An inference problem in a mismatched setting: a spin-glass model with Mattis interaction

The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as Sherrington-Kirkpatrick added Mattis interaction. exact solution of Ising spins rigorously proved to be given by variational principle on two order parameters, Parisi overlap distribution and magnetization. latter identified an ordinary turns out concentrate thermodynamic limit. leads computation Mean Square Error reconstruction. Gaussian signal case investigated corresponding phase diagram identified.