On-Line Estimation with the Multivariate Gaussian Distribution
Abstract
We consider on-line density estimation with the multivariate Gaussian distribution. In each of a sequence of trials, the learner must posit a mean μ and covariance Σ ; the learner then receives an instance x and incurs loss equal to the negative log-likelihood of x under the Gaussian density parameterized by ( μ , Σ ). We prove bounds on the regret for the follow-the-leader strategy, which amounts to choosing the sample mean and covariance of the previously seen data.
Cite
Text
Dasgupta and Hsu. "On-Line Estimation with the Multivariate Gaussian Distribution." Annual Conference on Computational Learning Theory, 2007. doi:10.1007/978-3-540-72927-3_21Markdown
[Dasgupta and Hsu. "On-Line Estimation with the Multivariate Gaussian Distribution." Annual Conference on Computational Learning Theory, 2007.](https://mlanthology.org/colt/2007/dasgupta2007colt-line/) doi:10.1007/978-3-540-72927-3_21BibTeX
@inproceedings{dasgupta2007colt-line,
title = {{On-Line Estimation with the Multivariate Gaussian Distribution}},
author = {Dasgupta, Sanjoy and Hsu, Daniel J.},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2007},
pages = {278-292},
doi = {10.1007/978-3-540-72927-3_21},
url = {https://mlanthology.org/colt/2007/dasgupta2007colt-line/}
}