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Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo

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journal contribution
posted on 01.05.1994, 00:00 by Han Liu, John D. Lafferty, Larry Wasserman
We consider the problem of estimating the joint density of a d-dimensional random vector X = (X1,X2, ...,Xd) 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 suit- ably defined sparsity condition, and the para- metric baseline density is smooth, the approach is shown to achieve near optimal minimax rates of convergence, and thus avoids the curse of dimensionality.


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© ACM, 1994. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution.



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