[Forum SIS] Seminari a Pavia mercoledì 28 febbraio 2018 ore 14:30

[Luca LA ROCCA]

Su richiesta di Emanuele Dolera, volentieri segnalo che

mercoledì 28 Febbraio 2018 alle ore 14:30

nell'aula Beltrami del Dipartimento di Matematica
dell'Università di Pavia (via Ferrata 1)

si terrà un seminario su un tema di statistical learning;
seguirà un secondo seminario su un tema probabilistico.

Tutti gli interessati trovano titoli e abstract in calce
e sono cordialmente invitati a partecipare.

Luca LR
http://www-dimat.unipv.it/luca/

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Ore 14.30:   Stephane Boucheron, Univ. Paris Diderot

Title: Concentration of excess risk in statistical learning.

Abstract: A theorem by Wilks asserts that in smooth parametric
density estimation the difference between the maximum likelihood
and the likelihood of the sampling distribution converges toward
a chi-square distribution where the number of degrees of freedom
coincides with the model dimension. This observation is at the core
of some goodness-of-fit testing procedures and of some classical
model selection methods. There exist versions of the Wilks phenonmenon
for various  contrast optimization procedures. In the field of
bounded contrast optimization techniques (supervized classification
for example), this can be established using concentration inequalities
for suprema of bounded non-centered (actually non-positive)
empirical processes. Recently, combining astute convexity arguments
and  concentration inequalities for suprema of empirical processes,
it has been possible to establish generic concentration inequalities
for excess penalized risk. I will discuss possible refinements
and extensions. In the Gaussian sequence model, concentration of
reconstruction error is likely to be improvable and might depend on
the effective  sparsity of the typical penalized estimator.
In the general setting, concentration of excess penalized risk
should be complemented by concentration of  empirical excess
penalized risk. Recent  results on penalized least square estimation
pave the way  to such a extensions.

Ore 15.30: Lorenzo Dello Schiavo, Universität Bonn

Characteristic functionals of Dirichlet measures and their algebraic
properties

Abstract: We consider Dirichlet—Ferguson (DF) measures,
a family of random probabilities on a locally compact Polish space X.
Introduced by T. S. Ferguson in Ann. Stat. 1(2) 209ff., 1973,
these measures have ever since found applications widely ranging from
Bayesian non-parametrics to population genetics and stochastic dynamics
of infinite particle systems. We compute the characteristic functionals
of DF measures relying on those of their finite-dimensional
marginalizations, the Dirichlet (D) distributions on standard simplices.
In finite dimensions, we identify the dynamical symmetry algebra L
of the characteristic functional of D as a simple Lie algebra of type A.
Additionally, we show that all integer semi-lattices of certain
posterior D distributions have a natural structure of weight Lie algebra
module for L. A probabilistic interpretation and a partial
generalization of these results to the infinite-dimensional case of
DF measures is at hand. If time permits, we will also address a second
characterization of DF measures by means of a Georgii—Nguyen—Zessin-type
formula (joint work with E. W. Lytvynov, Swansea University).