Probabilistic Circuits for Preferences (Ba/Ma)

Topic for a bachelor/master's thesis

Short Description:

Probabilistic circuits represent uncertainty through probability distributions in a way that is both expressive and still computationally tractable by imposing specific structural properties [1]. More specifically, the probability distribution is modelled as a computational graph specified via recursive mixtures (sum units) and factorizations (product units) of simpler distributions (input unit), e.g., parametric distributions such as Bernoullis or Gaussians. While this modelling approach is already well suited for learning scenarios where the target probability distribution (i.e., the distribution to be modelled) is numerical in nature and has been studied intensively, not much has yet been done for probability distributions on domains with a complex structure. An important example is distributions over the symmetric group modelling preference relations over specific objects in a probabilistic way [2]. The goal of this thesis is to investigate the potential of probabilistic circuits for modelling probability distributions over preferences. In particular, the advantages of such preference-based probabilistic circuits over classical parametric preference probability distributions for real data in terms of goodness of fit are to be investigated. Another goal of the thesis is to check whether some of the common statistical preference probability distributions can be specified via a (preference-based) probabilistic circuit.

Prerequisites

Good background in machine learning, experimental design and empirical studies, programming skills.

Contact

Dr. Viktor Bengs or Prof. Eyke Hüllermeier

References

• [1] Y. Choi, A. Vergari, G. Van den Broeck. Probabilistic circuits: A unifying framework for tractable probabilistic models. Technical report, 2020.
• [2] M. Alvo, L. H. Philip. Statistical methods for ranking data. Vol. 1341. New York: Springer, 2014.