# Learning Credal Sum-Product Networks

## TL;DR

This paper introduces methods for learning credal sum-product networks, extending tractable probabilistic models to handle imprecise probabilities, especially in scenarios with incomplete data, enhancing robustness and confidence quantification.

## Contribution

It proposes a novel approach to learn credal sum-product networks, generalizing tractable learning techniques for imprecise probabilistic representations.

## Key findings

- Credal sum-product networks can effectively model uncertainty with incomplete data.
- The proposed methods enable polynomial-time inference in credal networks.
- Enhanced robustness in probabilistic reasoning under data uncertainty.

## Abstract

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying. By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still admitting a range of probabilistic queries to be computable in time polynomial in the network size. While the progress is impressive, numerous data sources are incomplete, and in the presence of missing data, structure learning methods nonetheless revert to single distributions without characterizing the loss in confidence. In recent work, credal sum-product networks, an imprecise extension of sum-product networks, were proposed to capture this robustness angle. In this work, we are interested in how such representations can be learnt and thus study how the computational machinery underlying tractable learning and inference can be generalized for imprecise probabilities.