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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)

Xi Chen is an associate professor with tenure at Stern School of Business at New York University, who is also an affiliated professor to Computer Science and Center for Data Science. Before that, he was a Postdoc in the group of Prof. Michael Jordan at UC Berkeley. He obtained his Ph.D. from the Machine Learning Department at Carnegie Mellon University (CMU). He studies high-dimensional statistical learning, online learning, large-scale stochastic optimization, and applications to operations. He has published more than 20 journal articles in statistics, machine learning, and operations, and 30 top machine learning peer-reviewed conference proceedings. He received NSF Career Award, ICSA Outstanding Young Researcher Award, Faculty Research Awards from Google, Adobe, Alibaba, and Bloomberg, and was featured in Forbes list of “30 Under30 in Science”.

John Lafferty (Yale University)
Larry Wasserman (Carnegie Mellon University)

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