## 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.

Original language | English (US) |
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Pages (from-to) | 283-290 |

Number of pages | 8 |

Journal | Journal of Machine Learning Research |

Volume | 2 |

State | Published - Dec 1 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Software
- Statistics and Probability
- Artificial Intelligence