Efficient approximation of probability distributions with k-order decomposable models.

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k>2. In this work, we propose the fractal tree family of algorithms which approximates this problem with a computational complexity of O(k2⋅n2⋅N) in the worst case, where n is the number of implied random variables and N is the size of the training set.