Kernel Monte Carlo Estimators for Partial Rankings

Maria Lomeli (University of Cambridge)

Friday 16th February 15:00-16:00 Maths 311B

Abstract

In the modern age, rankings data is ubiquitous and is useful for a variety of applications such as recommender systems, multiobject tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which forbids the direct application of existing modelling tools for complete rankings. In this talk, we present a novel way to extend kernel methods for complete rankings to partial rankings, via consistent Monte Carlo estimators of Gram matrices. These Monte Carlo kernel estimators are given by extending kernel mean embeddings to the embedding of a set of full rankings consistent with an observed partial ranking. They form a computationally tractable alternative to previous approaches for partial rankings data. We also present a variance reduction scheme based on an antithetic variate construction between permutations to get an improved a Monte Carlo estimator. Once the Gram matrix estimators are obtained they can be used for supervised and unsupervised Machine Learning kernel methods. In particular, we present comparative simulation results demonstrating the efficacy of the proposed estimators for an MMD hypothesis test and a Gaussian process task by extending some of the existing methods in the GPy framework.
Maria Lomeli is a Research Associate at the Machine Learning group, CBL, University of Cambridge. Dr Lomeli is a member of Trinity Hall college. She obtained her PhD in Machine Learning at the Gatsby Unit, UCL, under the supervision of Yee Whye Teh. Before coming to the UK, Dr Lomeli did a MSc in Mathematical Sciences at the IIMAS institute, Universidad Nacional Autónoma de México. Her research interests include: Bayesian nonparametrics, kernel methods and probabilistic programming.

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