Figure 5.1: Maximum likelihood learning for for single hidden layer neural networks. The hidden layer is dependent on the inputs and the adaptable parameters U in a deterministic manner. The outputs in turn are dependent on the hidden layer and the adaptable parameters v in a deterministic manner. The bias parameters are omitted for clarity. The diagram on the left may be more concisely represented by that on the right, where w represents a set of parameters containing U and v. In the Bayesian approach we are undertaking, the adaptive parameters will be considered as an extra node in the graph — see Figure 5.2.