The scalable calculation of matrix determinants has been a bottleneck to thewidespread application of many machine learning methods such as determinantalpoint processes, Gaussian processes, generalised Markov random fields, graphmodels and many others. In this work, we estimate log determinants under theframework of maximum entropy, given information in the form of momentconstraints from stochastic trace estimation. The estimates demonstrate asignificant improvement on state-of-the-art alternative methods, as shown on awide variety of UFL sparse matrices. By taking the example of a general Markovrandom field, we also demonstrate how this approach can significantlyaccelerate inference in large-scale learning methods involving the logdeterminant.
展开▼
