Graph Learning as a Tensor Factorization Problem

Raphaël Bailly (1) , Guillaume Rabusseau (2)

1 CBMN - Chimie et Biologie des Membranes et des Nanoobjets
2 QARMA - éQuipe AppRentissage et MultimediA [Marseille]

Graphical models (CRFs, Markov Random Fields, Bayesian networks ...) are probabilistic models fairly widely used in machine learning and other areas (e.g. Ising model in statistical physics). For such models, computing a joint probability for a set of random variables relies on a Markov assumption on the dependencies between the variables. Even so, the calculation may be intractable in the general case, forcing one to consider approximation methods (MCMC, loopy belief propagation , etc.). Hence the maximum likelihood estimator is, except in very particular cases, impossible to compute. We propose a very general probabilistic model, for which parameter estimation can be obtained by tensor factorization techniques (similarly to spectral methods or methods of moments), bypassing the calculation of a joint probability thanks to algebraic results.

Domaines: Apprentissage [cs.LG]

Raphaël Bailly, Guillaume Rabusseau. Graph Learning as a Tensor Factorization Problem. 2017. ⟨hal-01519851⟩