论文标题
概率神经网络：频率和力矩学习
Probabilistic Neural Network: Frequency and Moment Learnings
论文作者
论文摘要
我们介绍了概率的神经网络，这些神经网络分别描述了在原子硬质空间和有限的真实分析功能的空间上进行无监督的同步学习。对于固定的厄贡矢量过程，我们证明概率神经网络在无初始化和后传播的情况下产生了全局优化中独特的神经元集合。在学习过程中，我们表明，从线性组合的意义上讲，所有神经元都相互通信，直到学习完成为止。此外，我们为神经元，估计方法和拓扑统计的稳定性提供了收敛结果，以欣赏概率神经网络的无监督估计。作为应用，我们将数值实验附加在由常驻波绘制的样品上。
We introduce probabilistic neural networks that describe unsupervised synchronous learning on an atomic Hardy space and space of bounded real analytic functions, respectively. For a stationary ergodic vector process, we prove that the probabilistic neural network yields a unique collection of neurons in global optimization without initialization and back-propagation. During learning, we show that all neurons communicate with each other, in the sense of linear combinations, until the learning is finished. Also, we give convergence results for the stability of neurons, estimation methods, and topological statistics to appreciate unsupervised estimation of a probabilistic neural network. As application, we attach numerical experiments on samples drawn by a standing wave.
