On-Line Estimation with the Multivariate Gaussian Distribution

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.

• Type: Conference
• Year: 2007
• Where: COLT
• Authors: Sanjoy Dasgupta, Daniel Hsu
• Keywords: COLT 2007, Gaussian Density, Machine Learning, Multivariate Gaussian Distribution, On-line Density Estimation