BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
BEGIN:VEVENT
UID:784@lincs.fr
DTSTART;TZID=Europe/Paris:20230926T150000
DTEND;TZID=Europe/Paris:20230926T170000
DTSTAMP:20230922T132021Z
URL:https://www.lincs.fr/events/phd-thesis-defense-unimodularity-in-random
 -networks-applications-to-the-null-recurrent-doeblin-graph-and-hierarchica
 l-clustering/
SUMMARY:Phd Thesis Defense : Unimodularity in Random Networks: Applications
 to the Null Recurrent Doeblin Graph and Hierarchical Clustering
DESCRIPTION:This thesis is based on the notion of unimodularity in the
 context of random networks and explores two domains of application:
 Coupling from the Past in the null recurrent case based on the associated
 Doeblin Graphs and unsupervised classification based on hierarchical
 clustering on point processes. The first part of this thesis focuses on the
 properties of a specific random graph called the Doeblin Graph\, which is
 associated with the Coupling from the Past algorithm used for perfect
 sampling of the stationary distribution of a Markov Chain. In the
 irreducible\, aperiodic\, and positive recurrent case\, it is known that
 the Bridge Doeblin Graph\, a subgraph of the Doeblin Graph\, is an infinite
 tree that is unimodularizable and contains a unique biinfinite path. This
 bi-infinite path plays a crucial role in constructing a perfect sample of
 the stationary state of the Markov chain. This thesis extends the study to
 the null recurrent case\, where it is shown that the Bridge Doeblin Graph
 is either an infinite tree or a forest composed of a countable collection
 of infinite trees. In the former case\, the infinite tree possesses a
 single end\, is not generally unimodularizable\, but exhibits local
 unimodularity. These properties are leveraged to investigate the stationary
 regime of measure-valued random dynamics on the Bridge Doeblin Tree\,
 particularly the taboo and potential random dynamics. The second part of
 this thesis introduces a novel hierarchical clustering model tailored for
 unsupervised classifications of datasets which are countably infinite.
 Clustering\, a widely used technique in unsupervised learning\, aims to
 identify groups within a dataset based on element similarities. The
 proposed algorithm employs multiple levels of clustering\, constructing
 clusters at each level using nearest-neighbor chains of points or clusters.
 This algorithm is applied to the Poisson point process\, and it is proven
 that the clustering algorithm defines a phylogenetic forest on the Poisson
 point process\, which is a factor of the point process and is therefore
 unimodular. Various properties of this random forest\, such as the mean
 sizes of clusters at each level or the mean size of the cluster of a
 typical node\, are examined.
CATEGORIES:PhD Defense
LOCATION:Inria\, salle Philippe Flajolet\, 2 rue Simone Iff\, Paris\,
 75012\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=2 rue Simone Iff\, Paris\,
 75012\, France;X-APPLE-RADIUS=100;X-TITLE=Inria\, salle Philippe
 Flajolet:geo:0,0
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20230326T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR