plan recognition, and prediction of students' actions during problem solving. We selected the largest ANDES network that was available to us, consisting of 223 nodes.

In contrast to the previous two networks, the depth of the ANDES network was significantly larger and so was its connectivity. There were only 22 leaf nodes. It is quite predictable that this kind of networks will pose difficulties to learning. We selected 20 evidence nodes randomly from the potential evidence nodes and tested 20 cases. All parameters were the same as those used in the CPCS network. We fixed the execution time of the algorithms to be 60 seconds. The learning overhead for the AIS-BN algorithm in the ANDES network was 13.4 seconds. In 60 seconds, AIS-BN generated about 114,000 samples, SIS generated about 98,000 samples and LW generated about 180,000 samples. In this network, LW still can generate almost two times the number of samples generated by the SIS algorithm.

We report our experimental results with the summary statistics in Table 5. The results show that also in the ANDES network the AIS-BN algorithm was significantly better than the SIS and LW algorithms. Since LW generated almost two times the number of samples that were generated by the SIS algorithm, its performance was better than that of the SIS
agorithm.

| AIS-BN   | S IS   | LW     |        |
|----------|--------|--------|--------|
| 0.0059   | 0.0628 | 0.0404 |        |
| f        |        |        |        |
| o        | 00000  | 0.102  | 0.0539 |
| min      | 0.0023 | 0.0028 | 0.0028 |
| median   | 0.0045 | 0.0190 | 0.0198 |
| 0.0237   | 0.321  | 0.221  |        |
| max      |        |        |        |

While the AIS-BN algorithm is on the average an order of magnitude more precise than the other two algorithms, the performance improvement is smaller than in the other two networks. The reason why the performance improvement of the AIS-BN algorithm over the SIS and LW algorithms in the ANDES network is smaller compared to that in the CPCS and PATHFINDER networks is that: (1) The ANDES network used in our tests was apparently not challenging enough for sampling algorithms in general. In the ANDES
network, SIS and LW also can perform well in some cases. The minimum MSE of SIS and LW in our tested cases is almost the same as that of AIS-BN. (2) The number of samples generated by AIS-BN in this network is significantly smaller than that in the previous two networks and AIS-BN needs more time to learn. Although increasing the number of samples will improve the performance of all three algorithms, it improves the performance of AIS- BN more since the convergence ratio of the AIS- BN algorithm is usually larger than that of SIS and LW  (see Figure 10). (3) The parameters that we used in this network were tuned for the CPCS network. (4) The large depth and fewer leaf nodes of the ANDES ntwork pose some difficulties to learning.