Fast Learning in Quantitative Finance with Extreme Learning Machine
Fast Learning in Quantitative Finance with Extreme Learning Machine
This paper explores the application of Extreme Learning Machine (ELM) to various quantitative finance problems, emphasizing computational speed. ELM uses a single-hidden-layer neural network with randomly initialized hidden weights and output weights determined via convex optimization (least squares), eliminating iterative gradient-based training. The authors demonstrate ELM's effectiveness in both supervised and unsupervised learning tasks. In supervised learning, ELM is applied to learn parametric pricing functions for stochastic volatility models (Heston and rough Heston), achieving comparable accuracy to deep neural networks (DNNs) but with significantly faster training and inference. It also outperforms Gaussian process regression in volatility surface fitting and logistic regression in high-frequency return prediction. In unsupervised learning, ELM is integrated into Physics-Informed Neural Networks (PINNs) to solve financial partial differential equations (PDEs) like the Black-Scholes equation, offering faster training than traditional PINNs. The paper also discusses incremental ELM variants (e.g., EIR-ELM) that automatically determine network architecture and adapt to changing parameter domains without full retraining. Overall, ELM provides a computationally efficient alternative to DNNs for time-sensitive financial applications, with theoretical guarantees on approximation and generalization.
Highlights
- 1Demonstrates that Extreme Learning Machine (ELM) achieves fast training and inference in quantitative finance tasks, outperforming deep neural networks in speed while maintaining accuracy.
- 2Applies ELM to supervised learning tasks including option pricing, volatility surface fitting, and intraday return prediction, showing competitive performance against DNNs, GPR, and logistic regression.
- 3Integrates ELM into Physics-Informed Neural Networks (PINNs) for unsupervised learning, enabling efficient solution of financial PDEs such as the Black-Scholes equation.
- 4Introduces incremental ELM variants (EIR-ELM) that automatically determine network architecture and adapt to expanding parameter domains without slow retraining.
- 5Provides theoretical justification for ELM's universal approximation capability and generalization bounds, supporting its use in time-sensitive financial applications.
Methods
- MExtreme Learning Machine (ELM) with single-hidden-layer architecture, random hidden weights, and convex optimization via least squares.
- MIncremental ELM (EIR-ELM) for automatic node selection and regularization.
- MPhysics-Informed Neural Networks (PINNs) combined with ELM for solving PDEs without iterative gradient-based training.
- MComparison with deep neural networks (DNNs), Gaussian process regression (GPR), and logistic regression (LR) on financial datasets.
Results
- RELM achieves comparable accuracy to DNNs in approximating implied volatility surfaces for Heston and rough Heston models, with significantly faster training and inference times.
- RIn intraday return prediction, ELM outperforms logistic regression in terms of accuracy and computational efficiency.
- RELM-based PINNs solve the Black-Scholes PDE with high accuracy and reduced training time compared to traditional PINNs.
- RIncremental ELM (EIR-ELM) adapts to expanded parameter ranges without full retraining, maintaining accuracy while reducing computational cost.
- RELM demonstrates strong generalization in volatility surface fitting, mitigating overfitting compared to GPR.
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