Hamilton–Jacobi equations for finite-rank matrix inference
Jean-Christophe Mourrat
Abstract
We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in Mourrat (2018) which consists in identifying a suitable Hamilton–Jacobi equation satisfied by the limit free energy. We simplify the approach of Mourrat (2018) using a notion of weak solution of the Hamilton–Jacobi equation which is more convenient to work with and is applicable whenever the nonlinearity in the equation is convex.
Topics & Concepts
Hamilton–Jacobi equationMathematicsLimit (mathematics)Rank (graph theory)Applied mathematicsInferenceMatrix (chemical analysis)Regular polygonNonlinear systemJacobi methodMathematical analysisComputer scienceCombinatoricsGeometryPhysicsArtificial intelligenceQuantum mechanicsMaterials scienceComposite materialSparse and Compressive Sensing TechniquesBlind Source Separation TechniquesMarkov Chains and Monte Carlo Methods