

![0_image_0.png](0_image_0.png)

follows: Pr(π t | o t ) is first used to sample π t ; F e r (s t | π t , o t ) is then used to sample s t .  Once we have obtained the sample for π t and st , we can proceed to sample the remaining nodes in the network B e r to obtain a sample for l t as usual. Finally, we note that the weight w t = Pr(o t ) can also be computed efficiently by:

$$\operatorname*{Pr}(o_{t})=\sum_{\pi_{t}^{0}}\operatorname*{Pr}\left(o_{t}\mid\pi_{t}^{0}\right)\operatorname*{Pr}\left(\pi_{t}^{0}\right)$$

In this evidence reversal procedure, for each value of π t , we need to perform exact inference on the structure of Fobs (st, ot | πβ). Thus the complexity of this procedure heavily depends on the complexity of the network structure of F . However, as we have noted, due to the nature of the factored representation, F usually has a sparse structure so that exact inference can be performed efficiently.  For example, in the special case where F
is completely factored into the product of M independent state variables which are then independently observed, the complexity becomes linear w.r.t. M.

## 6. Experimental Results

In this section, we present our experimental results with the policy recognition algorithm.  In subsection 6.1, we demonstrate the effectiveness of the Rao-Blackwellised sampling method for policy recognition by comparing the performance of our Rao-Blackwellised procedure against likelihood weighting sampling in a synthetic tracking task. In subsection 6.2, we present an application of the AHMM framework to the problem of traing human behaviours in a complex spatial environment using distributed video surveillance data.