Author name cluster

Jack K. Fitzsimons

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

2 papers

1 author row

UAI Conference 2018 Conference Paper

Improved Stochastic Trace Estimation using Mutually Unbiased Bases

Jack K. Fitzsimons
Michael A. Osborne
Stephen J. Roberts
Joseph F. Fitzsimons

The paper begins by introducing the definition and construction of mutually unbiased bases, which are a widely used concept in quantum information processing but have received little to no attention in the machine learning and statistics literature. We demonstrate their usefulness by using them to create a new sampling technique which offers an improvement on the previously well established bounds of stochastic trace estimation. This approach offers a new state of the art single shot sampling variance while requiring O(log(n)) random bits for x ∈ Rn which significantly improves on traditional methods such as fixed basis methods, Hutchinson’s and Gaussian estimators in terms of the number of random bits required and worst case sample variance.

Details

UAI Conference 2017 Conference Paper

Bayesian Inference of Log Determinants

Jack K. Fitzsimons
Kurt Cutajar
Maurizio Filippone
Michael A. Osborne
Stephen J. Roberts

The log determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few thousands. In the spirit of probabilistic numerics, we reinterpret the problem of computing the log determinant as a Bayesian inference problem. In particular, we combine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain probabilistic estimates for the log determinant and its associated uncertainty within a given computational budget. Beyond its novelty and theoretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log determinant, while also quantifying the uncertainty due to budgetconstrained evidence.

Details