python之回歸模型

創建線性回歸模型

import sklearn.linear_model as lm

sklearn.linear_model.LinearRegression()->線性回歸器
線性回歸器.fit(輸入樣本, 輸出標簽)
線性回歸器.predict(輸入樣本)->預測輸出標簽

4.94,4.37
-1.58,1.7
-4.45,1.88
-6.06,0.56
-1.22,2.23
-3.55,1.53
0.36,2.99
-3.24,0.48
1.31,2.76
2.17,3.99
2.94,3.25
-0.92,2.27
-0.91,2.0
1.24,4.75
1.56,3.52
-4.14,1.39
3.75,4.9
4.15,4.44
0.33,2.72
3.41,4.59
2.27,5.3
2.6,3.43
1.06,2.53
1.04,3.69
2.74,3.1
-0.71,2.72
-2.75,2.82
0.55,3.53
-3.45,1.77
1.09,4.61
2.47,4.24
-6.35,1.0
1.83,3.84
-0.68,2.42
-3.83,0.67
-2.03,1.07
3.13,3.19
0.92,4.21
4.02,5.24
3.89,3.94
-1.81,2.85
3.94,4.86
-2.0,1.31
0.54,3.99
0.78,2.92
2.15,4.72
2.55,3.83
-0.63,2.58
1.06,2.89
-0.36,1.99

import numpy as np
import sklearn.linear_model as lm
import sklearn.metrics as sm
import matplotlib.pyplot as mp

# x,y用來裝x,y上的點
x, y = [], []
with open('../ML/data/single.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])

x = np.array(x)
y = np.array(y)
# print(x)
# 創建線性回歸模型器
model = lm.LinearRegression()
# 導入數據
model.fit(x, y)
# 生成預測點
pred_y = model.predict(x)

# 畫訓練集的圖像
mp.figure('Linear Regression', facecolor='lightgray')
mp.title('Linear Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.55, s=60, label='Sample')

# 畫線性回歸的圖像
# argsort()函數是將x中的元素從小到大排列，提取其對應的index(索引)，然后輸出到y。
sorted_indices = x.T[0].argsort()
mp.plot(x[sorted_indices], pred_y[sorted_indices],
        'o-', c='orangered', label='Regression')

mp.legend()
mp.show()

保存模型

import numpy as np
import sklearn.linear_model as lm
import sklearn.metrics as sm
import matplotlib.pyplot as mp
# 導入pickle
import pickle

x, y = [], []
with open('../ML/data/single.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])

x = np.array(x)
y = np.array(y)
model = lm.LinearRegression()
model.fit(x, y)
pred_y = model.predict(x)

# sklearn中的回歸器性能評估方法

# 平均絕對值誤差（mean_absolute_error）
print(sm.mean_absolute_error(y, pred_y))
# 均方差（mean-squared-error）
print(sm.mean_squared_error(y, pred_y))
# 中值絕對誤差（Median absolute error）
print(sm.median_absolute_error(y, pred_y))
# R2 決定系數（擬合優度）
print(sm.r2_score(y, pred_y))

# 保存模型
with open('linear.pkl', 'wb') as f:
    pickle.dump(model, f)

mp.figure('Linear Regression', facecolor='lightgray')
mp.title('Linear Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.55, s=60, label='Sample')

sorted_indices = x.T[0].argsort()
mp.plot(x[sorted_indices], pred_y[sorted_indices],
        'o-', c='orangered', label='Regression')

mp.legend()
mp.show()

 導入模型

import numpy as np
import sklearn.linear_model as lm
import sklearn.metrics as sm
import matplotlib.pyplot as mp
import pickle

x, y = [], []
with open('../ML/data/single.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])
x = np.array(x)
y = np.array(y)

# 導入模型
with open('linear.pkl', 'rb') as f:
    model = pickle.load(f)
pred_y = model.predict(x)

mp.figure('Linear Regression', facecolor='lightgray')
mp.title('Linear Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.55, s=60, label='Sample')

sorted_indices = x.T[0].argsort()
mp.plot(x[sorted_indices], pred_y[sorted_indices],
        'o-', c='orangered', label='Regression')

mp.legend()
mp.show()

