Probabilistic Inference in the Era of Tensor Networks and Differential Programming
This work addresses probabilistic inference problems for machine learning practitioners by advancing tensor network methods, though it appears incremental as it builds on existing tensor network and quantum technology advances.
The paper tackled the lack of tensor network-based adaptations for common probabilistic inference tasks in graphical models by formulating and implementing tensor-based solutions for tasks like computing partition functions and marginals, and demonstrated that integrating quantum technologies with these algorithms significantly improves the effectiveness of existing methods.
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.