Quantitative Prediction

For a quantitative measure, the system was trained as usual on the interaction between the two individuals and learned the usual predictive mapping $p({\bf y},{\bf x})$. Since real-time is not an issue for this kind of test, the system was actually permitted to use more Gaussian models and more dimensions to learn $p({\bf y},{\bf x})$.

Once trained on a portion of the data, the system's ability to perform prediction was tested on the remainder of the sequence. Once again, the pdf allows us to compute an estimated ${\hat {\bf y}}$ for any given ${\bf x}$ short term memory. The expectation was used to predict ${\hat {\bf y}}$ and not the arg max since it is the least squares estimator. The prediction was then compared to the true ${\bf y}$result in the future of the time series and RMS errors were computed. Of course, the system only observed the immediate past reaction of both user A and user B which is contained in ${\bf x}$. Thus, the values ${\bf y}(t-1),...,{\bf y}(t-T)$ are effectively being used to compute ${\bf y}(t)$. In addition, the system is predicting the immediate reaction of both users (A and B) in the whole ${\bf y}(t)$ vector. For comparison, RMS errors are shown against the nearest neighbour and constant velocity estimates. The nearest neighbour estimate merely assumes that ${\bf y}(t) = {\bf y}(t-1)$ and the constant velocity assumes that ${\bf y}(t) = {\bf y}(t-1) + \Delta_t {\bf {\dot y}}(t-1)$.

 

Table 9.2: RMS Errors

Nearest Neighbour	Constant Velocity	ARL
1.57 %	0.85 %	0.62 %

 

Table 9.2 depicts the RMS errors on the test interaction and these suggest that the system is a better instantaneous predictor than the above two methods. Therefore, it should be useful as a Kalman filter-type of predictor for helping tracking systems.