Graph-valued regression

Han Liu; Xi Chen; John Lafferty; Larry Wasserman

Graph-valued regression

Han Liu^*, Xi Chen, John Lafferty, Larry Wasserman

^*Corresponding author for this work

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

17 Scopus citations

Abstract

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 graphG(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.

Original language	English (US)
Title of host publication	Advances in Neural Information Processing Systems 23
Subtitle of host publication	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
State	Published - Dec 1 2010
Event	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 - Vancouver, BC, Canada Duration: Dec 6 2010 → Dec 9 2010

Conference

Conference	24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010
Country/Territory	Canada
City	Vancouver, BC
Period	12/6/10 → 12/9/10

ASJC Scopus subject areas

Information Systems

Cite this

@inproceedings{90a6710b01304b558e2d6773e9152995,

title = "Graph-valued regression",

abstract = "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 graphG(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 = "Han Liu and Xi Chen and John Lafferty and Larry Wasserman",

year = "2010",

month = dec,

day = "1",

language = "English (US)",

isbn = "9781617823800",

booktitle = "Advances in Neural Information Processing Systems 23",

note = "24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 ; Conference date: 06-12-2010 Through 09-12-2010",

}

TY - GEN

T1 - Graph-valued regression

AU - Liu, Han

AU - Chen, Xi

AU - Lafferty, John

AU - Wasserman, Larry

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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 graphG(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.

AB - 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 graphG(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.

UR - http://www.scopus.com/inward/record.url?scp=84860614031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860614031&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84860614031

SN - 9781617823800

BT - Advances in Neural Information Processing Systems 23

T2 - 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Y2 - 6 December 2010 through 9 December 2010

ER -

Graph-valued regression

Abstract

Conference

ASJC Scopus subject areas

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