This internal project aims at studying and devising new bounds for the computational complexity of inferences in probabilistic circuits and their robust/credal counterpart, including approximation results and fixed-parameter tractability. It requires mathematical interest and good knowledge of theory of computation. This is a theoretical work and results are mostly obtained in the form of hardness proofs, but often (theoretical or practical) algorithms are devised to show the quality of approximation results.
Relevant literature:
https://www.sciencedirect.com/science/article/pii/S0888613X17307223
http://proceedings.mlr.press/v138/campos20a/campos20a.pdf
https://arxiv.org/pdf/1703.06045
http://proceedings.mlr.press/v62/mau%C3%A117a/mau%C3%A117a.pdf