\dm_csml_event_details UCL ELLIS

Kernel Monte Carlo estimators for partial rankings


Maria Lomeli


University of Cambridge


Friday, 02 February 2018






Roberts Building G08 Sir David Davies LT

Event series

DeepMind/ELLIS CSML Seminar Series


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.