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Main: GaussianLinearExperts

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

$$\xi^\theta(y) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(\theta'x_t-y)^2}{2\sigma^2}}, y\in \mathbb{R}$$

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 $\lambda(\xi^\theta,y) = -\ln \xi^\theta(y)$.

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Page last modified on September 06, 2010, at 10:45 PM