An inference problem in a mismatched setting: a spin-glass 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 Sherrington-Kirkpatrick 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 solution leads to the computation of the Mean Square Error of the mismatched reconstruction. The Gaussian signal distribution case is investigated and the corresponding phase diagram is identified.

arXiv comment37 pages, 1 figure

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• Revisiting the replica trick: Competition between spin glass and conventional order
• Free energy in spin glass models with conventional order
• Hidden collective oscillations in a disordered mean-field spin model with non-reciprocal interactions
• Spherical Integrals of Sublinear Rank
• Low-rank Matrix Estimation with Inhomogeneous Noise
• Color symmetry and ferromagnetism in Potts spin glass