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Abstract Details
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Activity Number:
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15
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Type:
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Topic Contributed
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Date/Time:
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Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #301241 |
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Title:
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Graph-Valued Regression
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Author(s):
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Han Liu*+
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Companies:
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The Johns Hopkins University
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Address:
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, Baltimore, MD, 21210, United States
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Keywords:
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Undirected graphical models ;
graph-optimized cart ;
graph-valued regression ;
risk minimization ;
oracle properties ;
Go-CART
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Abstract:
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Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the graph $G(x)$ of $Y$ conditioned on $X=x$ as ``graph-valued regression.'' In this paper, we propose a semiparametric method for estimating $G(x)$ that builds a tree on the $X$ space just as in CART (classification and regression trees), but at each leaf of the tree estimates a graph. We call the method ``Graph-optimized CART,'' or Go-CART. We study the theoretical properties of Go-CART using dyadic partitioning trees, establishing oracle inequalities on risk minimization and tree partition consistency. We also demonstrate the application of Go-CART to a meteorological dataset, showing how graph-valued regression can provide a useful tool for analyzing complex data.
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Authors who are presenting talks have a * after their name.
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