2.5 KiB
2.5 KiB
| title | localeTitle |
|---|---|
| Linear Regression | 线性回归 |
线性回归
线性回归有助于我们根据其他变量Y的得分预测变量X的得分。当绘制变量Y时，线性回归找到通过点的最佳拟合直线。最合适的线称为回归线。
在Python中：
#Price of wheat/kg and the average price of bread
wheat_and_bread = [[0.5,5],[0.6,5.5],[0.8,6],[1.1,6.8],[1.4,7]]
def step_gradient(b_current, m_current, points, learningRate):
b_gradient = 0
m_gradient = 0
N = float(len(points))
for i in range(0, len(points)):
x = points[i][0]
y = points[i][1]
b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
new_b = b_current - (learningRate * b_gradient)
new_m = m_current - (learningRate * m_gradient)
return [new_b, new_m]
def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
b = starting_b
m = starting_m
for i in range(num_iterations):
b, m = step_gradient(b, m, points, learning_rate)
return [b, m]
gradient_descent_runner(wheat_and_bread, 1, 1, 0.01, 100)
代码示例来自本文 。它还解释了梯度下降和深度学习的其他基本概念。
值得注意的是，并非所有线性回归都是通过梯度下降完成的。正规方程也可以用于找到线性回归系数，但是，这使用矩阵乘法，因此使用超过100,000或1,000,000个实例可能非常耗时。
在Python中： 使用scikit库直接应用，因此即使在大型数据集上也可以轻松使用线性回归。
import pandas as pd
from sklearn.cross_validation import train_test_split
from sklearn.linear_model import LinearRegression as lr
train = pd.read_csv('../input/train.csv')
test = pd.read_csv('../input/test.csv')
X = train.iloc[:, 0:4].values
y = train.iloc[:, 4].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
X_train
model = lr()
model.fit(X_train, y_train)
print(model.score(X_train,y_train))
y_pred_class = model.predict(X_test)
model.score(X_train,y_train)
print(model.coef_)
print(model.intercept_)
# calculate accuracy
from sklearn import metrics
print(metrics.accuracy_score(y_test, y_pred_class))