A Weighted Products of Gaussians

A well-known result is that a product of Gaussian PDFs collapses to a scaled Gaussian PDF (e.g. Every neuron in a G-GLN takes one-or-more Gaussian PDFs as input and produces a Gaussian PDF as output. This raises the question of what input to provide to neurons in the first layer, i.e. the base prediction. We consider three solutions: (1) None. The input sufficient statistics to each neuron are already concatenated with so-called "bias" Gaussians to ensure that the target mean falls within the convex hull defined by the input means (described in Section 3).