Welcome to Neurological LRD Analysis’s documentation!
A comprehensive library for estimating Hurst exponents in neurological time series data, featuring classical methods, machine learning baselines, and comprehensive benchmarking capabilities.
Research Context: This library is developed as part of PhD research in Biomedical Engineering at the University of Reading, UK by Davian R. Chin, focusing on Physics-Informed Fractional Operator Learning for Real-Time Neurological Biomarker Detection: A Framework for Memory-Driven EEG Analysis.
Features
Classical Methods: DFA, R/S Analysis, Higuchi, Generalized Hurst Exponent, Periodogram, GPH, Whittle MLE, DWT, Abry-Veitch, MFDFA
Machine Learning Baselines: Random Forest, SVR, Gradient Boosting, Ensemble methods with 74+ feature extraction
Comprehensive Benchmarking: Direct comparison between classical and ML methods with real performance data
Fast Inference: 10-50ms prediction times with pretrained models
Neurological Scenarios: EEG, ECG, respiratory signals with realistic artifacts
GPU Acceleration: JAX and NumPyro integration for Bayesian inference
Clinical Relevance: Specialized for Parkinson’s disease, epilepsy, and neurological conditions
Quick Start
Install the package:
pip install neurological-lrd-analysis
Basic usage:
Classical Methods:
from neurological_lrd_analysis import BiomedicalHurstEstimatorFactory, EstimatorType
# Create factory instance
factory = BiomedicalHurstEstimatorFactory()
# Estimate Hurst exponent using DFA
result = factory.estimate(
data=your_time_series,
method=EstimatorType.DFA,
confidence_method="bootstrap",
n_bootstrap=100
)
print(f"Hurst exponent: {result.hurst_estimate:.3f}")
Machine Learning Methods:
from neurological_lrd_analysis import (
create_pretrained_suite, quick_predict, quick_ensemble_predict
)
# Create pretrained models (one-time setup)
create_pretrained_suite("pretrained_models", force_retrain=True)
# Fast ML prediction (10-50ms)
hurst_ml = quick_predict(your_time_series, "pretrained_models", "random_forest")
# Ensemble prediction (best accuracy)
hurst_ensemble, uncertainty = quick_ensemble_predict(your_time_series, "pretrained_models")
Contents
Getting Started
User Guide
Machine Learning
Research
- Long-Range Dependence Estimators: A Comprehensive Survey of Classical, Machine Learning, and Neural Network Approaches
- Abstract
- 1. Introduction
- 2. Classical Methods
- 3. Machine Learning Methods
- 4. Neural Network Methods
- 5. Comparative Analysis and Performance Evaluation
- 6. Implementation Considerations
- 7. Applications and Case Studies
- 8. Future Directions and Emerging Trends
- 9. Practical Guidelines for Method Selection
- 10. Conclusion
- References
- Most Common Techniques for Estimating the Hurst Exponent in Time Series Data
- Wavelet-Based Long-Range Dependence Estimators: A Comprehensive Mathematical Framework
- Abstract
- 1. Introduction
- 2. Multiresolution Analysis and Wavelet Transforms
- 3. Classical Wavelet-Based Estimators
- 4. Non-Decimated Wavelet Transform Methods
- 5. Robust Trimean-Based Estimators
- 6. Multivariate Wavelet Estimators
- 7. Continuous Wavelet Transform Approaches
- 8. Statistical Properties and Performance Analysis
- 9. Practical Implementation Considerations
- 10. Applications and Case Studies
- 11. Software Implementation and Tools
- 12. Recent Developments and Future Directions
- 13. Limitations and Challenges
- 14. Comparative Performance Analysis
- 15. Conclusions and Recommendations
- References