房价预测的BP神经网络实现_python代码

# Package imports import pandas as pd import numpy as np import matplotlib.pyplot as plt def clc_accuracy(y_true, y_predict): """ use sklearn to calcuate the R2 score""" from sklearn.metrics import r2_score score = r2_score(y_true, y_predict) return score def sigmoid(Z): """ Compute the sigmoid of x Arguments: x -- A scalar or numpy array of any size. Return: s -- sigmoid(x) """ A = 1.0/(1.0+np.exp(-Z)) return A def sigmoid_backward(dA, cache): """ Implement the backward propagation for a single SIGMOID unit. Arguments: dA -- post-activation gradient, of any shape cache -- 'Z' where we store for computing backward propagation efficiently Returns: dZ -- Gradient of the cost with respect to Z """ Z = cache s = 1.0 / (1.0 + np.exp(-Z)) dZ = dA * s * (1 - s) assert (dZ.shape == Z.shape) return dZ def relu(Z): """ Implement the RELU function. Arguments: Z -- Output of the linear layer, of any shape Returns: A -- Post-activation parameter, of the same shape as Z cache -- a python dictionary containing "A" ; stored for computing the backward pass efficiently """ A = np.maximum(0, Z) assert (A.shape == Z.shape) return A def relu_backward(dA, cache): """ Implement the backward propagation for a single RELU unit. Arguments: dA -- post-activation gradient, of any shape cache -- 'Z' where we store for computing backward propagation efficiently Returns: dZ -- Gradient of the cost with respect to Z """ Z = cache dZ = np.array(dA, copy=True) # just converting dz to a correct object. # When z <= 0, you should set dz to 0 as well. dZ[Z <= 0] = 0 assert (dZ.shape == Z.shape) return dZ def layer_sizes(X, Y): """ Arguments: X -- input dataset of shape (input size, number of examples) Y -- labels of shape (output size, number of examples) Returns: n_x -- the size of the input layer n_h -- the size of the hidden layer n_y -- the size of the output layer """ n_x = X.shape[0] # size of input layer, number of features ? n_h = 4 n_y = Y.shape[0] # size of output layer return (n_x, n_h, n_y) def initialize_parameters(n_x, n_h, n_y): """ Argument: n_x -- size of the input layer n_h -- size of the hidden layer n_y -- size of the output layer Returns: params -- python dictionary containing your parameters: W1 -- weight matrix of shape (n_h, n_x) b1 -- bias vector of shape (n_h, 1) W2 -- weight matrix of shape (n_y, n_h) b2 -- bias vector of shape (n_y, 1) """ np.random.seed(2) # we set up a seed so that your output matches ours although the initialization is random. W1 = np.random.randn(n_h, n_x) * 0.01 b1 = np.zeros((n_h, 1)) W2 = np.random.randn(n_y, n_h) * 0.01 b2 = np.zeros((n_y, 1)) assert (W1.shape == (n_h, n_x)) assert (b1.shape == (n_h, 1)) assert (W2.shape == (n_y, n_h)) assert (b2.shape == (n_y, 1)) parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2} return parameters def forward_propagation(X, parameters): """ Argument: X -- input data of size (n_x, m) parameters -- python dictionary containing your parameters (output of initialization function) Returns: A2 -- The sigmoid output of the second activation cache -- a dictionary containing "Z1", "A1", "Z2" and "A2" """ # Retrieve each parameter from the dictionary "parameters" W1 = parameters["W1"] # b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] # Implement Forward Propagation to calculate A2 (probabilities) Z1 = np.dot(W1, X) + b1 #A1 = np.tanh(Z1) A1 = sigmoid(Z1) Z2 = np.dot(W2, A1) + b2 #A2 = sigmoid(Z2) A2 = Z2 assert (A2.shape == (1, X.shape[1])) cache = {"Z1": Z1, "A1": A1, "Z2": Z2, "A2": A2} return A2, cache def compute_cost(A2, Y, parameters): """ Computes the cross-entropy cost given in equation (13) Arguments: A2 -- The sigmoid output of the second activation, of shape (1, number of examples) Y -- "true" labels vector of shape (1, number of examples) parameters -- python dictionary containing your parameters W1, b1, W2 and b2 Returns: cost -- cross-entropy cost given equation (13) """ m = Y.shape[1] # number of example # Compute the cross-entropy cost #logprobs = np.multiply(np.log(A2), Y) + np.multiply(np.log(1 - A2), 1 - Y) logprobs = - 0.5 * np.multiply(A2-Y, A2-Y) cost = - 1.0 / m * np.sum(logprobs) cost = np.squeeze(cost) # makes sure cost is the dimension we expect. assert (isinstance(cost, float)) return cost def backward_propagation(parameters, cache, X, Y): """ Implement the backward propagation using the instructions above. Arguments: parameters -- python dictionary containing our parameters(W1,b1,W2,b2) cache -- a dictionary containing "Z1", "A1", "Z2" and "A2". X -- input data of shape (2, number of examples) Y -- "true" labels vector of shape (1, number of examples) Returns: grads -- python dictionary containing your gradients with respect to different parameters """ m = X.shape[1] # First, retrieve W1 and W2 from the dictionary "parameters". W1 = parameters["W1"] W2 = parameters["W2"] # Retrieve also A1 and A2 from dictionary "cache". A1 = cache["A1"] A2 = cache["A2"] Z1 = cache["Z1"] # Backward propagation: calculate dW1, db1, dW2, db2. dZ2 = A2 - Y dW2 = 1.0/m * np.dot(dZ2, A1.T) db2 = 1.0/m * np.sum(dZ2, axis=1, keepdims=True) #add each row, keep as 2D array dA1 = np.dot(W2.T, dZ2) #dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2)) dZ1 = sigmoid_backward(dA1, Z1) dW1 = 1.0/m * np.dot(dZ1, X.T) db1 = 1.0/m * np.sum(dZ1, axis=1, keepdims=True) grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2} return grads def update_parameters(parameters, grads, learning_rate=1.2): """ Updates parameters using the gradient descent update rule given above Arguments: parameters -- python dictionary containing your parameters grads -- python dictionary containing your gradients Returns: parameters -- python dictionary containing your updated parameters """ # Retrieve each parameter from the dictionary "parameters" W1 = parameters["W1"] b1 = parameters["b1"] W2 = parameters["W2"] b2 = parameters["b2"] # Retrieve each gradient from the dictionary "grads" dW1 = grads["dW1"] db1 = grads["db1"] dW2 = grads["dW2"] db2 = grads["db2"] # Update rule for each parameter W1 = W1 - learning_rate * dW1 b1 = b1 - learning_rate * db1 W2 = W2 - learning_rate * dW2 b2 = b2 - learning_rate * db2 parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2} return parameters def nn_model(X, Y, n_h, num_iterations=10000, print_cost=False): """ Arguments: X -- dataset of shape (2, number of examples) Y -- labels of shape (1, number of examples) n_h -- size of the hidden layer num_iterations -- Number of iterations in gradient descent loop print_cost -- if True, print the cost every 1000 iterations Returns: parameters -- parameters learnt by the model. They can then be used to predict. """ np.random.seed(3) n_x = layer_sizes(X, Y)[0] # (n_x, n_h, n_y) = layer_sizes(X, Y)