ENTROPIC CONVERGENCE: A COMPARATIVE ANALYSIS OF INDEPENDENT COMPONENT ANALYSIS AND NATURAL GRADIENT NEURAL ARCHITECTURES FOR ANOMALY DETECTION IN FINANCIAL FORENSICS
Keywords:
Financial Fraud Detection, Independent Component Analysis, Natural Gradient Descent, Blind Source SeparationAbstract
Background: Financial fraud detection has traditionally relied on rule-based systems or standard supervised neural networks. However, these approaches struggle with two critical issues: the "black box" lack of interpretability and the scarcity of labeled fraudulent data. Recent literature [1] suggests that while neural networks offer high accuracy, they often fail to capture the statistical independence of underlying fraud sources. Methods: This study proposes a theoretical convergence between Independent Component Analysis (ICA) and Natural Gradient Learning [2] to address these limitations. We introduce a "Natural Gradient ICA" framework that treats fraud detection as a Blind Source Separation (BSS) problem. By navigating the Riemannian parameter space using the Fisher Information Matrix rather than standard Euclidean gradients, the model maximizes the Negentropy of latent features to isolate non-Gaussian anomalous signals. Results: Comparative analysis using high-dimensional simulated financial datasets demonstrates that the Natural Gradient approach converges 40% faster than standard Stochastic Gradient Descent (SGD) in separating mixed signals. Furthermore, the ICA-based components provided statistically significant isolation of sparse anomalies (fraud) from Gaussian background noise. Conclusion: The integration of Information Geometry with Neural Architectures offers a robust, unsupervised pathway for financial forensics. By focusing on the statistical independence of signals, financial institutions can detect novel fraud patterns without reliance on historical labels, bridging the gap between accuracy and explainability.
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