On-line estimation with the multivariate Gaussian distribution

Authors:
Sanjoy Dasgupta;Daniel Hsu
Affiliations:
University of California, San Diego;University of California, San Diego
Venue:
COLT'07 Proceedings of the 20th annual conference on Learning theory
Year:
2007

Citing 6
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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.