On Testing for Parameters in Ising Models

Understand

We consider testing for the parameters of Ferromagnetic Ising models.

• While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high temperature regimes.
• Our matching upper bounds are adaptive over both underlying dependence graph and temperature parameter.
• Moreover our results include the nearest neighbor model on lattices, the sparse Erd\"{o}s-R\'{e}nyi random graphs, and regular rooted trees -- right up to the critical parameter in the high temperature regime.