm makes possible to learn Gaussian leaves parameters of SPNs with right, left or interval censored data. We show that our EM algorithm for incomplete data outperforms other strategies such as the midpoint for censored intervals or dropping incomplete values.