Testing Ising Models

Daskalakis, Constantinos; Dikkala, Nishanth; Kamath, Gautam

doi:10.1137/1.9781611975031.130

Cited by 15 publications

(14 citation statements)

References 17 publications

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“…In the case of logistic regression, there has been a lot of work showing that under certain hightemperature conditions on the Ising model (which are similar to the assumptions we make in our paper), one can perform many statistical tasks such as learning, testing and sampling of Ising models efficiently [28,14,13,15,25,17].…”

Section: Modeling Dependencementioning

confidence: 71%

Regression from dependent observations

Daskalakis

Dikkala

Panageas

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates.The assumption that the response variables are independent is, however, too strong. In many applications, these responses are collected on nodes of a network, or some spatial or temporal domain, and are dependent. Examples abound in financial and meteorological applications, and dependencies naturally arise in social networks through peer effects. Regression with dependent responses has thus received a lot of attention in the Statistics and Economics literature, but there are no strong consistency results unless multiple independent samples of the vectors of dependent responses can be collected from these models. We present computationally and statistically efficient methods for linear and logistic regression models when the response variables are dependent on a network. Given one sample from a networked linear or logistic regression model and under mild assumptions, we prove strong consistency results for recovering the vector of coefficients and the strength of the dependencies, recovering the rates of standard regression under independent observations. We use projected gradient descent on the negative log-likelihood, or negative log-pseudolikelihood, and establish their strong convexity and consistency using concentration of measure for dependent random variables.

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Section: Modeling Dependencementioning

confidence: 71%

Regression from dependent observations

Daskalakis

Dikkala

Panageas

2019

Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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“…Since lower bounds of [ADK15] show that distribution testing suffers from the curse of dimensionality, further structural assumptions must be made if one wishes to test multivariate distributions. This "highdimensional frontier" has also been studied on graphical models by [DDK18] and [CDKS17] (for Ising models and Bayesian networks, respectively).…”

Section: Related Workmentioning

confidence: 99%

Which Distribution Distances are Sublinearly Testable?

Daskalakis¹,

Kamath²,

Wright³

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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Given samples from an unknown distribution p and a description of a distribution q, are p and q close or far? This question of "identity testing" has received significant attention in the case of testing whether p and q are equal or far in total variation distance. However, in recent work [VV11a, ADK15, DP17], the following questions have been been critical to solving problems at the frontiers of distribution testing:• Alternative Distances: Can we test whether p and q are far in other distances, say Hellinger?• Tolerance: Can we test when p and q are close, rather than equal? And if so, close in which distances?Motivated by these questions, we characterize the complexity of distribution testing under a variety of distances, including total variation, 2 , Hellinger, Kullback-Leibler, and χ 2 . For each pair of distances d 1 and d 2 , we study the complexity of testing if p and q are close in d 1 versus far in d 2 , with a focus on identifying which problems allow strongly sublinear testers (i.e., those with complexity O(n 1−γ ) for some γ > 0 where n is the size of the support of the distributions p and q). We provide matching upper and lower bounds for each case. We also study these questions in the case where we only have samples from q (equivalence testing), showing qualitative differences from identity testing in terms of when tolerance can be achieved. Our algorithms fall into the classical paradigm of χ 2 -statistics, but require crucial changes to handle the challenges introduced by each distance we consider. Finally, we survey other recent results in an attempt to serve as a reference for the complexity of various distribution testing problems.

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“…The detection problem we consider is in part inspired by the works Addario-Berry et al (2010); Arias-Castro et al (2012, 2015b Berthet et al (2016); Mukherjee et al (2016). An interesting paper on testing goodness-of-fit in Ising models by Daskalakis et al (2018), uses tests based on minimal pairwise correlations which are similar in spirit to some of the tests we consider. In a related work Gheissari et al (2017) demonstrated that sums of pairwise correlations concentrate for general Ising models.…”

Section: Connectivitymentioning

confidence: 99%

Property testing in high-dimensional Ising models

Neykov¹,

Liu²

2019

Ann. Statist.

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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.

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Testing Ising Models

Cited by 15 publications

References 17 publications

Regression from dependent observations

Regression from dependent observations

Which Distribution Distances are Sublinearly Testable?

Property testing in high-dimensional Ising models

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