[ABE-L] Seminário - IME-USP - Modelos de Regressão e Aplicações - Rafael Izbicki - A flexible approach to high-dimensional nonparametric conditional density estimation

[Silvia Ferrari]

*Seminário - Projeto Temático: Modelos de Regressão e Aplicações*

*Título*: A flexible approach to high-dimensional nonparametric conditional
density estimation

*Palestrante*: Rafael Izbicki, Departamento de Estatística – Universidade
Federal de São Carlos

*Quando*: 4 de setembro, sexta-feira, às 11h.

*Onde*: Auditório Jacy Monteiro, Bloco B, piso térreo - IME-USP

*Resumo*. There is a growing demand for nonparametric conditional density
estimators (CDEs) in fields such as astronomy and economics.  In astronomy,
for example, one can dramatically improve estimates of the parameters that
dictate the  evolution of the Universe by working with full conditional
densities instead of regression (i.e., conditional mean) estimates. More
generally, standard regression falls short in any prediction problem where
the distribution of the response is more complex with multi-modality,
asymmetry or heteroscedastic noise. Nevertheless, much of the work on
high-dimensional inference concerns regression and classification only.
Here we propose a fully nonparametric approach to conditional density
estimation that reformulates CDE as a non-parametric orthogonal series
problem where the expansion coefficients are estimated by regression. By
taking such an approach, one can efficiently estimate conditional densities
in high dimensions by drawing upon the success in high-dimensional
regression. Depending on the choice of regression procedure, our method can
adapt to a variety of challenging high-dimensional settings with, for
example, a large number of irrelevant components or nonlinear manifold
structure in the data. We study the theoretical and empirical performance
of our proposed method, and we compare our approach with traditional
conditional density estimators on real-world as well as simulated data.

Joint work with Ann B. Lee - Carnegie Mellon University.
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