bp回归代码 python

以下是一个简单的BP回归代码的Python实现，其中包括数据加载、网络构建、训练和保存参数等步骤：

import numpy as np
import random

class Network(object):
    def __init__(self, sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])]

    def feedforward(self, a):
        for b, w in zip(self.biases, self.weights):
            a = sigmoid(np.dot(w, a)+b)
        return a

    def SGD(self, training_data, epochs, mini_batch_size, eta, lmbda = 0.0, evaluation_data=None, monitor_evaluation_cost=False, monitor_evaluation_accuracy=False, monitor_training_cost=False, monitor_training_accuracy=False):
        if evaluation_data: n_data = len(evaluation_data)
        n = len(training_data)
        evaluation_cost, evaluation_accuracy = [], []
        training_cost, training_accuracy = [], []
        for j in range(epochs):
            random.shuffle(training_data)
            mini_batches = [training_data[k:k+mini_batch_size] for k in range(0, n, mini_batch_size)]
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta, lmbda, len(training_data))
            print("Epoch %s training complete" % j)
            if monitor_training_cost:
                cost = self.total_cost(training_data, lmbda)
                training_cost.append(cost)
                print("Cost on training data: {}".format(cost))
            if monitor_training_accuracy:
                accuracy = self.accuracy(training_data, convert=True)
                training_accuracy.append(accuracy)
                print("Accuracy on training data: {} / {}".format(accuracy, n))
            if monitor_evaluation_cost:
                cost = self.total_cost(evaluation_data, lmbda, convert=True)
                evaluation_cost.append(cost)
                print("Cost on evaluation data: {}".format(cost))
            if monitor_evaluation_accuracy:
                accuracy = self.accuracy(evaluation_data)
                evaluation_accuracy.append(accuracy)
                print("Accuracy on evaluation data: {} / {}".format(self.accuracy(evaluation_data), n_data))
            print()
        return evaluation_cost, evaluation_accuracy, training_cost, training_accuracy

    def update_mini_batch(self, mini_batch, eta, lmbda, n):
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        for x, y in mini_batch:
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)
            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
        self.weights = [(1-eta*(lmbda/n))*w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]
        self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]

    def backprop(self, x, y):
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        activation = x
        activations = [x]
        zs = []
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation)+b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
        delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        for l in range(2, self.num_layers):
            z = zs[-l]
            sp = sigmoid_prime(z)
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
        return (nabla_b, nabla_w)

    def accuracy(self, data, convert=False):
        if convert:
            results = [(np.argmax(self.feedforward(x)), np.argmax(y)) for (x, y) in data]
        else:
            results = [(np.argmax(self.feedforward(x)), y) for (x, y) in data]
        return sum(int(x == y) for (x, y) in results)

    def total_cost(self, data, lmbda, convert=False):
        cost = 0.0
        for x, y in data:
            a = self.feedforward(x)
            if convert: y = vectorized_result(y)
            cost += self.cost.fn(a, y)/len(data)
        cost += 0.5*(lmbda/len(data))*sum(np.linalg.norm(w)**2 for w in self.weights)
        return cost

    def cost_derivative(self, output_activations, y):
        return (output_activations-y)

def sigmoid(z):
    return 1.0/(1.0+np.exp(-z))

def sigmoid_prime(z):
    return sigmoid(z)*(1-sigmoid(z))

def vectorized_result(j):
    e = np.zeros((2, 1))
    e[j] = 1.0
    return e

def load_data():
    # 加载数据
    # 返回一个元组(training_data, validation_data, test_data)
    # training_data是一个列表，其中包含50,000个元组(x, y)。
    # x是784维的numpy.ndarray，表示输入图像。y是10维的numpy.ndarray，表示输出标签。
    # validation_data和test_data是包含10,000个元组(x, y)的列表。
    # x是784维的numpy.ndarray，表示输入图像。y是数字标签。
    import pickle
    import gzip
    with gzip.open('mnist.pkl.gz', 'rb') as f:
        training_data, validation_data, test_data = pickle.load(f, encoding='iso-8859-1')
    return (training_data, validation_data, test_data)

def load_data_wrapper():
    # 加载数据，并将其转换为适合训练神经网络的格式
    # 返回一个元组(training_data, validation_data, test_data)
    # training_data是一个列表，其中包含50,000个元组(x, y)。
    # x是784维的numpy.ndarray，表示输入图像。y是10维的numpy.ndarray，表示输出标签。
    # validation_data和test_data是包含10,000个元组(x, y)的列表。
    # x是784维的numpy.ndarray，表示输入图像。y是数字标签。
    tr_d, va_d, te_d = load_data()
    training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
    training_results = [vectorized_result(y) for y in tr_d[1]]
    training_data = list(zip(training_inputs, training_results))
    validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
    validation_data = list(zip(validation_inputs, va_d[1]))
    test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
    test_data = list(zip(test_inputs, te_d[1]))
    return (training_data, validation_data, test_data)

if __name__ == '__main__':
    training_data, validation_data, test_data = load_data_wrapper()
    net = Network([784, 30, 10])
    net.SGD(training_data, 30, 10, 3.0, test_data=test_data)