Gaussian node

The Gaussian node is a variable node and the basic element in building hierarchical models. Figure 2 (leftmost subfigure) shows the schematic diagram of the Gaussian node. Its output is the value of a Gaussian random variable $s$, which is conditioned by the inputs $m$ and $v$. Denote generally by $\mathcal N(x; m_x, \sigma^2_x)$ the probability density function of a Gaussian random variable $x$ having the mean $m_x$ and variance $\sigma^2_x$. Then the conditional probability function (cpf) of the variable $s$ is $p(s \mid m, v) = \mathcal N(s; m, \exp(-v))$. As a generative model, the Gaussian node takes its mean input $m$ and adds to it Gaussian noise (or innovation) with variance $\exp(-v)$.

Variables can be latent or observed. Observing a variable means fixing its output $s$ to the value in the data. Section 4 is devoted to inferring the distribution over the latent variables given the observed variables. Inferring the distribution over variables that are independent of $t$ is also called learning.