Entropic trace estimates for log determinants

Conference item

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.

Authors: Fitzsimons, J; Granzio, D; Cutajar, K; Osborne, M; Filippone, M

• Publication status: Published
• Peer review status: Peer reviewed
• Host title: Machine Learning and Knowledge Discovery in Databases
• Journal: European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2017)
• Publication date: 2017-12-01
• Acceptance date: 2017-01-24
• DOI: 10.1007/978-3-319-71249-9_20