  The scalable calculation of matrix determinants has been a bottleneck to the
widespread application of many machine learning methods such as determinantal
point processes, Gaussian processes, generalised Markov random fields, graph
models and many others. In this work, we estimate log determinants under the
framework of maximum entropy, given information in the form of moment
constraints from stochastic trace estimation. The estimates demonstrate a
significant improvement on state-of-the-art alternative methods, as shown on a
wide variety of UFL sparse matrices. By taking the example of a general Markov
random field, we also demonstrate how this approach can significantly
accelerate inference in large-scale learning methods involving the log
determinant.
