On Entropic Learning from Noisy Time Series in the Small Data Regime

Area of Science:

• Computational statistics
• Machine learning
• Time series analysis

Background:

• Supervised classification of time-ordered data is challenging, especially with noise and high dimensionality.
• Existing methods struggle with non-stationary data where signal variance is low compared to noise variance.

Purpose of the Study:

• To present a novel methodology, Entropic Sparse Probabilistic Approximation with Markov regularization (eSPA-Markov), for supervised classification of time-ordered noisy data.
• To enable simultaneous learning of segmentation, feature discretization, and classification rules.
• To provide a computationally scalable solution for analyzing high-dimensional, non-stationary, and noisy time series.

Main Methods:

• eSPA-Markov extends entropic learning methodologies.
• It incorporates Markov regularization for improved pattern recognition.
• A one-shot numerical learning algorithm with linear scaling in dimension is proposed.

Main Results:

• The study proves the conditions for the existence and uniqueness of the learning problem solution.
• eSPA-Markov demonstrates efficient identification of persistent regimes and regime switches.
• Performance is validated against state-of-the-art methods on toy problems and real-world biological data (DNA/RNA Nanopore sequencing).

Conclusions:

• eSPA-Markov offers a robust and scalable approach for analyzing complex time series data.
• The methodology is particularly effective for high-dimensional, noisy, and non-stationary datasets.
• eSPA-Markov shows promise for applications in bioinformatics and other fields dealing with similar data challenges.