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Project: Battle of the credal networks: strong independence or forward irrelevance?


Bayesian networks are a popular model in AI. Credal networks are a robust version of Bayesian networks created by replacing the conditional probability mass functions describing the nodes by conditional credal sets (sets of probability mass functions).

Next to their nodes, Bayesian networks are defined by their network structure. This structure represents conditional independence relationships between the nodes. The same holds for credal networks. However, in the theory of imprecise probability, unlike in classical probability theory, there is no unique notion of independence. This gives rise to different possible definitions of credal networks. The classical approach to credal networks is based on the notion of strong independence. A more recent, alternative approach is based on the notion of epistemic irrelevance, an asymmetric notion of independence.

There exist theoretical results that compare these different approaches (e.g., in terms of computational complexity), but little has been done in terms of practical tests, such as benchmarking. Such a practical comparison would be valuable to the body of work on credal networks.

There exist various implementations of credal networks under strong independence, but as far as I know, there is no public implementation of credal networks under epistemic irrelevance. It would be an important step forward to have such an implementation.

Requirements & Activities

This project will require you to learn about a field you are not yet familiar with (imprecise probability theory, credal networks); this requires a strong mathematical background. It also requires you to be able to make a proof-of-concept implementation of a nontrivial algorithm; this means you must have some experience with this kind of activity as a programmer. Next to that, other activities that may be part of this project are testing, comparison, and benchmarking (including setting up a benchmark).

Erik Quaeghebeur
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