個別異常點對線性回歸線的影響

4.94,15
-1.58,1.7
-4.45,1.88
-6.06,0.56
-1.22,2.23
-3.55,1.53
0.36,2.99
-3.24,0.48
1.31,2.76
2.17,3.99
2.94,3.25
-0.92,2.27
-0.91,2.0
1.24,4.75
1.56,3.52
-4.14,1.39
3.75,10
4.15,12
0.33,2.72
3.41,4.59
2.27,5.3
2.6,3.43
1.06,2.53
1.04,3.69
2.74,3.1
-0.71,2.72
-2.75,2.82
0.55,3.53
-3.45,1.77
1.09,4.61
2.47,4.24
-6.35,1.0
1.83,3.84
-0.68,2.42
-3.83,0.67
-2.03,1.07
3.13,3.19
0.92,4.21
4.02,5.24
3.89,3.94
-1.81,2.85
3.94,4.86
-2.0,1.31
0.54,3.99
0.78,2.92
2.15,4.72
2.55,3.83
-0.63,2.58
1.06,2.89
-0.36,1.99

import numpy as np
import sklearn.linear_model as lm
import sklearn.metrics as sm
import matplotlib.pyplot as mp
x, y = [], []
#導入數據
with open('../../data/abnormal.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr
                in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])
x = np.array(x)
y = np.array(y)
model = lm.LinearRegression()
model.fit(x, y)
pred_y = model.predict(x)
print(sm.mean_absolute_error(y, pred_y))
print(sm.mean_squared_error(y, pred_y))
print(sm.median_absolute_error(y, pred_y))
print(sm.r2_score(y, pred_y))
mp.figure('Linear Regression', facecolor='lightgray')
mp.title('Linear Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.75,
           s=60, label='Sample')
sorted_indices = x.T[0].argsort()
mp.plot(x[sorted_indices], pred_y[sorted_indices],
        'o-', c='orangered', label='Regression')
mp.legend()
mp.show()

　　個別點對線性回歸模型影響

嶺回歸

　　用於消除個別點對線性模型的影響

　　

import numpy as np
import sklearn.linear_model as lm
import matplotlib.pyplot as mp
x, y = [], []
with open('../ML/data/abnormal.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])
x = np.array(x)
y = np.array(y)
# 線性回歸模型
model_ln = lm.LinearRegression()
model_ln.fit(x, y)
pred_y_ln = model_ln.predict(x)

# 嶺回歸模型
# fit_intercept是否修正截距，max_iter最大迭代次數，防止函數陷入死循環
model_rd = lm.Ridge(150, fit_intercept=True, max_iter=10000)
model_rd.fit(x, y)
pred_y_rd = model_rd.predict(x)

mp.figure('Ridge Regression', facecolor='lightgray')
mp.title('Ridge Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.75, s=60,
           label='Sample')

sorted_indices = x.T[0].argsort()
mp.plot(x[sorted_indices], pred_y_ln[sorted_indices],
        c='orangered', label='Linear')
mp.plot(x[sorted_indices], pred_y_rd[sorted_indices],
        c='limegreen', label='Ridge')
mp.legend()
mp.show()

　　嶺回歸減小了個別異常數據對整體的影響

多項式回歸分析

　　通過在原有特征中增加高次項，使得回歸線呈現多項式方程曲線特性，借以提高回歸的精度。

　　多項式次數過低可能導致欠擬合，即訓練樣本和測試樣本的精度都比較低，通過增加多項式次數可以提高精度，進而避免欠擬合，但若次數過高又會使得模型過於復雜，表現為對訓練樣本的高度匹配而與測試樣本則誤差奇大，這種現象稱為過擬合。

import numpy as np
# 導入管線
import sklearn.pipeline as pl
# 導入多項式
import sklearn.preprocessing as sp
import sklearn.linear_model as lm
import matplotlib.pyplot as mp
x, y = [], []
with open('../ML/data/single.txt', 'r') as f:
    for line in f.readlines():
        data = [float(substr) for substr in line.split(',')]
        x.append(data[:-1])
        y.append(data[-1])
x = np.array(x)
y = np.array(y)
# 創建多項式擴展器
pf = sp.PolynomialFeatures(10)
lr = lm.LinearRegression()
model = pl.make_pipeline(pf, lr)

model.fit(x, y)
# np.newaxis插入新的維度，使成為列
test_x = np.linspace(x.min(), x.max(), 1000)[:, np.newaxis]
pred_test_y = model.predict(test_x)

mp.figure('Polynomial Regression', facecolor='lightgray')
mp.title('Polynomial Regression', fontsize=20)
mp.xlabel('x', fontsize=14)
mp.ylabel('y', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.scatter(x, y, c='dodgerblue', alpha=0.75, s=60,
           label='Sample')
mp.plot(test_x, pred_test_y, c='orangered', label='Regression')
mp.legend()
mp.show()