Statistical inference of finite-rank tensors
Hongbin Chen, Jean-Christophe Mourrat, Jiaming Xia
Abstract
We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach consists of showing first that the limit free energy must be the viscosity solution to a certain Hamilton–Jacobi equation.
Topics & Concepts
Tensor (intrinsic definition)Rank (graph theory)Limit (mathematics)Statistical inferenceInferenceMathematicsApplied mathematicsEnergy (signal processing)Statistical physicsPure mathematicsMathematical analysisPhysicsCombinatoricsComputer scienceStatisticsArtificial intelligenceTensor decomposition and applicationsAdvanced Neuroimaging Techniques and ApplicationsMarkov Chains and Monte Carlo Methods