Interpretable Encoding of Densities Using Possibilistic Logic

Probability density estimation from data is a widely studied problem. Often, the primary goal is to faithfully mimic the underlying empirical density. Having an interpretable model that allows insight into why certain predictions were made is often of secondary importance. Using logic-based formalisms, such as Markov logic, can help with interpretability, but even in Markov logic it can be difficult to gain insight into a model's behavior due to interactions between the logical formulas used to specific the model. This paper explores an alternative approach to representing densities that makes use of possibilistic logic. Concretely, we propose a novel way to transform a learned density tree into a possibilistic logic theory. An advantage of our transformation is that it permits performing both MAP and, surprisingly, marginal inference, with the converted possibilistic logic theory. At the same time, we still retain the benefits conferred by using possibilistic logic, such as the ability to compact the theory and the interpretability of the model.