seminarios en cmat.edu.uy seminarios en cmat.edu.uy
Mie Oct 14 13:30:26 -03 2020

Seminario de Probabilidad y Estadística
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Título: "Near optimal estimation of the mean in Hilbert space"

Expositor: Roberto Imbuzeiro Oliveira (IMPA)

Resumen:

In this talk, we discuss an estimator that, given a n-point i.i.d. sample from a
distribution P over Hilbert space (with finite second moment), produces an
estimate of the sample mean with the following properties.

(P0) The estimator does not require knowledge of distribution parameters.

(P1) Fix a confidence level 1-\alpha. Fix also 0<\delta<1/2 and assume an
adversarial contamination model where up to \delta n sample points may be
modified arbitrarily. Our estimator achieves (non-asymptotically) the minimax-
optimal error for this problem, up to a constant factor.

(P2) Our estimator can be computed in a number of Hilbert space operations that
grows at most polynomially in n.

A recent construction due to Lugosi and Mendelson gives an estimator satisfying
(P0) and (P1), but not (P2). Other estimators had been shown to satisfy (P1) and
(P2), but not (P0). It had been conjectured that no near-minimax estimator could
satisfy the three properties. A novel "PAC-Bayesian" analysis will show that the
conjecture is false, and that a variant of previous estimator actually works.
The idea behind our estimator is based on the standard "trimmed mean".
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Viernes 16/10 a las 10:30, https://salavirtual-udelar.zoom.us/j/2301522749

Contacto: Alejandro Cholaquidis - acholaquidis en hotmail.com
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https://salavirtual-udelar.zoom.us/j/  230152  2749