Log-det approximation based on uniformly distributed seeds and its application to Gaussian process regression
✍ Scribed by Yunong Zhang; W.E. Leithead; D.J. Leith; L. Walshe
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 592 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
Maximum likelihood estimation (MLE) of hyperparameters in Gaussian process regression as well as other computational models usually and frequently requires the evaluation of the logarithm of the determinant of a positive-definite matrix (denoted by C hereafter). In general, the exact computation of log det C is of O(N 3 ) operations where N is the matrix dimension. The approximation of log det C could be developed with O(N 2 ) operations based on power-series expansion and randomized trace estimator. In this paper, the accuracy and effectiveness of using uniformly distributed seeds for log det C approximation are investigated. The research shows that uniform-seed based approximation is an equally good alternative to Gaussian-seed based approximation, having slightly better approximation accuracy and smaller variance. Gaussian process regression examples also substantiate the effectiveness of such a uniform-seed based log-det approximation scheme.