Linear Independent Factor Analysis

The addition and multiplication nodes can be used for building an affine transformation from Gaussian source nodes $\mathbf{s}(t)$ to Gaussian observation nodes $\mathbf{x}(t)$. This corresponds to linear factor analysis. With an independent mixture-of-Gaussians prior for each of the sources, the model corresponds to linear independent factor analysis [2]. Figure 3 shows how switches can be used to build such a prior for a source $s(t)$. A variance neuron is used in order to prevent multiple paths from the discrete node to the source.

Figure 3: A mixture-of-Gaussians prior for $s(t)$ is achieved using switches.