# LinearRegression,Ridge,Lasso
import numpy as np
from sklearn.linear_model import LinearRegression,Ridge,Lasso,RidgeCV,LassoCV
import matplotlib.pyplot as plt
%matplotlib inline
# 50个样本 200个特征
# 无解，无数个解
X = np.random.randn(50,200)
w = np.random.randn(200)
w
array([-0.71763223, -0.01975597, -1.66512775, 1.15509566, -1.30815193,
-0.07886716, -0.12621629, -0.48452705, -0.76894705, -1.27958424,
0.20661147, 0.07626266, -1.05664013, 1.43455568, 2.22725443,
0.13220785, 1.01291249, -1.87467501, -0.80073911, -0.86567154,
-1.24317069, 1.0130023 , 0.33956167, 0.75203886, 0.7022749 ,
-1.14882555, 0.634176 , -0.13809194, -2.03394849, -0.5516863 ,
1.1398463 , -0.51857542, -0.88925621, -0.27183436, 1.56244012,
0.66154914, 0.08529891, -0.18766498, -0.7229419 , 0.6913235 ,
1.66743931, 1.40285862, 0.50516722, 0.69088917, -0.13801636,
0.82850681, 0.62598677, 0.5211237 , 0.57181996, 0.91503186,
-1.14734987, 0.46803846, 0.49677025, -1.004296 , 1.3109282 ,
-1.91016754, 1.45630189, 0.08982377, -0.51922071, 0.46723805,
0.01055369, -0.48847605, -0.68935962, 1.6901229 , -0.23703418,
-0.64618434, -0.93594604, 1.48674155, 0.79347216, -2.45278997,
-0.1055643 , -1.10797711, 0.18312005, -1.63356662, 1.97703239,
-0.16488839, -0.64318795, -1.14363873, 0.66084745, 1.14099327,
0.9259731 , 0.04103045, -0.55955006, 0.52709757, -1.28036461,
0.74475445, -1.07053689, 0.20305404, 1.39808953, 0.31716686,
0.63150615, -1.00307068, -0.95333729, -0.69220477, -0.03925317,
-1.19738869, -0.01158072, -0.40013061, -2.18699458, -0.18176726,
1.16341707, -0.91878923, 1.03465085, -1.81036414, -0.8452893 ,
0.88631047, -0.07775361, -1.09726693, 1.18568627, 2.97868689,
0.15734896, 0.35259873, -1.18522538, -0.20386231, 1.06447013,
-1.50989228, -1.18713503, -2.72484655, 1.82771012, -0.56030818,
-1.26393399, 0.09519989, 0.75043212, 0.1845392 , 0.57406391,
0.32241044, -0.92922765, -1.81582008, -0.17089422, -0.82638478,
0.85685134, 0.33737166, -1.27335904, -0.12061047, 0.43116238,
0.69293522, -0.3116372 , 2.10697826, 0.22059706, -2.04990896,
1.20031869, -0.65923924, 0.21741321, 2.69016452, 1.79752197,
0.07034715, -0.74076325, 1.17818112, 1.27788198, 1.62346993,
-0.61267043, -0.50887636, 0.0502629 , -0.63902576, 1.78457654,
0.36369644, -1.59256726, 0.25070796, 0.02888558, 0.27984078,
0.79969306, 0.81636017, 0.09265504, -1.29414286, -0.41225244,
-0.90373965, -0.78816351, -0.81712267, 0.35288045, 0.46918612,
0.43737485, 1.29382308, 0.07552618, -2.20126151, -1.16065126,
-1.34731012, -0.61742243, 1.55812234, -0.5166435 , 0.79979653,
-1.12110086, 0.33189134, 0.63867508, 0.77258482, -0.78317738,
-0.00803317, -0.28364481, -1.92934529, -1.33925024, 0.01404032,
-1.69134308, 0.81528267, 0.26279143, 0.0321547 , -0.03219929,
-0.00751312, -0.08025871, -1.24736631, 0.52277507, 0.30633436])
# 将其中的190个置为0
index = np.arange(0,199)
np.random.shuffle(index)
index
array([102, 166, 151, 76, 68, 140, 60, 99, 92, 55, 125, 94, 132,
33, 177, 23, 111, 42, 110, 81, 179, 129, 192, 106, 34, 152,
29, 139, 171, 109, 52, 142, 173, 180, 131, 73, 98, 36, 26,
