Abstract
Probabilistic circuits are deep, tractable generative models capable of computing various types of exact inferences. However, their traditional specifications do not fully account for epistemic uncertainty. To address this, credal probabilistic circuits were introduced, incorporating a way to manage such uncertainty. We propose a novel framework for learning the structure and parameters of credal probabilistic circuits, leveraging the Dempster-Shafer theory of evidence. Unlike previous credal approaches, the framework handles both discrete and continuous data and allows for the use of multiple classification criteria. We conclude by presenting some preliminary experimental results, demonstrating the performance of the proposed models compared to commonly used probabilistic circuits across a range of classification tasks.
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Notes
- 1.
The leaf distributions parameterised by \(\varTheta \) may also be relaxed to imprecise models in an analogous manner, but for simplicity we will not consider this here.
- 2.
Essentially, that \(\mathcal {C}\) is ‘separately specified’ using ‘local models’ for each sum node, and that each local model is sufficiently nice, i.e. non-empty, closed, and convex.
- 3.
- 4.
It is worth noting that the criteria from Sect. 3.1 also applies to the general case of multi-class classification.
- 5.
Iterative Row-wise Quadratic Programming Evidential Clustering.
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Acknowledgements
The authors thank the support from the Eindhoven Artificial Intelligence Systems Institute and the Department of Mathematics and Computer Science of TU Eindhoven. The authors thank Erik Quaeghebeur for their valuable insights and discussions on credal PCs. Cassio de Campos thanks the support of EU European Defence Fund Project KOIOS (EDF-2021-DIGIT-R-FL-KOIOS).
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Montalván Hernández, D.R., Krak, T., de Campos, C. (2024). Dempster-Shafer Credal Probabilistic Circuits. In: Bi, Y., Jousselme, AL., Denoeux, T. (eds) Belief Functions: Theory and Applications. BELIEF 2024. Lecture Notes in Computer Science(), vol 14909. Springer, Cham. https://doi.org/10.1007/978-3-031-67977-3_4
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