Low-cost scalable discretization, prediction, and feature selection for complex systems.

Area of Science:

• Computational modeling
• Data science
• Machine learning

Background:

• Discretization is essential for modeling complex systems.
• Existing methods like K-means clustering have limitations in quality, scalability, and cost.
• There is a need for efficient and accurate discretization techniques.

Purpose of the Study:

• To introduce a novel scalable probabilistic approximation (SPA) algorithm.
• To enable simultaneous data-driven optimal discretization, feature selection, and prediction.
• To demonstrate the algorithm's efficiency and performance improvements over existing methods.

Main Methods:

• Development of a low-cost, high-quality scalable probabilistic approximation (SPA) algorithm.
• Mathematical proofs of optimality, parallel efficiency, and linear scalability.
• Cross-validated applications to large-scale data classification and prediction tasks.

Main Results:

• SPA achieves simultaneous optimal discretization, feature selection, and prediction.
• The algorithm demonstrates linear scalability of iteration cost and parallel efficiency.
• Significant cost and performance improvements were observed in cross-validated applications.
• Example: Next-day European surface temperature predictions with 0.75°C mean error on a PC.

Conclusions:

• SPA offers a superior alternative to conventional discretization methods.
• The algorithm provides substantial cost reductions (5-6 orders of magnitude) and error improvements (~40%).
• SPA enables highly accurate predictions for complex systems, even on standard hardware.