Coefficient Calibration as Selection Pressure in Symbolic Regression

Mattia Billa, Veronica Guidetti, Federica Mandreoli

In memetic symbolic regression, candidate structures are compared after coefficient calibration, so the calibration protocol itself contributes to evolutionary selection. Standard centralized calibration evaluates each structure at its pooled-sample optimum, ignoring how stable this calibration is under covariate shifts, and can thus favor structures whose fit relies on sample-specific coefficients. We propose Dirichlet-Sinkhorn Constant Averaging (DSCA), a calibration strategy that partitions the optimization data into equally sized subsets with different covariate distributions, calibrates each candidate independently on every partition, and evaluates it at the mean of the resulting parameters. We show that the excess loss of DSCA relative to centralized calibration vanishes at the population level for correctly specified, identifiable expressions, whereas under misspecification it persists when partition-specific calibrations do not aggregate to the pooled optimum. On synthetic benchmarks and ten real-world datasets, DSCA improves functional recovery and the accuracy-complexity trade-off over centralized Broyden-Fletcher-Goldfarb-Shanno and Levenberg-Marquardt calibration,…