Sample ACE Problems

Several sample problems from public literature are provided in the ace.samples subpackage. The one from [Wang04] is particularly good at demonstrating the power of the ACE algorithm. It starts by building test data using the following formula:

\[y(X) = \text{log}\left(4 + \text{sin}(4 X_0) + |X_1| + X_2^2 + X_3^3 + X_4 + 0.1\epsilon\right)\]

where \(\epsilon\) is sampled from standard normal distribution. The input data (N=200) is shown below. As you can see, it’s pretty ugly, and it’d be difficult to understand the underlying structure by doing normal regressions.

But go ahead and try running ACE on it, like this:

from ace.samples import wang04
wang04.run_wang04()

This will produce resulting transforms that look like the ones in the figure below. As you can see, ACE performed surprisingly well at extracting the underlying structure. You can clearly see the sine wave, the absolute value, the cubic, etc. It’s fabulous!