Younes L. : Estimation and annealing for Gibbsian fields. Annales de l'Institut Henri Poincar'e, 24(2), 269-294,. 1992  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... This method has given good results, even in more complex situations where the form of the noise corresponding to each class is not known, 14, 15] or still in hierarchical models, 18, 20] To apply ICE, one needs an estimator from complete data (X; Y ) and the choice of the stochastic gradient [8], with the difference that it would be applied to (X; Y ) instead of X, for this estimator could be a good one. In fact, the use of the stochastic gradient with ICE has already given good results in the context of fuzzy Markov random fields [17] which is more complex that the classical context ....

Younes L. : Estimation and annealing for Gibbsian fields. Annales de l'Institut Henri Poincar'e, 24(2), 269-294,. 1992

....relative strengths of a great many possible pairwise interactions and recover most characteristic ones to represent a given texture type. Then, the desired MLE of the potentials for the chosen families C a is refined by a stochastic approximation technique similar to the one introduced by YOUNES [1988]. As shown by BARNDORFF NIELSEN ( 1978] the GPD in (4) is the regular exponential family distribution with minimal canonical parameter V and minimal sufficient statistic H cn (g) if and only if the following conditions are both satisfied: i) the vectors V are affinely independent and (ii) the ....

....at the unique maximum point of the likelihood function. The samples g having a given GPD can be generated by well known pixel wise stochastic relaxation techniques (METRO POLIS et al. 1953] CROSS and JAIN [1983] GEMAN and GEMAN [1984] CHELLAPPA and JAIN [1993] This makes possible (YOUNES [1988]) to find the desired MLE by solving the system (26) with a stochastic approximation starting from a first approximation of the potentials. The Analytic First Approximation of the MLEV is derived in (GIMEL FARB [1996a] by expanding the log likelihood function into a truncated Taylor s series ....

[Article contains additional citation context not shown here]

Younes, L.: Estimation and annealing for Gibbsian fields. Annales de l'Institut Henri Poincare 24:2 (1988) 269-294

....needed for almost sure convergence (for example in the Robbins Monro case) is P n fl ff n 1 for some ff 1. But, in the present case, one can exhibit situations (cf. paragraph 6.3) for which divergence may occur even with fl n = a=n, if the constant a is too large. In fact, it is shown in [21] (in a special context) that a sufficient condition for almost sure convergence is fl n = a=n with a small enough. An important ingredient for this result was the fact that f( was bounded, which yielded useful a priori bounds on the norm of n . However since these bounds were a priori, ....

....n = a=n with a small enough. An important ingredient for this result was the fact that f( was bounded, which yielded useful a priori bounds on the norm of n . However since these bounds were a priori, they necessarily were very rough, and the value of the constant a which was provided in [21] was too small to be used in practice. In fact, good practical results have been obtained with larger values of a. Note that almost sure convergence results are often given under the additional hypothesis of boundedness of the sequence ( n ) In practice, it is always possible to use a ....

[Article contains additional citation context not shown here]

L. Younes : Estimation and annealing for Gibbsian fields. Annales de l'Institut Henri Poincar'e, vol 2.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC