符号回归中作为选择压力的系数校准
Coefficient Calibration as Selection Pressure in Symbolic Regression
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中文总结 AI 辅助
该研究针对符号回归的集中式校准易偏向样本特定系数的问题，提出DSCA校准策略，经实验验证其可提升函数恢复与精度-复杂度权衡，为符号回归提供互补选择压力。
中文摘要 AI 辅助
在模因符号回归中，候选结构在系数校准后进行比较，因此校准协议本身会对进化选择产生影响。标准集中式校准会在合并样本的最优值处评估每个结构，忽略该校准在协变量偏移下的稳定性，因此可能偏向于那些拟合依赖于样本特定系数的结构。我们提出了Dirichlet-Sinkhorn常数平均（DSCA），这是一种校准策略，它将优化数据划分为具有不同协变量分布的等大小子集，在每个分区上独立校准每个候选结构，并在所得参数的均值处对其进行评估。我们表明，对于正确指定且可识别的表达式，DSCA相对于集中式校准的超额损失在总体水平上会消失；而在误指定情况下，当特定分区的校准无法聚合到合并最优值时，该超额损失会持续存在。在合成基准和10个真实世界数据集上，DSCA在负对数似然以及Akaike和贝叶斯信息准则的选择下，相比集中式Broyden-Fletcher-Goldfarb-Shanno和Levenberg-Marquardt校准，提升了函数恢复效果和精度-复杂度权衡。机制分析将DSCA的超额损失与泛化差距相关联，并表明重复集中式拟合无法复现该效应。这些结果表明，受控异质校准为符号回归搜索提供了一种互补的选择压力来源。
英文摘要
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, under selection by negative log-likelihood and by the Akaike and Bayesian information criteria. Mechanism analyses associate the DSCA excess loss with the generalization gap and show that the effect is not reproduced by repeated centralized fitting. These results indicate that controlled heterogeneous calibration provides a complementary source of selection pressure in symbolic-regression search.
发表机构
- University of Modena and Reggio Emilia（摩德纳大学与雷焦艾米利亚大学）
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