On the Difficulty of Selecting Ising Models with Approximate Recovery

Scarlett, Jonathan; Cevher, Volkan

doi:10.1109/tsipn.2016.2596439

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…As such, the present paper is a significant extension and generalization of this perspective. Our bounds further improve the approximate recovery lower bounds of [SC16].…”

Section: Related Workmentioning

confidence: 64%

Limits on Testing Structural Changes in Ising Models

Gangrade,

Nazer,

Saligrama

2020

Preprint

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We present novel information-theoretic limits on detecting sparse changes in Ising models, a problem that arises in many applications where network changes can occur due to some external stimuli. We show that the sample complexity for detecting sparse changes, in a minimax sense, is no better than learning the entire model even in settings with local sparsity. This is a surprising fact in light of prior work rooted in sparse recovery methods, which suggest that sample complexity in this context scales only with the number of network changes. To shed light on when change detection is easier than structured learning, we consider testing of edge deletion in forest-structured graphs, and high-temperature ferromagnets as case studies. We show for these that testing of small changes is similarly hard, but testing of large changes is well-separated from structure learning. These results imply that testing of graphical models may not be amenable to concepts such as restricted strong convexity leveraged for sparsity pattern recovery, and algorithm development instead should be directed towards detection of large changes.

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“…As such, the present paper is a significant extension and generalization of this perspective. Our bounds further improve the approximate recovery lower bounds of [SC16].…”

Section: Related Workmentioning

confidence: 64%

Limits on Testing Structural Changes in Ising Models

Gangrade,

Nazer,

Saligrama

2020

Preprint

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“…The bounded correlation property P2 then implies that atanh(ρ min ) ≤ |θ i,j | ≤ atanh(ρ max ). Note that although property P1 is a common assumption that simplifies the presentation (Tandon et al, 2014;Scarlett & Cevher, 2016;Nikolakakis et al, 2019a;Bresler & Karzand, 2020), the extension of our results to the case where the marginals are not necessarily uniform can be readily obtained by following the approach outlined by Katiyar et al (2020).…”

Section: System Modelmentioning

confidence: 86%

“…Properties P1 and P2 are common assumptions in the literature on learning Ising models (Tandon et al, 2014;Scarlett & Cevher, 2016;Nikolakakis et al, 2019a;Bresler & Karzand, 2020), while P3 ensures that no node is independent of any other node due to noise (Katiyar et al, 2020). For an Ising model with zero external field, the joint distribution given by (1) can be expressed as (Bresler & Karzand, 2020)…”

Section: System Modelmentioning

confidence: 99%

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SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples

Tandon¹,

Yuan²,

Tan³

2021

Preprint

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We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise with unknown statistics. Katiyar et al. (2020) showed that although the exact tree structure cannot be recovered, one can recover a partial tree structure; that is, a structure belonging to the equivalence class containing the true tree. This paper presents a systematic improvement of Katiyar et al. (2020). First, we present a novel impossibility result by deriving a bound on the necessary number of samples for partial recovery. Second, we derive a significantly improved sample complexity result in which the dependence on the minimum correlation ρ min is ρ −8 min instead of ρ −24 min . Finally, we propose Symmetrized Geometric Averaging (SGA), a more statistically robust algorithm for partial tree recovery. We provide error exponent analyses and extensive numerical results on a variety of trees to show that the sample complexity of SGA is significantly better than the algorithm of Katiyar et al. (2020). SGA can be readily extended to Gaussian models and is shown via numerical experiments to be similarly superior.

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“…Structure learning of the edge set in the Ising model is a well-studied problem in the statistics literature. Considerable attention has been given to finding theoretic information bounds for learning Ising graph structures (Scarlett and Cevher, 2016;Tandon et al, 2014;Santhanam and Wainwright, 2012). Table 1 in Scarlett and Cevher (2016) gives a useful summary of the graphical assumptions for which these information theoretic bounds are known.…”

Section: Introductionmentioning

confidence: 99%

An Expectation Maximization Algorithm for High-Dimensional Model Selection for the Ising Model with Misclassified States

Sinclair¹,

Hooker²

2017

Preprint

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We propose the misclassified Ising Model; a framework for analyzing dependent binary data where the binary state is susceptible to error. We extend the theoretical results of the model selection method presented in Ravikumar et al. (2010) to show that the method will still correctly identify edges in the underlying graphical model under suitable misclassification settings. With knowledge of the misclassification process, an expectation maximization algorithm is developed that accounts for misclassification during model selection. We illustrate the increase of performance of the proposed expectation maximization algorithm with simulated data, and using data from a functional magnetic resonance imaging analysis.

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On the Difficulty of Selecting Ising Models with Approximate Recovery

Cited by 7 publications

References 27 publications

Limits on Testing Structural Changes in Ising Models

Limits on Testing Structural Changes in Ising Models

SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples

An Expectation Maximization Algorithm for High-Dimensional Model Selection for the Ising Model with Misclassified States

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