Robustness of symbolic-regression performance

Determine whether the observed generalization of the compact PACE-like chlorophyll-a retrieval expression is robust to different data partitions and to the stochastic nature of the symbolic-regression search.

Background

The study reports strong performance for a compact symbolic-regression expression using PACE-like hyperspectral reflectances, but the initial evaluation relies on a single train–validation–test partition. Because both the partition and the evolutionary symbolic-regression search can influence the selected equation, the authors identify the robustness of the observed behavior as an unresolved issue.

The paper subsequently performs repeated data splits and independent searches as an empirical assessment, but the motivating question concerns whether the result is generally robust rather than an artifact of a particular split or stochastic search realization.

References

Although the held out results demonstrate that a compact PACE-like expression can generalize beyond the data used for model selection, a single train-test partition cannot establish whether this behavior is robust to different data partitions or to the stochastic nature of the symbolic regression search.

— How Much Hyperspectral Information Does Chlorophyll Retrieval Really Need?  (2609.18531 - Hammoud et al., 16 Sep 2026) in Section 4.2, “PACE-like Hyperspectral Ocean Color Models”