Efficient high dimensional maximum entropy modeling via symmetric partition functions

Maximum entropy (MaxEnt) modeling is a popular choice for sequence analysis in applications such as natural language processing, where the sequences are embedded in discrete, tractably-sized spaces. We consider the problem of applying MaxEnt to distributions over paths in continuous spaces of high dimensionality— a problem for which inference is generally intractable. Our main contribution is to show that this intractability can be avoided as long as the constrained features possess a certain kind of low dimensional structure. In this case, we show that the associated partition function is symmetric and that this symmetry can be exploited to compute the partition function efficiently in a compressed form. Empirical results are given showing an application of our method to learning models of high-dimensional human motion capture data.