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On the Information Theoretic Limits of Learning Ising Models
Rashish Tandon · Karthikeyan Shanmugam · Pradeep Ravikumar · Alex Dimakis

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D

We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d. samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for Erdos-Renyi graphs in a certain dense setting.

Author Information

Rashish Tandon (The University of Texas at Austin)
Karthikeyan Shanmugam (IBM Research, NY)
Pradeep Ravikumar (Carnegie Mellon University)
Alex Dimakis (University of Texas, Austin)

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