Mixed integer programming formulation of unsupervised learning

A central open question in machine learning is the effective handling of unlabeled data [1, 2]. The construction of balanced representative datasets for supervised machine learning for the most part still requires a very close and time consuming human direction, so the development of efficient learning from data algorithms in an unsupervised fashion is a very active area of research [1, 2]. A general framework to deal with unlabeled data is the Boltzmann machine paradigm, in which is attempted to learn a probability distribution for the patterns in the data without any previous identification of input and output variables. In its most general setups however, the training of Blotzmann machines is computationally intractable [2, 3, 4]. In this contribution is established a relation, which to the best of my knowledge was previously unknown, between Mixed Integer Programing (MIP) and the full Boltzmann machine in binary variables. Is hoped that this novel formulation opens the road to more efficient learning algorithms by taking advantage of the great variety of techniques available for MIP. 1