An inference problem in a mismatched setting: a spinglass model with Mattis interaction
Abstract
The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a SherringtonKirkpatrick model with added Mattis interaction. The exact solution of the model with Ising spins is rigorously proved to be given by a variational principle on two order parameters, the Parisi overlap distribution and the Mattis magnetization. The latter is identified by an ordinary variational principle and turns out to concentrate in the thermodynamic limit. The Gaussian signal distribution case is investigated and the corresponding phase diagram is identified.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.11689
 Bibcode:
 2021arXiv210711689C
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Mathematical Physics;
 68T07;
 82XX;
 82D30
 EPrint:
 32 pages, 1 figure