Unsupervised Structural Learning
Context
Unsupervised Structural Learning covers a set of algorithms that can discover any kind and any number of probabilistic relationships between variables in a dataset. The number of Bayesian networks that can be found for a given set of variables can be so large that it is impossible, except in trivial cases, to carry out an exhaustive search for the best network.
| Number of Variables | Number of Possible Networks |
|---|---|
| 1 | 1 |
| 2 | 3 |
| 3 | 25 |
| 4 | 543 |
| 5 | 29,281 |
| 6 | 3,781,503 |
| 7 | 1.1 x 109 |
| 8 | 7.8 x 1011 |
| 9 | 1.2 x 1015 |
| 10 | 4.2 x 1018 |
| … | … |
| 100 | 1.11 x 101631 |
Hence, learning algorithms must rely on a set of heuristics that allow reducing the enormously large search space. BayesiaLab comes with four conceptually different structural learning algorithms that can discover a network structure and estimate the corresponding conditional probability tables. Given that the heuristics employed with each algorithm are different, the resulting networks can be different as well. However, each learning method uses the same metric, i.e., the Minimum Description Length Score (MDL Score), so that the resulting networks can be compared easily. The MDL Score is reported in the Console and added automatically to the Comment associated with the network: the lower the MDL Score, the better the network.