### Abstract

Original language | English |
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Pages | 452-457 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 1 Oct 2007 |

Event | IEEE 22nd International Symposium on Intelligent Control, 2007. ISIC 2007. - Guangzhou, China Duration: 1 Oct 2007 → … |

### Conference

Conference | IEEE 22nd International Symposium on Intelligent Control, 2007. ISIC 2007. |
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Country | China |

City | Guangzhou |

Period | 1/10/07 → … |

### Fingerprint

### Keywords

- gaussian process
- matrix inverse approximation
- quasi-Newton BFGS method
- random scaling

### Cite this

*Random scaling of quasi-Newton BFGS method to improve the o(N^2)-operation approximation of covariance-matrix inverse in Gaussian process*. 452-457. Paper presented at IEEE 22nd International Symposium on Intelligent Control, 2007. ISIC 2007. , Guangzhou, China. https://doi.org/10.1109/ISIC.2007.4450928

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**Random scaling of quasi-Newton BFGS method to improve the o(N^2)-operation approximation of covariance-matrix inverse in Gaussian process.** / Zhang, Y.; Leithead, W.E.; Leith, D.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Random scaling of quasi-Newton BFGS method to improve the o(N^2)-operation approximation of covariance-matrix inverse in Gaussian process

AU - Zhang, Y.

AU - Leithead, W.E.

AU - Leith, D.

PY - 2007/10/1

Y1 - 2007/10/1

N2 - Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.

AB - Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. Similar to other computational models, Gaussian process frequently encounters the matrix-inverse problem during its model-tuning procedure. The matrix inversion is generally of O(N3) operations where N is the matrix dimension. We proposed using the O(N2)-operation quasi-Newton BFGS method to approximate/replace the exact inverse of covariance matrix in the GP context. As inspired during a paper revision, in this paper we show that by using the random-scaling technique, the accuracy and effectiveness of such a BFGS matrix-inverse approximation could be further improved. These random-scaling BFGS techniques could be widely generalized to other machine-learning systems which rely on explicit matrix-inverse.

KW - gaussian process

KW - matrix inverse approximation

KW - quasi-Newton BFGS method

KW - random scaling

U2 - 10.1109/ISIC.2007.4450928

DO - 10.1109/ISIC.2007.4450928

M3 - Paper

SP - 452

EP - 457

ER -