  Symbolic Regression tries to find a mathematical expression that describes
the relationship of a set of explanatory variables to a measured variable. The
main objective is to find a model that minimizes the error and, optionally,
that also minimizes the expression size. A smaller expression can be seen as an
interpretable model considered a reliable decision model. This is often
performed with Genetic Programming which represents their solution as
expression trees. The shortcoming of this algorithm lies on this representation
that defines a rugged search space and contains expressions of any size and
difficulty. These pose as a challenge to find the optimal solution under
computational constraints. This paper introduces a new data structure, called
Interaction-Transformation (IT), that constrains the search space in order to
exclude a region of larger and more complicated expressions. In order to test
this data structure, it was also introduced an heuristic called SymTree. The
obtained results show evidence that SymTree are capable of obtaining the
optimal solution whenever the target function is within the search space of the
IT data structure and competitive results when it is not. Overall, the
algorithm found a good compromise between accuracy and simplicity for all the
generated models.

Artificial Intelligence