On the Information Theoretic Limits of Learning Ising Models

2014/11/05 by Karthikeyan Shanmugam, Shanmugam, Karthikeyan, Rashish Tandon +5
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Neural Networks and Applications #cs.LG

paper · pdf · doi:10.48550/arxiv.1411.1434

21 pages; to appear in NIPS 2014

openalex publication_date 2014/11/05 · arxiv created 2014/12/05 · arxiv updated 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Erdős-Rényi graphs in a certain dense setting.

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