feature selection in the context of joint modeling, mentioned in Section 5.1. Table 11 shows the error rates obtained by MFGN using different attribute subsets 9. To take advantage of its general inference properties, the MFGN model must be applied to the attribute subset of interest. If the inference task is fixed and the number of attributes is very large, alternative methods should be used.

| used.                                                     | ˆ PE    |             |
|-----------------------------------------------------------|---------|-------------|
| METHOD                                                    | (distribution, 10 initializations)         | ˆ PE (best) |
| 6 Selected attributes                                     |         |             |
| MFGN 2 components                                         | .32±.00 | .32         |
| MFGN 3 components                                         | .20±.05 | .18         |
| MFGN 4 components                                         | .19±.02 | .18         |
| MFGN 5 components                                         | .20±.02 | .18         |
| MFGN 6 components                                         | .19±.03 | .16         |
| MFGN 7 components                                         | .20±.04 | .18         |
| MFGN 10 components                                        | .22±.04 | .18         |
| MFGN 12 components                                        | .19±.03 | .16         |
| MFGN 15 components                                        | .19±.04 | .15         |
| 8 Selected attributes                                     |         |             |
| MFGN 4 components                                         | .22±.01 | .21         |
| MFGN 6 components                                         | .21±.02 | .19         |
| MFGN 8 components                                         | .21±.03 | .18         |
| MFGN 10 components                                        | .23±.02 | .18         |
| MFGN 12 components                                        | .21±.02 | .18         |
| MFGN 15 components                                        | .21±.02 | .18         |
| 23 Selected attributes                                    |         |             |
| MFGN 6 components                                         | .28±.02 | .25         |
| MFGN 8 components                                         | .29±.03 | .25         |
| MFGN 10 components                                        | .34±.08 | .25         |
| MFGN 15 components                                        | .34±.06 | .28         |
| Table 11. Horse Colic Database Results (random rate = .5) |         |             |

## 5.4.4 Monk'S Problems

The Monk's problems are three concept learning tasks from 6 symbolic attributes, widely used as benchmarks for inductive learning algorithms (Thrun et al. 1991). As seen in Table 12, MFGN fails on MONK1 (where acceptable generalization is not obtained) and MONK2 (where the training examples cannot even be stored). In contrast, MFGN correctly solves MONK3. This behavior is related to the fact that the MONK's problems are based on deterministic or abstract concepts which may lack the kind of geometric regularities in the attribute space required by probabilistic models 10.