概率神经网络：频率和矩学习
Probabilistic Neural Network: Frequency and Moment Learnings
摘要：
我们介绍了概率神经网络，描述无监督同步学习的原子哈代空间和空间的有界实解析函数，分别。对于一个平稳的遍历向量过程，我们证明了概率神经网络产生一个独特的收集神经元的全局优化没有初始化和反向传播。在学习过程中，我们表明，所有的神经元相互沟通，在线性组合的意义上，直到学习完成。此外，我们给出收敛结果的稳定性的神经元，估计方法，和拓扑统计欣赏无监督估计的概率神经网络。作为应用，我们附上了驻波采样的数值实验。
英文摘要：
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.
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