scikit learning 線性回歸學習

多項式回歸損失函式為均方誤差，迭代計算方式為梯度下降；在scikit-learning中，多項式回歸由sklearn.linear_model.linearregression。

當特徵不足導致欠擬合時，可以採用特徵組合的方式產生多項式特徵,在scikit-learning中，用sklearn.preprocessing.polynomialfeatures產生多項式特徵。

sklearn.pipline.pipline可以把多個模型串聯起來，執行起來相當於乙個模型。

import matplotlib.pyplot as plt

import numpy as np
from sklearn.linear_model import linearregression
from sklearn.preprocessing import polynomialfeatures
from sklearn.pipeline import pipeline
from sklearn.metrics import mean_squared_error
#多項式回歸由sklearn.linear_model.linearregression實現
#sklearn.preprocessing.polynomialfeatures產生多項式特徵
#sklearn.pipline.pipline把生成多項式特徵和線性回歸訓練串聯起來
defgenerate_dot
(dot_num, left, right)
:    x = np.linspace(left, right, dot_num)
y = np.cos(x)
+0.2
* np.random.random(dot_num)
-0.1
x = x.reshape(-1
,1)    y = y.reshape(-1
,1)return
(x,y)
defpolynomial_regression
(degree=1)
:    polynomial_features = polynomialfeatures(degree=degree, include_bias=
false
)    linear_regression_model = linearregression(normalize=
true
)#資料歸一化
new_model = pipeline([(
"polynomial_features"
, polynomial_features),(
"linear_regression"
, linear_regression_model)])
return new_model
deftrain_model
(x,y,degrees)
:   
res =
for degree in degrees:
model = polynomial_regression(degree)
model.fit(x, y)
train_score = model.score(x, y)
#**點的值和其實際值均方根誤差
mse = mean_squared_error(y, model.predict(x)))
for r in res:
print
("degree: {}; train score: {}; mean squared error: {}"
.format
(r["degree"
], r[
"score"
], r[
"mse"])
)return res
x,y = generate_dot(
100,-7
,7)degrees =[2
,3,4
,5,6
,10]result = train_model(x,y,degrees)
#視覺化
plt.figure(figsize=(12
,7), dpi=
300)
for index, dic in
enumerate
(result)
:    fig = plt.subplot(2,
3, index +1)
plt.title(
"modle degree : %d"
%dic[
"degree"])
plt.scatter(x, y, s=
4, alpha=
0.5)
plt.plot(x, dic[
"model"
].predict(x)
,'r--'
)plt.show(
)

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