### Abstract

Nonparametric density estimation is a fundamental problem of statistics and data mining. Even though kernel density estimation is the most widely used method, its performance highly depends on the choice of the kernel bandwidth, and it can become computationally expensive for large data sets. WTe present an adaptive sparse-grid-based density estimation method which discretizes the estimated density function on basis functions centered at grid points rather than on kernels centered at the data points. Thus, the costs of evaluating the estimated density function are independent from the number of data points. We give details on how to estimate density functions on sparse grids and develop a cross validation technique for the parameter selection. We show numerical results to confirm that our sparse-grid-based method is well-suited for large data sets, and, finally, employ our method for the classification of astronomical objects to demonstrate that it is competitive to current kernel-based density estimation approaches with respect to classification accuracy and runtime. Copyright

Original language | English (US) |
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Title of host publication | SIAM International Conference on Data Mining 2014, SDM 2014 |

Editors | Mohammed J. Zaki, Arindam Banerjee, Srinivasan Parthasarathy, Pang Ning-Tan, Zoran Obradovic, Chandrika Kamath |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 443-451 |

Number of pages | 9 |

Volume | 1 |

ISBN (Electronic) | 9781510811515 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 14th SIAM International Conference on Data Mining, SDM 2014 - Philadelphia, United States Duration: Apr 24 2014 → Apr 26 2014 |

### Other

Other | 14th SIAM International Conference on Data Mining, SDM 2014 |
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Country | United States |

City | Philadelphia |

Period | 4/24/14 → 4/26/14 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Software

### Cite this

*SIAM International Conference on Data Mining 2014, SDM 2014*(Vol. 1, pp. 443-451). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611973440.51

**Density estimation with adaptive sparse grids for large data sets.** / Peherstorfer, Benjamin; Pflüger, Dirk; Bungartz, Hans Joachim.

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

*SIAM International Conference on Data Mining 2014, SDM 2014.*vol. 1, Society for Industrial and Applied Mathematics Publications, pp. 443-451, 14th SIAM International Conference on Data Mining, SDM 2014, Philadelphia, United States, 4/24/14. https://doi.org/10.1137/1.9781611973440.51

}

TY - GEN

T1 - Density estimation with adaptive sparse grids for large data sets

AU - Peherstorfer, Benjamin

AU - Pflüger, Dirk

AU - Bungartz, Hans Joachim

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Nonparametric density estimation is a fundamental problem of statistics and data mining. Even though kernel density estimation is the most widely used method, its performance highly depends on the choice of the kernel bandwidth, and it can become computationally expensive for large data sets. WTe present an adaptive sparse-grid-based density estimation method which discretizes the estimated density function on basis functions centered at grid points rather than on kernels centered at the data points. Thus, the costs of evaluating the estimated density function are independent from the number of data points. We give details on how to estimate density functions on sparse grids and develop a cross validation technique for the parameter selection. We show numerical results to confirm that our sparse-grid-based method is well-suited for large data sets, and, finally, employ our method for the classification of astronomical objects to demonstrate that it is competitive to current kernel-based density estimation approaches with respect to classification accuracy and runtime. Copyright

AB - Nonparametric density estimation is a fundamental problem of statistics and data mining. Even though kernel density estimation is the most widely used method, its performance highly depends on the choice of the kernel bandwidth, and it can become computationally expensive for large data sets. WTe present an adaptive sparse-grid-based density estimation method which discretizes the estimated density function on basis functions centered at grid points rather than on kernels centered at the data points. Thus, the costs of evaluating the estimated density function are independent from the number of data points. We give details on how to estimate density functions on sparse grids and develop a cross validation technique for the parameter selection. We show numerical results to confirm that our sparse-grid-based method is well-suited for large data sets, and, finally, employ our method for the classification of astronomical objects to demonstrate that it is competitive to current kernel-based density estimation approaches with respect to classification accuracy and runtime. Copyright

UR - http://www.scopus.com/inward/record.url?scp=84921664859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921664859&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973440.51

DO - 10.1137/1.9781611973440.51

M3 - Conference contribution

AN - SCOPUS:84921664859

VL - 1

SP - 443

EP - 451

BT - SIAM International Conference on Data Mining 2014, SDM 2014

A2 - Zaki, Mohammed J.

A2 - Banerjee, Arindam

A2 - Parthasarathy, Srinivasan

A2 - Ning-Tan, Pang

A2 - Obradovic, Zoran

A2 - Kamath, Chandrika

PB - Society for Industrial and Applied Mathematics Publications

ER -