Entropic trace estimates for log determinants

Fitzsimons, Jack; Granziol, Diego; Cutajar, Kurt; Osborne, Michael; Filippone, Maurizio; Roberts, Stephen
ECML/PKDD 2017, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, September 18-22, 2017, Skopje, Macedonia


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.

Type:
Conference
City:
Skopje
Date:
2017-09-18
Department:
Data Science
Eurecom Ref:
5265

PERMALINK : https://www.eurecom.fr/publication/5265