Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications
Summary: arXiv:2604.00987v1 Announce Type: cross
Abstract: We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling.
Introduction
Recent advancements in artificial intelligence have highlighted the importance of integrating structured knowledge with neural network models. The introduction of Structured-Knowledge-Informed Neural Networks (SKINNs) marks a significant step in this direction, allowing for a more comprehensive understanding of complex data-driven environments, particularly in finance.
Key Features of SKINNs
SKINNs present several innovative features that enhance their applicability in various fields, especially in finance:
- Unified Estimation Framework: SKINNs integrate both neural network parameters and structural parameters into a single optimization problem.
- Theoretical Consistency: The framework enforces theoretical consistency across a broader input domain, not just on observed data.
- Combination of Techniques: SKINNs combine various existing methodologies, including functional GMM, Bayesian updating, and surrogate modeling.
- Asymptotic Properties: They define a class of M-estimators that are consistent and asymptotically normal, ensuring robustness in parameter recovery.
Identification of Structural Parameters
One of the significant advantages of SKINNs is their ability to identify structural parameters while maintaining joint flexibility. This characteristic is vital in the context of finance, where market conditions can change rapidly. The framework provides:
- Generalization Bounds: SKINNs offer generalization and target-risk bounds, which are crucial for managing risks in financial portfolios.
- Bias-Variance Tradeoff: A restricted-optimal characterization of the weighting parameter governs the bias-variance tradeoff, enhancing model performance.
Financial Applications
An illustrative application of SKINNs in option pricing demonstrates their potential to improve financial decision-making:
- Out-of-Sample Valuation: SKINNs significantly enhance out-of-sample valuation and hedging performance, especially during periods of high volatility.
- Parameter Recovery: The framework recovers economically interpretable structural parameters, providing insights into market dynamics.
- Stability: Compared to conventional calibration methods, SKINNs exhibit improved stability in parameter estimation.
Conclusion
In summary, SKINNs represent a groundbreaking advancement in econometric frameworks by combining model-based reasoning with high-dimensional, data-driven estimation. Their application in finance, particularly in option pricing, showcases their potential to transform traditional approaches, offering enhanced performance and stability in parameter estimation.