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<DIV><FONT face=Calibri><SPAN class=apple-style-span><B
style="mso-bidi-font-weight: normal"><U><SPAN
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Conjunto UFSCar/ICMC-USP – 22/08/2014 (sexta-feira) -
14h00</SPAN></U></B></SPAN></FONT></DIV>
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<P style="mso-line-height-alt: 13.5pt"><SPAN><STRONG><SPAN
style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 14pt">LOCAL: </SPAN>Sala de
Seminários 1 (DEs-UFSCar)</STRONG></SPAN><SPAN> <STRONG><SPAN
style="mso-spacerun: yes"> </SPAN><o:p></o:p></STRONG></SPAN></P>
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class=MsoNormal><STRONG><SPAN><SPAN
style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 14pt">TÍTULO</SPAN>: A
Spectral Series Approach to High-Dimensional Nonparametric Inference</SPAN><SPAN
style="FONT-FAMILY: myriadroman; COLOR: #001f46; FONT-SIZE: 14pt; mso-bidi-font-family: tahoma; mso-font-kerning: 18.0pt"><o:p></o:p></SPAN></STRONG></P>
<P style="mso-line-height-alt: 13.5pt"><SPAN><STRONG><SPAN
style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 14pt">PALESTRANTE</SPAN>:
Rafael Izbicki</STRONG></SPAN><SPAN><FONT face="Times New Roman">
</FONT><STRONG><SPAN style="mso-spacerun: yes"> </SPAN>–
DEs-UFSCar<o:p></o:p></STRONG></SPAN></P>
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class=MsoNormal><SPAN><STRONG><SPAN
style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 14pt">RESUMO</SPAN>:
</STRONG></SPAN><SPAN style="FONT-SIZE: 14pt"><BR><BR></SPAN><SPAN
style="FONT-FAMILY: 'Arial','sans-serif'; FONT-SIZE: 14pt">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.<o:p></o:p></SPAN></P></SPAN></SPAN></FONT></DIV>
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