Quantized Minimum Error Entropy Criterion

TL;DR

This paper introduces a quantized version of the minimum error entropy criterion to reduce computational complexity in nonlinear, non-Gaussian signal processing, enabling efficient large-scale data analysis.

Contribution

It proposes the QMEE criterion, which significantly lowers computational costs of MEE using quantization, making it suitable for large datasets.

Findings

QMEE reduces computational complexity from quadratic to linear scale.

QMEE maintains high performance in nonlinear, non-Gaussian scenarios.

Illustrative examples confirm the effectiveness of QMEE.

Abstract

Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy estimator, called information potential (IP), is a popular MEE cost in information theoretic learning (ITL). The computational complexity of IP is however quadratic in terms of sample number due to double summation. This creates computational bottlenecks especially for large-scale datasets. To address this problem, in this work we propose an efficient quantization approach to reduce the computational burden of IP, which decreases the complexity from O(N*N) to O (MN) with M << N. The new learning criterion is called the quantized MEE (QMEE). Some basic properties of QMEE are presented. Illustrative examples are provided to verify the excellent performance of QMEE.