2010/06/21 by Han Liu, Liu, Han, Xi Chen +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Bioinformatics and Genomic Networks #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Inference #stat.ME #stat.ML
paper · pdf · doi:10.48550/arxiv.1006.3972
arxiv created 2010/06/21 · openalex publication_date 2010/06/21 · arxiv updated 2010/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.