Review for NeurIPS paper: Limits on Testing Structural Changes in Ising Models

Strengths: The problems studied in this paper are well motivated as the statistical limits on the sample complexity of functional inference over two or more graph models have not been established for a wide class of problems. This paper tries to make a contribution in that direction by considering the detection and learning of changes between Ising models. The analysis primarily uses standard information theoretic workhorses like Le Cam's method and Chi-squared based bounds with novel and non-trivial ensemble constructions to derive the results. The paper establishes theoretically that the lower bounds on the detection and learning of changes in the Ising models have approximately the same scaling behavior as that of structure learning for a wide range of regimes. This is in contrast to the claims in several existing algorithmic approaches that imply that recovery of sparse changes is possible with smaller sample complexity than structure learning of the complete graphs.