Learning parameters of Gibbs random fields using unconditional and conditional MLE of potentials

Abstract

Two parameter learning schemes for Gibbs random field image models with translation invariant multiple pairwise pixel interactions are discussed. The schemes allow to estimate both the interaction structure and strengths (Gibbs potentials) from a given training sample. The first scheme is based on the unconditional MLE of the potentials. The estimates are specified in an implicit form and can be obtained in three steps: (i) an analytic first approximation of the potentials for a big many possible neighbours, (ii) a search for most characteristic neighbours, and (iii) a stochastic approximation refinement of the estimates for a chosen set of neighbours. The second scheme uses the conditional MLE suggesting that the training sample has the least upper bound (top rank) in its total Gibbs energy within the parent population. This scheme allows to deduce an explicit, to scaling factors, analytic form of the potentials. Then only the scaling factors have to be learnt using their MLE in a like three-step manner. The conditional MLE of the potentials seems to be close to the unconditional ones and extends capabilities of the Gibbs image models.