[ABE-L] Seminário Conjunto UFSCar/ICMC - 22/08/2014 (sexta-feira) - 14h00 - DEs-UFSCar

[Carlos Diniz]

Seminário Conjunto UFSCar/ICMC-USP – 22/08/2014 (sexta-feira) - 14h00

LOCAL: Sala de Seminários 1 (DEs-UFSCar)  

TÍTULO: A Spectral Series Approach to High-Dimensional Nonparametric Inference

PALESTRANTE: Rafael Izbicki  – DEs-UFSCar

RESUMO: 

A key question in modern statistics is how to make efficient inferences for complex, high-dimensional data, such as images, spectra, and trajectories. While a large body of work has revolved on adapting nonparametric regression methods to high dimensions, statisticians have devoted less effort to redesigning estimators of other quantities to such settings. Some of these tasks are of key importance for the sciences; an example is the conditional density estimation problem, which plays an important role in modern cosmology. In this talk, we propose a nonparametric framework for estimating unknown functions in high dimensions. The basic idea is to expand these functions in terms of a spectral basis -- the eigenfunctions of a kernel-based operator. If the kernel is appropriately chosen, then the eigenfunctions adapt to the intrinsic geometry of the data, forming an efficient Fourier-like orthogonal basis for smooth functions on the data. We show how this framework can be used for estimating several quantities We provide theoretical guarantees on the developed estimators and illustrate their use for several applications.



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