Learning in Gibbsian fields: how accurate and how fast can it be?

In this article, we present a unified framework for learning Gibbs models from training images. We identify two key factors that determine the accuracy and speed of learning Gibbs models: (1). Fisher information, and (2). The accuracy of Monte Carlo estimate for partition functions. We propose three new learning algorithms under the unified framework. (I). The maximum partial likelihood estimator. (II). The maximum patch likelihood estimator, and (III). The maximum satellite likelihood estimator. The first two algorithms can speed up the minimax entropy algorithm by about 2D times without losing much accuracy. The third one makes use of a set of known Gibbs models as references-dubbed "satellites" and can approximately estimate the minimax entropy model in the speed of 10 seconds.