A Unified Approach to Learning Ising Models: Beyond Independence and
  Bounded Width
Jason Gaitonde Elchanan Mossel
We revisit the problem of efficiently learning the underlying parameters of
Ising models from data. Current algorithmic approaches achieve essentially
optimal sample complexity when given i.i.d. samples from the stationary measure
and the underlying model satisfies "width" bounds on the total $\ell_1$
interaction involving each node. We show that a simple existing approach based
on node-wise logistic regression provably succeeds at recovering the underlying
model in several new settings where these assumptions are violated:
  (1) Given dynamically generated data from a wide variety of local Markov
chains, like block or round-robin dynamics, logistic regression recovers the
parameters with optimal sample complexity up to $\log\log n$ factors. This
generalizes the specialized algorithm of Bresler, Gamarnik, and Shah [IEEE
Trans. Inf. Theory'18] for structure recovery in bounded degree graphs from
Glauber dynamics.
  (2) For the Sherrington-Kirkpatrick model of spin glasses, given
$\mathsf{poly}(n)$ independent samples, logistic regression recovers the
parameters in most of the known high-temperature regime via a simple reduction
to weaker structural properties of the measure. This improves on recent work of
Anari, Jain, Koehler, Pham, and Vuong [ArXiv'23] which gives distribution
learning at higher temperature.
  (3) As a simple byproduct of our techniques, logistic regression achieves an
exponential improvement in learning from samples in the M-regime of data
considered by Dutt, Lokhov, Vuffray, and Misra [ICML'21] as well as novel
guarantees for learning from the adversarial Glauber dynamics of Chin, Moitra,
Mossel, and Sandon [ArXiv'23].
  Our approach thus significantly generalizes the elegant analysis of Wu,
Sanghavi, and Dimakis [Neurips'19] without any algorithmic modification.