14:00 – 15:00 – Igor Prünster (Bocconi University)
Title: Multivariate species sampling models
Abstract:
Species sampling processes have long served as the fundamental framework
for modeling random discrete distributions and exchangeable sequences.
However, when analyzing data from distinct, though related, sources, a
broader notion of probabilistic invariance is required, and partial
exchangeability represents the natural choice. Over the past two
decades, numerous models for partially exchangeable data, collectively
known as dependent nonparametric priors, have been proposed. These
include the hierarchical, nested and additive processes, widely used in
Statistics and Machine Learning. However, a unifying framework remains
elusive, leaving key questions about their underlying learning
mechanisms unanswered.
We fill this gap by introducing multivariate species sampling models, a
new general class of nonparametric priors that encompasses most existing
dependent nonparametric processes. These models are characterized by
their partially exchangeable partition probability function, which
encodes the induced multivariate clustering structure. We establish
their core distributional properties and analyze their dependence
structure, demonstrating that borrowing of information across groups is
entirely determined by shared ties. This provides new insights into the
underlying learning mechanisms, offering, for instance, a principled
rationale for the previously unexplained correlation structure observed
in existing models.
Beyond providing a cohesive theoretical foundation, our approach serves
as a constructive tool for developing new models and opens new research
directions aimed at capturing even richer dependence structures beyond
the framework of multivariate species sampling processes.
Refreshments available between 15:00 – 15:30, Huxley Common Room (HXLY 549)