Combined Pruning for Nested Cross-Validation to Accelerate Automated Hyperparameter Optimization for Embedded Feature Selection in High-Dimensional Data with Very Small Sample Sizes

Background: Embedded feature selection in high-dimensional data with very small sample sizes requires optimized hyperparameters for the model building process. For this hyperparameter optimization, nested cross-validation must be applied to avoid a biased performance estimation. The resulting repeated training with high-dimensional data leads to very long computation times. Moreover, it is likely to observe a high variance in the individual performance evaluation metrics caused by outliers in tiny validation sets. Therefore, early stopping applying standard pruning algorithms to save time risks discarding promising hyperparameter sets. Result: To speed up feature selection for high-dimensional data with tiny sample size, we adapt the use of a state-of-the-art asynchronous successive halving pruner. In addition, we combine it with two complementary pruning strategies based on domain or prior knowledge. One pruning strategy immediately stops computing trials with semantically meaningless results for the selected hyperparameter combinations. The other is a new extrapolating threshold pruning strategy suitable for nested-cross-validation with a high variance of performance evaluation metrics. In repeated experiments, our combined pruning strategy keeps all promising trials. At the same time, the calculation time is substantially reduced compared to using a state-of-the-art asynchronous successive halving pruner alone. Up to 81.3\% fewer models were trained achieving the same optimization result. Conclusion: The proposed combined pruning strategy accelerates data analysis or enables deeper searches for hyperparameters within the same computation time. This leads to significant savings in time, money and energy consumption, opening the door to advanced, time-consuming analyses.