87, 28, 190, 183, 69, 88, 141, 178, 119, 48, 78, 169, 137,
25, 104, 120, 130, 5, 147, 146, 148, 107, 187, 79, 32, 4,
181, 77, 156, 112, 50, 59, 149, 172, 46, 114, 12, 134, 93,
31, 71, 138, 19, 66, 70, 10, 3, 96, 195, 61, 14, 49,
16, 182, 27, 193, 9, 196, 136, 15, 150, 75, 157, 116, 155,
133, 165, 145, 160, 162, 97, 121, 56, 84, 122, 82, 108, 194,
115, 124, 63, 7, 62, 86, 0, 30, 175, 58, 64, 18, 91,
6, 89, 53, 8, 189, 17, 143, 90, 51, 154, 159, 100, 164,
128, 174, 170, 1, 191, 39, 37, 117, 184, 105, 80, 144, 176,
101, 168, 186, 44, 67, 153, 41, 54, 11, 163, 47, 65, 22,
197, 24, 21, 167, 95, 161, 126, 74, 35, 2, 83, 127, 188,
198, 13, 135, 103, 118, 123, 38, 185, 85, 72, 45, 20, 40,
57, 43, 113, 158])
w[index[:190]] = 0
w
array([ 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
-1.24317069, 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
1.66743931, 0. , 0. , 0.69088917, 0. ,
0.82850681, 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0.08982377, 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0.18312005, 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0.74475445, 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , -0.20386231, 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0.02888558, 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0.30633436])
y = X.dot(w)
y
array([-3.87237903, 2.20010955, -0.2256118 , -0.37557475, -4.14212192,
1.04985011, -2.10190133, -3.26354501, -0.97369551, 6.60477669,
-1.41760307, 3.99964396, -0.80688322, -1.80704093, -0.22938875,
-0.17397568, -1.73476906, 2.66256959, -1.1235785 , -1.79337405,
-0.68295749, 0.84934801, 3.8256913 , -1.53396707, 2.78321804,
4.81322558, 5.66743923, -3.47945016, -0.5536171 , 3.44103892,
4.39879306, -2.25096992, 4.57986203, -1.27052193, 1.37985431,
-4.79615756, -0.1770027 , 0.12112281, -3.08041981, -0.69028005,
-4.23879438, -0.16577193, -2.06806875, 4.00844061, 0.05162934,
-4.99438005, -1.92438892, -5.47358088, -0.34889523, -1.70204475])
import warnings
warnings.filterwarnings('ignore') #针对粉红色的提示，在导入此包后不会再有
linear = LinearRegression()
ridge = RidgeCV(alphas=[0.001,0.01,0.1,1,2,5,10],cv = 5)
lasso = LassoCV(alphas=[0.001,0.01,0.1,1,2,5,10],cv = 3)
linear.fit(X,y)
ridge.fit(X,y)
lasso.fit(X,y)
LassoCV(alphas=[0.001, 0.01, 0.1, 1, 2, 5, 10], copy_X=True, cv=3, eps=0.001,
fit_intercept=True, max_iter=1000, n_alphas=100, n_jobs=None,
normalize=False, positive=False, precompute='auto', random_state=None,
selection='cyclic', tol=0.0001, verbose=False)
a = lasso.alphas_
a
array([ 1.00000000e+01, 5.00000000e+00, 2.00000000e+00,
1.00000000e+00, 1.00000000e-01, 1.00000000e-02,
1.00000000e-03])
linear_w = linear.coef_
ridge_w = ridge.coef_
lasso_w = lasso.coef_
plt.figure(figsize=(12,9))
axes = plt.subplot(2,2,1)
axes.plot(w)
axes = plt.subplot(2,2,2)
axes.plot(linear_w)
axes.set_title('linear')
axes = plt.subplot(2,2,3)
axes.plot(ridge_w)
axes.set_title('ridge')
axes = plt.subplot(2,2,4)
axes.plot(lasso_w)
axes.set_title('lasso')
Text(0.5,1,'lasso')
# 套索回归和标准回归最像