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.
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