# Quantized Minimum Error Entropy Criterion

arXiv: https://arxiv.org/abs/1710.04089 · HTML: https://mlsanity.com/paper/1710.04089/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [Error Loss Networks](https://mlsanity.com/paper/2106.03722/) (2021)
- [What Scales in Cross-Entropy Scaling Law?](https://mlsanity.com/paper/2510.04067/) (2025)
- [Reshaping Action Error Distributions for Reliable Vision-Language-Action Models](https://mlsanity.com/paper/2602.04228/) (2026)
- [Quantized criterion-based kernel recursive least squares adaptive filtering for time series prediction](https://mlsanity.com/paper/2307.01442/) (2023)
- [Robust Sparse Bayesian Learning Based on Minimum Error Entropy for Noisy High-Dimensional Brain Activity Decoding](https://mlsanity.com/paper/2508.11657/) (2025)

## Abstract (arXiv)

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.