Quantized Minimum Error Entropy Criterion
This work addresses a computational problem for researchers and practitioners in signal processing and machine learning dealing with large-scale datasets, though it is incremental as it builds on existing MEE methods.
The paper tackles the computational bottleneck of the minimum error entropy (MEE) criterion, which has quadratic complexity, by proposing a quantization approach that reduces complexity from O(N^2) to O(MN) with M << N, resulting in the quantized MEE (QMEE) method.
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.