はじめに
sklearnのdatasets.make_regressionで回帰問題用のランダムなデータを作成することができる。ここでは各種パラメータが生成するデータに及ぼす影響について説明する。
解説
モジュールのインポートなど
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import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
plt.rcParams['scatter.edgecolors'] = "gray"
バージョン
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#version
import matplotlib
print(matplotlib.__version__)
3.3.3
import sklearn
print(sklearn.__version__)
0.24.0
n_samples
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#n_samples
X1,Y1 = make_regression(n_samples=10,n_features=1,n_informative=1)
X2,Y2 = make_regression(n_samples=20,n_features=1,n_informative=1)
X3,Y3 = make_regression(n_samples=50,n_features=1,n_informative=1)
X4,Y4 = make_regression(n_samples=100,n_features=1,n_informative=1)
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X1[:,0],Y1,s=20)
ax[1].scatter(X2[:,0],Y2,s=20)
ax[2].scatter(X3[:,0],Y3,s=20)
ax[3].scatter(X4[:,0],Y4,s=20)
ax[0].set_title("n_samples=10")
ax[1].set_title("n_samples=20")
ax[2].set_title("n_samples=50")
ax[3].set_title("n_samples=100")
plt.tight_layout()
plt.savefig("n_samples.png",dpi=120)
plt.show()
n_samplesを変化させることでサンプル数を変えることができる。
n_features
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#n_features
X1,Y1 = make_regression(n_features=2)
X2,Y2 = make_regression(n_features=3)
X3,Y3 = make_regression(n_features=4)
X4,Y4 = make_regression(n_features=5)
X1.shape,X2.shape,X3.shape,X4.shape
((100, 2), (100, 3), (100, 4), (100, 5))
データの列数を変えることができる。
n_informative
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#n_informative
X1,Y1 = make_regression(n_features=4,n_informative=1)
X2,Y2 = make_regression(n_features=4,n_informative=2)
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X1[:,0],Y1,s=10)
ax[1].scatter(X1[:,1],Y1,s=10)
ax[2].scatter(X1[:,2],Y1,s=10)
ax[3].scatter(X1[:,3],Y1,s=10)
plt.suptitle("n_informative=1")
plt.tight_layout()
plt.savefig("n_informative1.png",dpi=120)
plt.show()
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X2[:,0],Y2,s=10)
ax[1].scatter(X2[:,1],Y2,s=10)
ax[2].scatter(X2[:,2],Y2,s=10)
ax[3].scatter(X2[:,3],Y2,s=10)
plt.suptitle("n_informative=2")
plt.tight_layout()
plt.savefig("n_informative2.png",dpi=120)
plt.show()
線形モデルに適合するデータ（列）の数を設定できる。1と2とした場合は以下のようになる。2は左上と右下が線形モデルに合うように思える。
n_targets
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#n_targets
X1,Y1 = make_regression(n_features=1,n_informative=1,n_targets=1)
X2,Y2 = make_regression(n_features=1,n_informative=1,n_targets=2)
X3,Y3 = make_regression(n_features=1,n_informative=1,n_targets=3)
X4,Y4 = make_regression(n_features=1,n_informative=1,n_targets=4)
Y1.shape,Y2.shape,Y3.shape,Y4.shape
((100,), (100, 2), (100, 3), (100, 4))
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X4[:,0],Y4[:,0],s=10)
ax[1].scatter(X4[:,0],Y4[:,1],s=10)
ax[2].scatter(X4[:,0],Y4[:,2],s=10)
ax[3].scatter(X4[:,0],Y4[:,3],s=10)
plt.suptitle("n_targets=4")
plt.tight_layout()
plt.savefig("n_targets.png",dpi=120)
plt.show()
n_targetsは出力値Yの数となる。n_targets=4として異なるYとXをプロットすると以下のようになる。
bias
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#bias
X1,Y1 = make_regression(n_features=1,n_informative=1,bias=100)
X2,Y2 = make_regression(n_features=1,n_informative=1,bias=0)
X3,Y3 = make_regression(n_features=1,n_informative=1,bias=-100)
X4,Y4 = make_regression(n_features=1,n_informative=1,bias=-200)
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X1[:,0],Y1,s=10)
ax[1].scatter(X2[:,0],Y2,s=10)
ax[2].scatter(X3[:,0],Y3,s=10)
ax[3].scatter(X4[:,0],Y4,s=10)
ax[0].plot(0,100,"ro")
ax[1].plot(0,0,"ro")
ax[2].plot(0,-100,"ro")
ax[3].plot(0,-200,"ro")
ax[0].set_title("bias=100")
ax[1].set_title("bias=0")
ax[2].set_title("bias=-100")
ax[3].set_title("bias=-200")
plt.tight_layout()
plt.savefig("bias.png",dpi=120)
plt.show()
biasは切片の値となる。
noise
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#noise
X1,Y1 = make_regression(n_features=1,n_informative=1,noise=10)
X2,Y2 = make_regression(n_features=1,n_informative=1,noise=20)
X3,Y3 = make_regression(n_features=1,n_informative=1,noise=50)
X4,Y4 = make_regression(n_features=1,n_informative=1,noise=100)
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X1[:,0],Y1,s=10)
ax[1].scatter(X2[:,0],Y2,s=10)
ax[2].scatter(X3[:,0],Y3,s=10)
ax[3].scatter(X4[:,0],Y4,s=10)
ax[0].set_title("noise=10")
ax[1].set_title("noise=20")
ax[2].set_title("noise=50")
ax[3].set_title("noise=100")
plt.tight_layout()
plt.savefig("noise.png",dpi=120)
plt.show()
noiseでばらつきを付与できる。
random_state
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#random_state
X1,Y1 = make_regression(n_features=1,n_informative=1,random_state=1)
X2,Y2 = make_regression(n_features=1,n_informative=1,random_state=2)
X3,Y3 = make_regression(n_features=1,n_informative=1,random_state=3)
X4,Y4 = make_regression(n_features=1,n_informative=1,random_state=4)
fig, ax = plt.subplots(nrows=2,ncols=2,sharex=True,sharey=True,dpi=140)
ax =ax.ravel()
ax[0].scatter(X1[:,0],Y1,s=10)
ax[1].scatter(X2[:,0],Y2,s=10)
ax[2].scatter(X3[:,0],Y3,s=10)
ax[3].scatter(X4[:,0],Y4,s=10)
ax[0].set_title("random_state=1")
ax[1].set_title("random_state=2")
ax[2].set_title("random_state=3")
ax[3].set_title("random_state=4")
plt.tight_layout()
plt.savefig("random_state.png",dpi=120)
plt.show()
random_stateを変えることで再現可能な乱数を生成することができる。
coef
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#coef
X1,Y1,coef = make_regression(n_features=1,n_informative=1,coef=True)
coef
array(22.1601716)
X2,Y2,coef = make_regression(n_features=4,n_informative=2,coef=True)
coef
array([ 0. , 1.5863515 , 0. , 41.66548154])
coefをTrueとすることで線形モデルの係数を得ることができる。デフォルトはFalse.
n_features=4とすれば4つのcoefが得られる。
参考
make_regression
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