Gaussian Linear Experts

Gaussian linear experts in the protocol of online regression incorporate information about the Gaussian nature of the noise in the outcomes. Each expert ⚠ $\theta \in {ℝ}^n$ predicts the following probability distribution over the outcomes ⚠ $y\in ℝ$:

at each step, where the variance ⚠ ${\sigma }^2$ is the same for all the experts, and is assumed to be known. The natural loss function for these experts is the logarithmic loss function ⚠ $\lambda ({\xi }^{\theta },y)=-{\ln \xi }^{\theta }\left(y\right)$.

• Fedor Zhdanov and Vladimir Vovk. Competing with Gaussian linear experts. Technical report, arXiv:0910.4683 [cs.LG], arXiv.org e-Print archive, 2009.