

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

useful. This is reflected in the importance ranking returned by the forest, where the original attributes have low scores that may be lower than scores of random attributes in the case of data sets with few objects. This effect is decreasing for the larger sets. One possible reason is the decrease of the apparent importance of the random attributes with increasing number of objects, due to decreasing influence of random fluctuations. Another possibility is that the growing tree size increases the chance that at least two truly informative attributes are used for a tree construction, and therefore increases the importance of the cooperative attributes.

## 4.2 Semi-Synthetic Data

The experiment performed on four families of semi-synthetic data sets reveals some general tendencies, nevertheless it shows also that results for any data set may be significantly influenced by properties of the particular set, see Figure 4.

In three families of semi-synthetic data Boruta algorithm finds all attributes deemed important in the original data set in all extended sets, but in one set
(German credit) the number of retrieved attributes declines steadily with increasing number of added variables. Interestingly, in one case (House votes) the attributes that were not deemed important in the original data set gained importance in extended data set (data not shown); this was not very strong effect
(two new attributes compared with the eleven original ones), but consistent across all repetitions. In three families the number of false positive hits returned by Boruta was a slowly increasing function of number of attributes, starting from roughly 2 for system described with 125 attributes and reaching 6 for systems described with 2000 of attributes. In these three cases doubling of total number of attributes adds roughly one additional false positive attribute. This association does not turn up in the case of Vehicle data set, where the number of false positive hits is roughly constant for all set sizes.