# Benchmarking optimality of time series classification methods in distinguishing diffusions

arXiv: https://arxiv.org/abs/2301.13112 · HTML: https://mlsanity.com/paper/2301.13112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [To tune or not to tune the number of trees in random forest?](https://mlsanity.com/paper/1705.05654/) (2017)
- [Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories](https://mlsanity.com/paper/2007.15174/) (2020)

## Abstract (arXiv)

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.