Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits

TL;DR

This paper introduces a novel approach for probabilistic reasoning in circuits that effectively manages epistemic and aleatory uncertainties, improving confidence estimation and handling dependencies better than existing methods.

Contribution

It proposes a new framework using beta-distributed leaves in probabilistic circuits to better estimate uncertainties and relaxes the independence assumption in probabilistic reasoning.

Findings

Improved epistemic uncertainty estimation over state-of-the-art methods

Handles general probabilistic circuits with modest computational overhead

Provides an algorithm for Bayesian learning from sparse, complete observations

Abstract

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for probabilistic reasoning in order to determine the confidence (or epistemic uncertainty) in the probabilities in light of the training data. We propose an approach to overcome the independence assumption behind most of the approaches dealing with a large class of probabilistic reasoning that includes Bayesian networks as well as several instances of probabilistic logic. We provide an algorithm for Bayesian learning from sparse, albeit complete, observations, and for deriving inferences and their confidences keeping track of the dependencies between variables when they are manipulated within the unifying computational formalism provided by probabilistic circuits. Each leaf of such circuits is labelled with a beta-distributed random variable that provides us with an elegant framework for representing uncertain probabilities. We achieve better estimation of epistemic uncertainty than state-of-the-art approaches, including highly engineered ones, while being able to handle general circuits and with just a modest increase in the computational effort compared to using point probabilities.