Elja Arjas, Professor Emeritus of Mathematics and Statistics, University of Helsinki

Probabilistic Preference Learning With The Mallows Rank Model

Abstract: Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational complexity has limited its use to a form based on Kendall distance. Here, new computationally tractable methods for Bayesian inference in Mallows models are developed that work with any right-invariant distance. The method performs inference on the consensus ranking of the items, also when based on partial rankings, such as top-k items or pairwise comparisons. When assessors are many or heterogeneous, a mixture model is proposed for clustering them in homogeneous subgroups, with cluster-specific consensus rankings. Approximate stochastic algorithms are introduced that allow a fully probabilistic analysis, leading to coherent quantification of uncertainties. The method can be used, for example, for making probabilistic predictions on the class membership of assessors based on their ranking of just some items, and for predicting missing individual preferences, as needed in recommendation systems..

Machine Learning Coffee seminars are weekly seminars held jointly by the Aalto University and the University of Helsinki. The seminars aim to gather people from different fields of science with interest in machine learning. Talks will begin at 9:15 am and porridge and coffee will be served from 9:00 am.

Next talks:

September 25, Otaniemi: Hannu Toivonen

October 2, Kumpula: Flyura Djurabekova, Machine learning for Materials Research

October 9, Otaniemi: TBA

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