Convergent Time-Varying Regression Models for Data Streams: Tracking Concept Drift by the Recursive Parzen-Based...

Area of Science:

• Data Mining
• Machine Learning
• Time Series Analysis

Background:

• Massive data streams present unique challenges: single-pass processing, constant memory, and adapting to stream changes.
• Existing data stream methods primarily focus on classification, with limited regression solutions often relying on heuristics.
• Concept drift in data streams necessitates models that can adapt to evolving data patterns.

Purpose of the Study:

• To develop mathematically justified regression models for time-varying data streams.
• To introduce and analyze incremental versions of generalized regression neural networks (IGRNNs).
• To prove the tracking properties (weak and strong convergence) of IGRNNs under various concept drift scenarios.

Main Methods:

• Development of incremental generalized regression neural networks (IGRNNs) utilizing Parzen kernels.
• Mathematical analysis to prove weak (in probability) and strong (with probability one) convergence properties.
• Simulation studies comparing IGRNNs against heuristic approaches (forgetting mechanisms, sliding windows).

Main Results:

• IGRNNs are presented for both stationary and time-varying systems under nonstationary noise.
• Convergence properties of IGRNNs are proven under different concept drift scenarios.
• Simulations demonstrate the effectiveness of IGRNNs compared to heuristic methods.

Conclusions:

• IGRNNs provide a mathematically robust framework for regression in dynamic data streams.
• The proposed method effectively handles concept drift, ensuring model adaptability.
• Application to currency exchange rate prediction demonstrates real-world utility.