Entropic trace estimates for log determinants

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 elds, 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 signicant improvement on state-of-the-art alternative methods, as shown on a wide variety of matrices from the SparseSuite Matrix Collection. By taking the example of a general Markov random eld, we also demonstrate how this approach can signicantly accelerate inference in large-scale learning methods involving the log determinant.