Bassetti Davide, Pospíšil Lukáš, Horenko Illia
Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, 67663 Kaiserslautern, Germany.
Department of Mathematics, Faculty of Civil Engineering, VŠB-TUO, Ludvika Podeste 1875/17, 708 33 Ostrava, Czech Republic.
Entropy (Basel). 2024 Jun 28;26(7):553. doi: 10.3390/e26070553.
In this work, we present a novel methodology for performing the supervised classification of time-ordered noisy data; we call this methodology Entropic Sparse Probabilistic Approximation with Markov regularization (eSPA-Markov). It is an extension of entropic learning methodologies, allowing the simultaneous learning of segmentation patterns, entropy-optimal feature space discretizations, and Bayesian classification rules. We prove the conditions for the existence and uniqueness of the learning problem solution and propose a one-shot numerical learning algorithm that-in the leading order-scales linearly in dimension. We show how this technique can be used for the computationally scalable identification of persistent (metastable) regime affiliations and regime switches from high-dimensional non-stationary and noisy time series, i.e., when the size of the data statistics is small compared to their dimensionality and when the noise variance is larger than the variance in the signal. We demonstrate its performance on a set of toy learning problems, comparing eSPA-Markov to state-of-the-art techniques, including deep learning and random forests. We show how this technique can be used for the analysis of noisy time series from DNA and RNA Nanopore sequencing.
在这项工作中，我们提出了一种用于对时间序列噪声数据进行监督分类的新方法；我们将这种方法称为带马尔可夫正则化的熵稀疏概率近似（eSPA - Markov）。它是熵学习方法的扩展，允许同时学习分割模式、熵最优特征空间离散化和贝叶斯分类规则。我们证明了学习问题解的存在性和唯一性条件，并提出了一种一次性数值学习算法，该算法在主导阶上与维度呈线性比例关系。我们展示了如何将该技术用于从高维非平稳噪声时间序列中以计算可扩展的方式识别持久（亚稳态）状态归属和状态转换，即当数据统计量的大小与其维度相比很小时，以及当噪声方差大于信号方差时。我们在一组玩具学习问题上展示了它的性能，将eSPA - Markov与包括深度学习和随机森林在内的最新技术进行了比较。我们展示了如何将该技术用于分析来自DNA和RNA纳米孔测序的噪声时间序列。
