Patel Ashok, Kosko Bart
Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089-2564, USA.
Neural Netw. 2009 Jul-Aug;22(5-6):697-706. doi: 10.1016/j.neunet.2009.06.044. Epub 2009 Jul 3.
Five new theorems and a stochastic learning algorithm show that noise can benefit threshold neural signal detection by reducing the probability of detection error. The first theorem gives a necessary and sufficient condition for such a noise benefit when a threshold neuron performs discrete binary signal detection in the presence of additive scale-family noise. The theorem allows the user to find the optimal noise probability density for several closed-form noise types that include generalized Gaussian noise. The second theorem gives a noise-benefit condition for more general threshold signal detection when the signals have continuous probability densities. The third and fourth theorems reduce this noise benefit to a weighted-derivative comparison of signal probability densities at the detection threshold when the signal densities are continuously differentiable and when the noise is symmetric and comes from a scale family. The fifth theorem shows how collective noise benefits can occur in a parallel array of threshold neurons even when an individual threshold neuron does not itself produce a noise benefit. The stochastic gradient-ascent learning algorithm can find the optimal noise value for noise probability densities that do not have a closed form.
五个新定理和一种随机学习算法表明，噪声可以通过降低检测错误的概率来提高阈值神经信号检测的性能。第一个定理给出了在阈值神经元存在加性尺度族噪声时进行离散二进制信号检测时，这种噪声益处的充要条件。该定理允许用户针对包括广义高斯噪声在内的几种闭式噪声类型找到最优噪声概率密度。第二个定理给出了信号具有连续概率密度时更一般阈值信号检测的噪声益处条件。第三和第四个定理表明，当信号密度连续可微且噪声对称且来自尺度族时，这种噪声益处可归结为检测阈值处信号概率密度的加权导数比较。第五个定理表明，即使单个阈值神经元本身不会产生噪声益处，在阈值神经元的并行阵列中也会出现集体噪声益处。随机梯度上升学习算法可以为没有闭式的噪声概率密度找到最优噪声值。
