The Meta-Learning Gap: Combining Hydra and Quant for Large-Scale Time Series Classification

Time series classification faces a fundamental trade-off between accuracy and computational efficiency. While comprehensive ensembles like HIVE-COTE 2.0 achieve state-of-the-art accuracy, their 340-hour training time on the UCR benchmark renders them impractical for large-scale datasets. We investigate whether targeted combinations of two efficient algorithms from complementary paradigms can capture ensemble benefits while maintaining computational feasibility. Combining Hydra (competing convolutional kernels) and Quant (hierarchical interval quantiles) across six ensemble configurations, we evaluate performance on 10 large-scale MONSTER datasets (7,898 to 1,168,774 training instances). Our strongest configuration improves mean accuracy from 0.829 to 0.836, succeeding on 7 of 10 datasets. However, prediction-combination ensembles capture only 11% of theoretical oracle potential, revealing a substantial meta-learning optimization gap. Feature-concatenation approaches exceeded oracle bounds by learning novel decision boundaries, while prediction-level complementarity shows moderate correlation with ensemble gains. The central finding: the challenge has shifted from ensuring algorithms are different to learning how to combine them effectively. Current meta-learning strategies struggle to exploit the complementarity that oracle analysis confirms exists. Improved combination strategies could potentially double or triple ensemble gains across diverse time series classification applications.