Optimal spanning tree reconstruction in symbolic regression

The paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to a primitive function. An edge assigns a superposition of two functions. The weight of an edge is equal to the probability of superposition. To generate an optimal model, one has to reconstruct its structure from its graph adjacency matrix. The proposed algorithm reconstructs the minimum spanning tree from the weighted colored graph. The paper presents a novel solution based on the prize-collecting Steiner tree algorithm. This algorithm is compared with its alternatives.