# Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits

arXiv: https://arxiv.org/abs/2102.10865 · HTML: https://mlsanity.com/paper/2102.10865/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 72 references that are in the map.
- First posted on arXiv 22 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [A Unified Approach for Learning the Parameters of Sum-Product Networks](https://mlsanity.com/paper/1601.00318/) (2016)
- [Bayesian Learning of Sum-Product Networks](https://mlsanity.com/paper/1905.10884/) (2019)
- [Automatic Bayesian Density Analysis](https://mlsanity.com/paper/1807.09306/) (2018)
- [Approximate Knowledge Compilation by Online Collapsed Importance Sampling](https://mlsanity.com/paper/1805.12565/) (2018)
- [Solving #SAT and Bayesian Inference with Backtracking Search](https://mlsanity.com/paper/1401.3458/) (2014)
- [Probabilistic Logic Programming with Beta-Distributed Random Variables](https://mlsanity.com/paper/1809.07888/) (2018)

## Built on by (most cited first, 9 of 9)

- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Probabilistic Circuits That Know What They Don't Know](https://mlsanity.com/paper/2302.06544/) (2023)
- [Accurate Passive Radar via an Uncertainty-Aware Fusion of Wi-Fi Sensing Data](https://mlsanity.com/paper/2407.04733/) (2024)
- [Neuro-Symbolic Fusion of Wi-Fi Sensing Data for Passive Radar with Inter-Modal Knowledge Transfer](https://mlsanity.com/paper/2407.04734/) (2024)
- [Assessing the Robustness of Intelligence-Driven Reinforcement Learning](https://mlsanity.com/paper/2311.09027/) (2023)
- [Uncertain Bayesian Networks: Learning from Incomplete Data](https://mlsanity.com/paper/2208.04221/) (2022)
- [SOLBP: Second-Order Loopy Belief Propagation for Inference in Uncertain Bayesian Networks](https://mlsanity.com/paper/2208.07368/) (2022)
- [Research Note on Uncertain Probabilities and Abstract Argumentation](https://mlsanity.com/paper/2208.10932/) (2022)
- [Methodological Insights into Structural Causal Modelling and Uncertainty-Aware Forecasting for Economic Indicators](https://mlsanity.com/paper/2509.07036/) (2025)

## Abstract (arXiv)

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.