Gauss mixture approximations

The Gauss basis functions are given by

\[ \ell_m(t) = b_m \exp\left(-\frac{1}{2}\left(\frac{t - \mu_m}{\sigma_m}\right)^2\right), \qquad b_m = \frac{1}{\sqrt{2 \pi \sigma_m^2}}, \]

where \(b_m\) is a normalization factor, and the mean \(\mu_m\) and the standard deviation \(\sigma_m\) are hyperparameters.