Electronic Journal of Statistics

An oracle approach for interaction neighborhood estimation in random fields

Matthieu Lerasle and Daniel Y. Takahashi

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Abstract

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points.

We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

Article information

Source
Electron. J. Statist. Volume 5 (2011), 534-571.

Dates
First available in Project Euclid: 15 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1308143122

Digital Object Identifier
doi:10.1214/11-EJS618

Mathematical Reviews number (MathSciNet)
MR2813554

Zentralblatt MATH identifier
1274.62641

Subjects
Primary: 62M40: Random fields; image analysis
Secondary: 62M45: Neural nets and related approaches

Keywords
Ising model model selection computationally efficient algorithm

Citation

Lerasle, Matthieu; Takahashi, Daniel Y. An oracle approach for interaction neighborhood estimation in random fields. Electron. J. Statist. 5 (2011), 534--571. doi:10.1214/11-EJS618. https://projecteuclid.org/euclid.ejs/1308143122.


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