Property testing in high-dimensional Ising models
| Autor: | Han Liu, Matey Neykov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Property testing Discrete mathematics Property (philosophy) correlation tests two-point function bounds Clique (graph theory) Minimax 01 natural sciences Upper and lower bounds 010104 statistics & probability Ising models Dobrushin’s comparison theorem minimax testing Graph (abstract data type) Ising model 62H15 antiferromagnetic Curie–Weiss detection 62F03 0101 mathematics Statistics Probability and Uncertainty Graph property Mathematics |
| Zdroj: | Ann. Statist. 47, no. 5 (2019), 2472-2503 |
| Popis: | This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can be statistically and/or computationally more efficient than graph recovery based algorithms. Understanding the statistical complexity of property testing requires the distinction of ferromagnetic (i.e., positive interactions only) and general Ising models. Using combinatorial constructs such as graph packing and strong monotonicity, we characterize how target properties affect the corresponding minimax upper and lower bounds within the realm of ferromagnets. On the other hand, by studying the detection of an antiferromagnetic (i.e., negative interactions only) Curie–Weiss model buried in Rademacher noise, we show that property testing is strictly more challenging over general Ising models. In terms of methodological development, we propose two types of correlation based tests: computationally efficient screening for ferromagnets, and score type tests for general models, including a fast cycle presence test. Our correlation screening tests match the information-theoretic bounds for property testing in ferromagnets in certain regimes. |
| Databáze: | OpenAIRE |
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