Learning Mixtures of Selective Mallows Models

Πολλάτος, Βασίλειος; Pollatos, Vasileios

dc.contributor.author	Πολλάτος, Βασίλειος	el
dc.contributor.author	Pollatos, Vasileios	en
dc.date.accessioned	2022-09-23T09:34:18Z
dc.date.available	2022-09-23T09:34:18Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/55730
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.23428
dc.rights	Default License
dc.subject	Ranking Aggregation, Mallow Mixture Model, Selective Mallows Model, Distribution Learning , Parameter Estimation, Method Of Moments, Clustering.	en
dc.title	Learning Mixtures of Selective Mallows Models	en
heal.type	bachelorThesis
heal.classification	Μαθηματικά	el
heal.classification	Συνάθροιση ∆ειγµάτων Κατάταξης, Μίγµατα Κατανοµών Κατάταξης, Μάθηση από Ελλιπή ∆είγµατα, Εκµάθηση Κατανοµών, Εκτίµηση Παραµέτρων, Μέθοδος Ροπών, Συσταδοποίηση.	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2022-03-11
heal.abstract	In this thesis we study the problem of learning mixtures of rankings using noisy incomplete samples. Ranking distributions have drawn interest in the fields of social choice theory and theoretical machine learning for many decades. Apart from the extensive theoretical research ranking distributions have various real world applications including crowdsourcing, voting and recommendation systems and web search. Ranking aggregation is about using a collection of ranking samples drawn from a certain population in order to estimate the underlying ground truth about the preferences of the population on a set of n items. The samples are either complete or incomplete. In the first case each sample is a permutation of the full range of n items whereas in the second case each sample is a permutation of some subset of the full set of n items. The first step in our setting is to assume a generative model so our problem is well formulated and optimisation is possible. Popular generative models are the Mallows Model, the Plackett Luce Model and The Repeated Insertion Model. In our work we focus on the Mallows Model and particularly on its selective variation, where samples are incomplete. A further generalisation of the classical Mallows model is to assume that the underlying ranking distribution is a mixture of k Mallows models rather than a single one. This assumption models the heterogeneity of the preferences of a population by dividing it into several clusters (e.g women and men). In this work we study the identifiability of the Selective Mallow Mixture Model and suggest algorithms for distribution estimation and (when possible) parameter estimation. We suggest algorithms that work in the general case and for the specific case where centers are well separated we show that there exist much more efficient ones. We provide provable guarantees for the behavior of the suggested algorithms as well as experimental results.	en
heal.advisorName	Φωτάκης, Δημήτριος
heal.committeeMemberName	Πασπύρου, Νικόλαος
heal.committeeMemberName	Παγουρτζής, Άρης
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Τεχνολογίας Πληροφορικής και Υπολογιστών	el
heal.academicPublisherID	ntua
heal.numberOfPages	112
heal.fullTextAvailability	false