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Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in general the analytical evaluation of error entropy is not possible. By the Parzen windowing approach, the estimated error entropy converges asymptotically to the entropy of the error plus an independent random variable whose probability density function (PDF) corresponds to the kernel function in the Parzen method. This quantity of entropy is called the smoothed error entropy, and the corresponding optimality criterion is named the smoothed MEE (SMEE) criterion. In this paper, we study theoretically the SMEE criterion in supervised machine learning where the learning machine is assumed to be nonparametric and universal. Some basic properties are presented. In particular, we show that when the smoothing factor is very small, the smoothed error entropy equals approximately the true error entropy plus a scaled version of the Fisher information of error. We also investigate how the smoothing factor affects the optimal solution. In some special situations, the optimal solution under the SMEE criterion does not change with increasing smoothing factor. In general cases, when the smoothing factor tends to infinity, minimizing the smoothed error entropy will be approximately equivalent to minimizing error variance, regardless of the conditional PDF and the kernel. [ABSTRACT FROM AUTHOR]

The minimum error entropy (MEE) criterion has been receiving increasing attention due to its promising perspectives for applications in signal processing and machine learning. In the context of Bayesian estimation, the MEE criterion is concerned with the estimation of a certain random variable based on another random variable, so that the error's entropy is minimized. Several theoretical results on this topic have been reported. In this work, we present some further results on the MEE estimation. The contributions are twofold: (1) we extend a recent result on the minimum entropy of a mixture of unimodal and symmetric distributions to a more general case, and prove that if the conditional distributions are generalized uniformly dominated (GUD), the dominant alignment will be the MEE estimator; (2) we show by examples that the MEE estimator (not limited to singular cases) may be non-unique even if the error distribution is restricted to zero-mean (unbiased). [ABSTRACT FROM AUTHOR]

The spiking neural network (SNN) is regarded as a promising candidate to deal with the great challenges presented by current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the online meta-learning performance of artificial neural networks. Importantly, existing spike-based online meta-learning models do not target the robust learning based on spatio-temporal dynamics and superior machine learning theory. In this invited article, we propose a novel spike-based framework with minimum error entropy, called MeMEE, using the entropy theory to establish the gradient-based online meta-learning scheme in a recurrent SNN architecture. We examine the performance based on various types of tasks, including autonomous navigation and the working memory test. The experimental results show that the proposed MeMEE model can effectively improve the accuracy and the robustness of the spike-based meta-learning performance. More importantly, the proposed MeMEE model emphasizes the application of the modern information theoretic learning approach on the state-of-the-art spike-based learning algorithms. Therefore, in this invited paper, we provide new perspectives for further integration of advanced information theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) can be deployed as base stations (BSs) for emergency communications of user equipments (UEs) in 5G/6G networks. In multi-UAV communication networks, UAVs' load balancing and UEs' data rate fairness are two challenging problems and can be optimized by UAV deployment strategies. In this work, we found that these two problems are related by the same performance metric, which makes it possible to optimize the two problems simultaneously. To solve this joint optimization problem, we propose a UAV diffusion deployment algorithm based on the virtual force field method. Firstly, according to the unique performance metric, we define two new virtual forces, which are the UAV-UAV force and UE-UAV force defined by FU and FV, respectively. FV is the main contributor to load balancing and UEs' data rate fairness, and FU contributes to fine tuning the UEs' data rate fairness performance. Secondly, we propose a diffusion control stratedy to the update UAV-UAV force, which optimizes FV in a distributed manner. In this diffusion strategy, each UAV optimizes the local parameter by exchanging information with neighbor UAVs, which achieve global load balancing in a distributed manner. Thirdly, we adopt the successive convex optimization method to update FU, which is a non-convex problem. The resultant force of FV and FU is used to control the UAVs' motion. Simulation results show that the proposed algorithm outperforms the baseline algorithm on UAVs' load balancing and UEs' data rate fairness. [ABSTRACT FROM AUTHOR]