Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo

Han Liu, John Lafferty, Larry Wasserman
; Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:283-290, 2007.

Abstract

We consider the problem of estimating the joint density of a d-dimensional random vector X = (X_1 , X_2, ..., X_d ) when d is large. We assume that the density is a product of a parametric component and a nonparametric component which depends on an unknown subset of the variables. Using a modification of a recently developed nonparametric regression framework called rodeo (regularization of derivative expectation operator), we propose a method to greedily select bandwidths in a kernel density estimate. It is shown empirically that the density rodeo works well even for very high dimensional problems. When the unknown density function satisfies a suitably defined sparsity condition, and the parametric baseline density is smooth, the approach is shown to achieve near optimal minimax rates of convergence, and thus avoids the curse of dimensionality.

Cite this Paper


BibTeX
@InProceedings{pmlr-v2-liu07a, title = {Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo}, author = {Han Liu and John Lafferty and Larry Wasserman}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {283--290}, year = {2007}, editor = {Marina Meila and Xiaotong Shen}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/liu07a/liu07a.pdf}, url = {http://proceedings.mlr.press/v2/liu07a.html}, abstract = {We consider the problem of estimating the joint density of a d-dimensional random vector X = (X_1 , X_2, ..., X_d ) when d is large. We assume that the density is a product of a parametric component and a nonparametric component which depends on an unknown subset of the variables. Using a modification of a recently developed nonparametric regression framework called rodeo (regularization of derivative expectation operator), we propose a method to greedily select bandwidths in a kernel density estimate. It is shown empirically that the density rodeo works well even for very high dimensional problems. When the unknown density function satisfies a suitably defined sparsity condition, and the parametric baseline density is smooth, the approach is shown to achieve near optimal minimax rates of convergence, and thus avoids the curse of dimensionality.} }
Endnote
%0 Conference Paper %T Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo %A Han Liu %A John Lafferty %A Larry Wasserman %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-liu07a %I PMLR %J Proceedings of Machine Learning Research %P 283--290 %U http://proceedings.mlr.press %V 2 %W PMLR %X We consider the problem of estimating the joint density of a d-dimensional random vector X = (X_1 , X_2, ..., X_d ) when d is large. We assume that the density is a product of a parametric component and a nonparametric component which depends on an unknown subset of the variables. Using a modification of a recently developed nonparametric regression framework called rodeo (regularization of derivative expectation operator), we propose a method to greedily select bandwidths in a kernel density estimate. It is shown empirically that the density rodeo works well even for very high dimensional problems. When the unknown density function satisfies a suitably defined sparsity condition, and the parametric baseline density is smooth, the approach is shown to achieve near optimal minimax rates of convergence, and thus avoids the curse of dimensionality.
RIS
TY - CPAPER TI - Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo AU - Han Liu AU - John Lafferty AU - Larry Wasserman BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics PY - 2007/03/11 DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-liu07a PB - PMLR SP - 283 DP - PMLR EP - 290 L1 - http://proceedings.mlr.press/v2/liu07a/liu07a.pdf UR - http://proceedings.mlr.press/v2/liu07a.html AB - We consider the problem of estimating the joint density of a d-dimensional random vector X = (X_1 , X_2, ..., X_d ) when d is large. We assume that the density is a product of a parametric component and a nonparametric component which depends on an unknown subset of the variables. Using a modification of a recently developed nonparametric regression framework called rodeo (regularization of derivative expectation operator), we propose a method to greedily select bandwidths in a kernel density estimate. It is shown empirically that the density rodeo works well even for very high dimensional problems. When the unknown density function satisfies a suitably defined sparsity condition, and the parametric baseline density is smooth, the approach is shown to achieve near optimal minimax rates of convergence, and thus avoids the curse of dimensionality. ER -
APA
Liu, H., Lafferty, J. & Wasserman, L.. (2007). Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in PMLR 2:283-290

Related Material