Hamilton-Jacobi equations for nonsymmetric matrix inference

Understand

We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix.

• The matrix is expressed as the outer product of two vectors, not necessarily independent.
• The distributions of the two vectors are only assumed to have scaled bounded supports.
• We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the convergence rate of a simpler free energy in a decoupled system.