[机器学习-实践篇]学习之线性回归、岭回归、Lasso回归，tensorflow实现的线性回归

前言

本章主要介绍线性回归、岭回归、Lasso回归，tensorflow实现的线性回归的简单例子代码。
原理篇看这里
[机器学习-原理篇]学习之线性回归、岭回归、Lasso回归

1.线性回归

from sklearn import linear_model
def test_linearRegression(X, y):
    clf = linear_model.LinearRegression()
    clf.fit(X, y)
    print('linearRegression coef:',clf.coef_)
    print('linearRegression intercept:',clf.intercept_)
if __name__ == '__main__':
    X = [[0, 0], [1, 1], [2, 2.]]
    y = [[0], [1], [2.]]
    test_linearRegression(X, y)

linearRegression coef: [[0.5 0.5]]
linearRegression intercept: [1.11022302e-16]

2. 岭回归

from sklearn import linear_model
def test_ridge(X, y):
    clf = linear_model.Ridge(alpha=.1)
    clf.fit(X, y)
    print('ridge coef:',clf.coef_)
    print('ridge intercept',clf.intercept_)
if __name__ == '__main__':
    X = [[0, 0], [1, 1], [2, 2.]]
    y = [[0], [1], [2.]]
    test_ridge(X, y)

ridge coef: [[0.48780488 0.48780488]]
ridge intercept [0.02439024]

3. Lasso回归

from sklearn import linear_model
def test_lasso(X, y):
    clf = linear_model.Lasso(alpha=0.1)
    clf.fit(X, y)
    print('lasso coef:',clf.coef_)
    print('lasso intercept: ',clf.intercept_)
if __name__ == '__main__':
    X = [[0, 0], [1, 1], [2, 2.]]
    y = [[0], [1], [2.]]
    test_lasso(X, y)    

从这个例子看出，第二特征的权重直接是0， 由此可以进一步得出结论
lasso 可以用来做 feature selection，而 ridge 不行。或者说，lasso 更容易使得权重变为 0，而 ridge 更容易使得权重接近 0。

lasso coef: [0.85 0.  ]
lasso intercept:  [0.15]

4. tensorflow利用梯度下降实现的线性回归

import tensorflow as tf
TRAIN_STEPS = 10
def test_tensorflow1(X, y):
    w = tf.Variable(initial_value=[[1.0],[1.0]])
    #w2 = tf.Variable(initial_value=1.0)
    b = tf.Variable(initial_value=0.)

    optimizer = tf.keras.optimizers.SGD(0.1)
    mse = tf.keras.losses.MeanSquaredError()

    for i in range(TRAIN_STEPS):
        #print("epoch:", i)
        #print("w1:", w.numpy())
        #print("b:", b.numpy())
        with tf.GradientTape(persistent=True,watch_accessed_variables=True) as g:
            logit = tf.matmul(X, w) + b
            loss = mse(y, logit)
            #loss = (y - logit)*(y - logit)

        gradients = g.gradient(target=loss, sources=[w, b]) # 计算梯度
        #print(gradients)
        optimizer.apply_gradients(zip(gradients, [w, b]))  # 更新梯度
    print("test_tensorflow1 w1:", w.numpy())
    print("test_tensorflow1 b:", b.numpy())

def test_tensorflow2(X, y):
    w = tf.Variable(initial_value=[[1.0],[1.0]])
    #w2 = tf.Variable(initial_value=1.0)
    b = tf.Variable(initial_value=0.)

    optimizer = tf.keras.optimizers.SGD(0.1)
    mse = tf.keras.losses.MeanSquaredError()

    for i in range(TRAIN_STEPS):
        #print("epoch:", i)
        #print("w1:", w.numpy())
        #print("b:", b.numpy())
        with tf.GradientTape(persistent=True,watch_accessed_variables=True) as g:
            logit = tf.matmul(X, w) + b
            loss = tf.square((y - logit))
            loss = tf.reduce_sum(loss)/3

        gradients = g.gradient(target=loss, sources=[w, b]) # 计算梯度
        #print(gradients)
        optimizer.apply_gradients(zip(gradients, [w, b]))  # 更新梯度

    print("test_tensorflow2 w1:", w.numpy())
    print("test_tensorflow2 b:", b.numpy())

if __name__ == '__main__':
    X = [[0, 0], [1, 1], [2, 2.]]
    #X = [[0], [1], [2]]
    y = [[0], [1], [2.]]
    test_linearRegression(X, y)
    test_lasso(X, y)
    test_ridge(X, y)
    test_tensorflow1(X, y)
    test_tensorflow2(X, y)

test_tensorflow1 w1: [[0.5456011]
 [0.5456011]]
test_tensorflow1 b: -0.13680318
test_tensorflow2 w1: [[0.5456011]
 [0.5456011]]
test_tensorflow2 b: -0.13680318