Training Mode

For training, two humans interact with each other in a somewhat natural way while the system accumulates information about the actions and reactions. This is depicted in detail in Figure 8.1.

  

Figure 8.1: Training Mode

Here, the operation is straightforward. The two users are interacting and the learning system is being fed ${\bf x}(t)$ on one end and ${\bf y}(t)$ on the other. Then, once many pairs of data are accumulated, the system uses CEM to optimize a conditioned Gaussian mixture model which represents $p({\bf y}\vert{\bf x})$. Once again, we note the role of the integration symbol which indicates the pre-processing of the past time-series via an attentional window over the past T samples of measurements. This window can be represented compactly in an eigenspace with ${\bf x}(t)$.

Typically the two users interact for a few minutes indicating to the system some specific patterns of behaviour via a distribution of $({\bf x},{\bf y})$ pairs. Once the CEM converges to a maximum conditional likelihood solution that approximates this distribution, the interaction of the two users has been learned and can be used to generate predictions.