cost = 1/(2*m) * np.sum((predictions - y)**2)
时间: 2023-11-14 12:49:42 浏览: 48
这是一个简单的均方误差(Mean Squared Error,MSE)的计算公式,用于衡量预测值与真实值之间的差异。其中,predictions 是预测值,y 是真实值,m 是样本数。具体来说,公式中的 (predictions - y)**2 表示每个样本的预测值与真实值之差的平方,再求和后除以 2*m 就得到了均方误差。均方误差越小,表示模型的预测能力越好。
相关问题
用python实现bp神经网络算法
以下是使用Python实现BP神经网络算法的步骤:
1.导入必要的库
```python
import numpy as np
```
2.定义sigmoid函数
```python
def sigmoid(x):
return 1 / (1 + np.exp(-x))
```
3.初始化权重和偏置
```python
def init_weights(layer_sizes):
weights = []
biases = []
for i in range(len(layer_sizes) - 1):
w = np.random.randn(layer_sizes[i], layer_sizes[i+1])
b = np.zeros((1, layer_sizes[i+1]))
weights.append(w)
biases.append(b)
return weights, biases
```
4.前向传播
```python
def forward_propagation(X, weights, biases):
a = X
activations = [a]
zs = []
for i in range(len(weights)):
z = np.dot(a, weights[i]) + biases[i]
a = sigmoid(z)
zs.append(z)
activations.append(a)
return activations, zs
```
5.计算代价函数
```python
def compute_cost(Y, Y_hat):
m = Y.shape[0]
cost = -1/m * np.sum(Y * np.log(Y_hat) + (1-Y) * np.log(1-Y_hat))
return cost
```
6.反向传播
```python
def backward_propagation(X, Y, weights, biases, activations, zs):
m = Y.shape[0]
dA = -(np.divide(Y, activations[-1]) - np.divide(1 - Y, 1 - activations[-1]))
dZ = dA * sigmoid(zs[-1]) * (1 - sigmoid(zs[-1]))
dW = 1/m * np.dot(activations[-2].T, dZ)
db = 1/m * np.sum(dZ, axis=0, keepdims=True)
dA_prev = np.dot(dZ, weights[-1].T)
dWs = [dW]
dbs = [db]
for i in range(len(weights) - 2, -1, -1):
dZ = dA_prev * sigmoid(zs[i]) * (1 - sigmoid(zs[i]))
dW = 1/m * np.dot(activations[i].T, dZ)
db = 1/m * np.sum(dZ, axis=0, keepdims=True)
dA_prev = np.dot(dZ, weights[i].T)
dWs.append(dW)
dbs.append(db)
dWs.reverse()
dbs.reverse()
return dWs, dbs
```
7.更新权重和偏置
```python
def update_weights(weights, biases, dWs, dbs, alpha):
for i in range(len(weights)):
weights[i] -= alpha * dWs[i]
biases[i] -= alpha * dbs[i]
return weights, biases
```
8.训练模型
```python
def train(X, Y, layer_sizes, alpha, epochs):
weights, biases = init_weights(layer_sizes)
for i in range(epochs):
activations, zs = forward_propagation(X, weights, biases)
cost = compute_cost(Y, activations[-1])
dWs, dbs = backward_propagation(X, Y, weights, biases, activations, zs)
weights, biases = update_weights(weights, biases, dWs, dbs, alpha)
if i % 100 == 0:
print("Epoch {}: cost = {}".format(i, cost))
return weights, biases
```
9.使用模型进行预测
```python
def predict(X, weights, biases):
activations, zs = forward_propagation(X, weights, biases)
predictions = (activations[-1] > 0.5).astype(int)
return predictions
```
Python matplotlib实现批量梯度下降
的过程中,如何画出损失函数随迭代次数变化的图像?
你可以使用以下代码来画出损失函数随迭代次数变化的图像:
```python
import matplotlib.pyplot as plt
# 初始化参数
theta = np.zeros([2, 1])
theta[0] = -10
theta[1] = -1
# 迭代次数和步长
iterations = 100
alpha = 0.01
# 初始化数据
X = np.random.rand(100)
Y = np.random.rand(100)
# 定义损失函数
def compute_cost(theta, X, Y):
m = len(Y)
predictions = X.dot(theta)
cost = 1/(2*m) * np.sum(np.square(predictions-Y))
return cost
# 执行梯度下降
def gradient_descent(theta, X, Y, alpha, iterations):
m = len(Y)
cost_history = np.zeros(iterations)
theta_history = np.zeros([iterations, 2])
for i in range(iterations):
predictions = X.dot(theta)
theta = theta - alpha * (1/m) * X.T.dot(predictions-Y)
theta_history[i] = theta.T
cost_history[i] = compute_cost(theta, X, Y)
return theta_history, cost_history
# 运行梯度下降并记录每次的theta和cost
theta_history, cost_history = gradient_descent(theta, X, Y, alpha, iterations)
# 画出损失函数随迭代次数变化的图像
plt.plot(range(iterations), cost_history)
plt.xlabel('迭代次数')
plt.ylabel('损失函数')
plt.show()
```
这段代码会生成一个损失函数随迭代次数变化的图像,可以清晰地看到损失函数在不断下降,说明梯度下降在有效地优化参数。
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