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Graph-Valued Regression
Han Liu · Xi Chen · John Lafferty · Larry Wasserman

Wed Dec 08 11:15 AM -- 11:20 AM (PST) @ Regency Ballroom
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.

Author Information

Han Liu (Carnegie Mellon University)
Xi Chen (NYU)
John Lafferty (Yale University)
Larry Wasserman (Carnegie Mellon University)

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