| In this thesis we set out to find whether the true data generating formula behind a set of data points can be automatically inferred from the data points alone. We start with the topic of machine learning and quickly realize that black box models can only approximate the real world which creates the motivation to move on to evolutionary algorithms as a vehicle to implement symbolic regression. Through a series of experiments we discover that the mean-squared error cost function is easily fooled by decoy solutions and is unable to make use of all the information presented in the training examples. Based on this result we develop the concept of feature signatures which uniquely define a set of training examples and possess several desirable properties, the most important being invariance to linear transformations. Armed with this concept we conduct several more numerical experiments based on common analytical functions and real world data sets which ultimately lead to the experimental evidence we need to support the thesis. |
