Joint estimation of parameters in Ising model

Ghosal, Promit; Mukherjee, Sumit

doi:10.48550/arxiv.1801.06570

Cited by 5 publications

(24 citation statements)

References 17 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section we collect results regarding inference in the classical two parameter Ising model -which follow from similar proof ideas to those pursued in the rest of this paper. For a fixed pair of real numbers (β, Ghosal and Mukherjee (2018) provide pseudolikelihood estimates of (β, h) and show joint √ n-consistency of the estimates under certain classes of Q. Here we extend our previous results to show the optimality of their results in some of these situations.…”

Section: 22supporting

confidence: 64%

“…These results provide further intuition that at criticality it might be possible to detect lower signals. (V) Our results imply minimax optimality of pseudo-likelihood based estimator of the magnetization for many examples in classical two parameter Ising models Ghosal and Mukherjee (2018).…”

supporting

confidence: 52%

“…To provide a more complete picture, we also provide a minimax lower bound for estimation of β -which matches the upper bound provided in Ghosal and Mukherjee (2018) in many cases.…”

mentioning

confidence: 92%

“…Inference of parameters in a dependent system of observations, especially of parameters in a Markov Random Field (MRF), has received a lot of attention in recent times. The main activities in this regard can be broadly classified in two categories: (i) infer the strength of dependence and individual significance of vertices given a single sample from the MRF (Bhattacharya and Ghosal and Mukherjee, 2018;Daskalakis, Dikkala and Kamath, 2018;Chatterjee, 2007), and (i) infer underlying graphical/dependence sructure among individuals given multiple i.i.d. samples from the MRF (Bresler, 2015;Anandkumar et al, 2011;Wu, Srikant and Ni, 2013;Santhanam and Wainwright, 2012).…”

mentioning

confidence: 99%

“…, where G n is the adjacency matrix of G n . Under model (1.1) we will in most parts of the paper be interested in testing In section 3 we shall also briefly discuss some results regarding the inference of both β and µ µ µ as well as its connections to some recent results in parameter estimation in Ising models (Chatterjee, 2007;Bhattacharya and Mukherjee, 2015;Ghosal and Mukherjee, 2018) .…”

mentioning

confidence: 99%

See 4 more Smart Citations

On Testing for Parameters in Ising Models

Mukherjee¹,

Ray²

2019

Preprint

View full text Add to dashboard Cite

We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high temperature regimes. Our matching upper bounds are adaptive over both underlying dependence graph and temperature parameter. Moreover our results include the nearest neighbor model on lattices, the sparse Erdös-Rényi random graphs, and regular rooted trees -right up to the critical parameter in the high temperature regime. We also provide parallel results for the entire low temperature regime in nearest neighbor model on latticeshowever in the plus boundary pure phase. Our results for the nearest neighbor model crucially depends on finite volume analogues of correlation decay property for both high and low temperature regimes -the derivation of which borrows crucial ideas from FK-percolation theory and might be of independent interest. Finally, we also derive lower bounds for estimation and testing rates in two parameter Ising models -which turn out to be optimal according to several recent results in this area.

show abstract

Section: 22supporting

confidence: 64%

supporting

confidence: 52%

“…To provide a more complete picture, we also provide a minimax lower bound for estimation of β -which matches the upper bound provided in Ghosal and Mukherjee (2018) in many cases.…”

mentioning

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

On Testing for Parameters in Ising Models

Mukherjee¹,

Ray²

2019

Preprint

View full text Add to dashboard Cite

show abstract

Regression from dependent observations

Daskalakis

Dikkala

Panageas

2019

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

View full text Add to dashboard Cite

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.

show abstract

Sub-critical Exponential random graphs: concentration of measure and some applications

Ganguly¹,

Nam²

2019

Preprint

View full text Add to dashboard Cite

The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding of ERGM, most notably in [5], through the analysis of a natural Heat-bath Glauber dynamics and in [14] and [21], via a large deviation theoretic perspective, several basic questions have remained unanswered owing to the lack of exact solvability unlike the much studied Curie-Weiss model (Ising model on the complete graph). In this paper, we establish a series of new concentration of measure results for the ERGM throughout the entire sub-critical phase, including a Poincaré inequality, Gaussian concentration for Lipschitz functions, and a central limit theorem. In addition, partial results about exponential decay of entropy along Glauber dynamics and a new proof of a quantitative bound on the W1−Wasserstein distance to Erdős-Rényi graphs, previously obtained in [43], are also presented. The arguments rely on translating refined temporal mixing properties of Glauber dynamics to static spatial mixing properties of the equilibrium measure and have the potential of being useful in proving similar functional inequalities for other Gibbsian systems, beyond the perturbative regime.

show abstract

Joint estimation of parameters in Ising model

Cited by 5 publications

References 17 publications

On Testing for Parameters in Ising Models

On Testing for Parameters in Ising Models

Regression from dependent observations

Sub-critical Exponential random graphs: concentration of measure and some applications

Contact Info

Product

Resources

About