This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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35
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Type:
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Contributed
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Date/Time:
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Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract - #306779 |
Title:
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On the Predictive Potential of Kernel Principal Components
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Author(s):
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Andreas Artemiou*+ and Bing Li
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Companies:
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Penn State and Penn State
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Address:
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325 Thomas Building, University Park , PA, 16802,
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Keywords:
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kernel principal components ;
random covariance operator ;
Cauchy distribution ;
unitary invariance
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Abstract:
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In this paper we give a systematic probabilistic analysis of a phenomenon that is well known in statistics but until recently has no convincing explanation; that is, the first few principal components tend to possess predictive power for a response variable not designed in any way to be related to these principal components. We show that the phenomenon goes far beyond linear regression and principal components: if nature picks an arbitrary distribution for the predictor $X$ and an arbitrary conditional distribution of the response $Y$ given $X$, then $Y$ is more likely to have stronger correlation with higher-ranking kernel principal components than with lower-ranking kernel principal components. We formulate the ``arbitrariness'' by unitary invariance, and explicitly quantify the frequency of this tendency by exploring the relation between unitary invariance and the Cauchy distri
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