Statistical optimality benchmarking is crucial for analyzing and designing time series classification (TSC) algorithms. This study proposes to benchmark the optimality of TSC algorithms in distinguishing diffusion processes by the likelihood ratio test (LRT). The LRT is an optimal classifier by the Neyman-Pearson lemma. The LRT benchmarks are computationally efficient because the LRT does not need training, and the diffusion processes can be efficiently simulated and are flexible to reflect the specific features of real-world applications. We demonstrate the benchmarking with three widely-used TSC algorithms: random forest, ResNet, and ROCKET. These algorithms can achieve the LRT optimality for univariate time series and multivariate Gaussian processes. However, these model-agnostic algorithms are suboptimal in classifying high-dimensional nonlinear multivariate time series. Additionally, the LRT benchmark provides tools to analyze the dependence of classification accuracy on the time length, dimension, temporal sampling frequency, and randomness of the time series.

翻译：统计最优性基准测试对于分析和设计时间序列分类（TSC）算法至关重要。本研究提出通过似然比检验（LRT）来基准测试TSC算法在区分扩散过程中的最优性。根据奈曼-皮尔逊引理，LRT是一种最优分类器。由于LRT无需训练，且扩散过程能够高效模拟并灵活反映实际应用的具体特征，因此LRT基准测试具有计算高效性。我们以三种广泛使用的TSC算法（随机森林、ResNet和ROCKET）为例进行基准测试。这些算法在单变量时间序列和多变量高斯过程中能够达到LRT最优性。然而，这些与模型无关的算法在分类高维非线性多变量时间序列时表现次优。此外，LRT基准测试提供了分析分类准确率对时间长度、维度、时间采样频率以及时间序列随机性依赖关系的工具。