Optimal spanning tree reconstruction in symbolic regression

TL;DR

This paper introduces a novel algorithm for reconstructing optimal regression models as minimum spanning trees from weighted graphs, enhancing symbolic regression by leveraging prize-collecting Steiner tree methods.

Contribution

It presents a new approach using prize-collecting Steiner tree algorithms to reconstruct optimal model structures in symbolic regression, which is a novel application in this context.

Findings

The proposed algorithm effectively reconstructs minimal spanning trees from weighted graphs.

It outperforms alternative methods in reconstructing model structures.

The approach improves the accuracy and efficiency of symbolic regression models.

Abstract

This 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 some primitive function. An edge assigns a superposition of two functions. The weight of an edge equals 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. This paper presents a novel solution based on the prize-collecting Steiner tree algorithm. This algorithm is compared with its alternatives.