python – 神经网络训练平稳的梯度下降

我一直在尝试在python中实现一个基本的back-propogation神经网络,并完成了初始化和训练权重集的编程.然而,在我训练的所有集合上,误差(均方)总是收敛到一个奇怪的数字 – 错误总是在进一步的迭代中减少,但从未真正接近零.
任何帮助将非常感激.

import csv
import numpy as np

class NeuralNetwork:
layers = 0
shape = None
weights = []

layerIn = []
layerOut = []

def __init__(self, shape):
    self.shape = shape
    self.layers = len(shape) - 1

    for i in range(0,self.layers):
        n = shape[i]
        m = shape[i+1]
        self.weights.append(np.random.normal(scale=0.2, size = (m,n+1)))

def sgm(self, x):
    return 1/(1+np.exp(-x))

def dersgm(self, x):
    y = self.sgm(x)
    return y*(y-1)


def run(self, input):
    self.layerIn = []
    self.layerOut = []

    for i in range(self.layers):
        if i == 0:
            layer = self.weights[0].dot(np.vstack((input.transpose(), np.ones([1,input.shape[0]]))))
        else:
            layer = self.weights[i].dot(np.vstack((self.layerOut[-1], np.ones([1,input.shape[0]]))))
        self.layerIn.append(layer)
        self.layerOut.append(self.sgm(layer))

    return self.layerOut[-1].T

def backpropogate(self, input, y, learning_rate):
    deltas = []
    y_hat = self.run(input)

    #Calculate deltas
    for i in reversed(range(self.layers)):

        #for last layer
        if i == self.layers-1:
            error = y_hat - y
            msq_error = sum(.5 * ((error) ** 2))
            #returns delta, k rows for k inputs, m columns for m nodes
            deltas.append(error * self.dersgm(y_hat))
        else:

            error = deltas[-1].dot(self.weights[i+1][:,:-1])
            deltas.append(self.dersgm(self.layerOut[i]).T * error)

    #Calculate weight-deltas
    wdelta = []
    ordered_deltas = list(reversed(deltas)) #reverse order because created backwards

    #returns weight deltas, k rows for k nodes, m columns for m next layer nodes
    for i in range(self.layers):
        if i == 0:
            #add bias
            input_with_bias = np.vstack((input.T, np.ones(input.shape[0])))
            #some over n rows of deltas for n training examples to get one delta for all examples
            #for all nodes
            wdelta.append(ordered_deltas[i].T.dot(input_with_bias.T))
        else:
            with_bias = np.vstack((self.layerOut[i-1], np.ones(input.shape[0])))
            wdelta.append(ordered_deltas[i].T.dot(with_bias.T))



    #update_weights
    def update_weights(self, weight_deltas, learning_rate):
        for i in range(self.layers):
            self.weights[i] = self.weights[i] +\
                              (learning_rate * weight_deltas[i])


    update_weights(self, wdelta, learning_rate)

    return msq_error

    #end backpropogate

def train(self, input, target, lr, run_iter):
    for i in range(run_iter):
        if i % 100000 == 0:
            print self.backpropogate(input, target, lr)

解决方法:

以下场景中的误差函数不能为0,因为误差函数为0将要求点与曲线完美匹配.

拥有更多神经元肯定会减少误差,因为该功能可以具有更复杂和精确的形状.但是,如果您对数据非常适合,则会出现称为过度拟合的问题,如下图所示.从左到右,曲线要么不适合数据集,要么几乎正确拟合,然后右边的过度拟合.

右边的场景会导致错误为0,但这不是必需的,你想避免这种情况.怎么样？

确定网络中神经元数量是否理想(具有良好拟合)的最简单方法是通过反复试验.将您的数据分成训练数据(80％ – 训练网络)和测试数据(20％ – 仅保留用于在训练后测试网络).虽然只训练训练数据,但可以在测试数据集上绘制性能.

您还可以使用第3个数据集进行验证,请参阅：
whats is the difference between train, validation and test set, in neural networks?

标签：python,machine-learning,neural-network,numpy,gradient-descent
来源： https://codeday.me/bug/20190628/1317390.html