CITI Talk: “Clustering and Data Anonymization by Mutual Information”, Pablo Piantanida, Associate Professor at CentraleSupélec, TD D

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Title
Clustering and Data Anonymization by Mutual Information

Abstract
In this talk, we first introduce  the Shannon theoretic
multi-clustering problem and investigate its properties, uncovering
connections with many other coding problems in the literature. The figure
of merit for this information-theoretic problem is mutual information, the
mathematical properties of which make the multi-clustering problem amenable
to techniques that could not be used in a general rate-distortion setting.
We start by considering the case of two sources, where we derive
singleletter bounds for the achievable region by connecting our setting to
hypothesis testing and pattern recognition recognition problems in the
information theory literature. We then generalize the problem setup to an
arbitrary number of sources and study a CEO problem with logarithmic loss
distortion and multiple description coding. Drawing from the theory of
submodular functions, we prove a tight inner and outer bound for the
resulting achievable region under a suitable conditional independence
assumption. Furthermore, we present a proof of the well-known two-function
case of a conjecture by Kumar and Courtade (2013), showing that the
dictator functions are essentially the only Boolean  functions maximizing
mutual information.  The key step in our proof is a careful analysis of the
Fourier spectrum of the two Boolean functions. Finally, we study
information-theoretic applications to the problem of statistical  data
anonymization via mutual information and deep learning methods in which the
identity of the data writer must remain private even from the learner.

Joint works with Dr. Georg Pichler (TU Wien, Austria), Prof. Gerald Matz
(TU Wien, Austria),  Clément Feutry (CentraleSupélec, France) and Yoshua
Bengio (Montréal, Canada)

Short biography
Pablo Piantanida received both B.Sc. in Electrical
Engineering and B.Sc. in Mathematics degrees from the University of Buenos
Aires (Argentina) in 2003, and the Ph.D. from Université Paris-Sud (Orsay,
France) in 2007. Since October 2007 he has joined the Laboratoire des
Signaux et Systèmes (L2S), at CentraleSupélec together with CNRS (UMR 8506)
and Université Paris-Sud, as an Associate Professor of Network Information
Theory. He is an IEEE Senior Member, coordinator of the Information Theory
and its Applications group (ITA) at L2S, and  coordinator of the
International Associate Laboratory (LIA) of the CNRS “Information, Learning
and Control” with several institutions in Montréal and General Co-Chair of
the 2019 IEEE International Symposium on Information Theory (ISIT). His
research interests lie broadly in information theory and its interactions
with other fields, including multi-terminal information and Shannon theory,
machine learning, statistical inference, communication mechanisms for
security and privacy, and representation learning.