  Probabilistic inference is a fundamental task in modern machine learning.
Recent advances in tensor network (TN) contraction algorithms have enabled the
development of better exact inference methods. However, many common inference
tasks in probabilistic graphical models (PGMs) still lack corresponding
TN-based adaptations. In this work, we advance the connection between PGMs and
TNs by formulating and implementing tensor-based solutions for the following
inference tasks: (i) computing the partition function, (ii) computing the
marginal probability of sets of variables in the model, (iii) determining the
most likely assignment to a set of variables, and (iv) the same as (iii) but
after having marginalized a different set of variables. We also present a
generalized method for generating samples from a learned probability
distribution. Our work is motivated by recent technical advances in the fields
of quantum circuit simulation, quantum many-body physics, and statistical
physics. Through an experimental evaluation, we demonstrate that the
integration of these quantum technologies with a series of algorithms
introduced in this study significantly improves the effectiveness of existing
methods for solving probabilistic inference tasks.
