线性回归预测与训练数据不匹配

Question

我是机器学习的新手。我正在尝试使用线性回归和遵循特定模式的 "made up" 数据进行简单预测。由于某种原因，预测与训练数据不匹配。你能让我知道我需要修理什么吗？示例代码如下

from sklearn import linear_model
import numpy as np

X = np.random.randint(3, size=(3, 1000))
Y = np.random.randint(10, size=(1, 1000))
# f1, f2, f3 - min = 0, max = 2
# f1 = 0 and f2 = 1  then 7 <= Y < 10, irrespective of f3
# f1 = 1 and f2 = 2 Y is 0, irrespective of f3
# f1 = 0 and f2 = 2 if f3 = 2 then 3 <= Y < 7 else Y = 0
for i in range(1000):
    if ((X[0][i] == 0 and X[1][i] == 1) or (X[0][i] == 1 and X[1][i] == 0)):
        Y[0][i] = np.random.randint(7, 10)
    elif ((X[0][i] == 1 and X[1][i] == 2) or (X[0][i] == 2 and X[1][i] == 1)):
        Y[0][i] = 0
    elif ((X[0][i] == 0 and X[1][i] == 2 and X[2][i] == 2) or
         (X[0][i] == 2 and X[1][i] == 0 and X[2][i] == 2)):
        Y[0][i] = np.random.randint(3, 7)
    else:
        Y[0][i] = 0

X1 = X.transpose()
Y1 = Y.reshape(-1, 1)
print zip(X1, Y1)

# create and fit the model
clf = linear_model.LinearRegression()
clf.fit(X1, Y1)

Z = np.array([[0, 0, 0, 0, 1, 1],
              [1, 1, 2, 2, 2, 2],
              [1, 2, 1, 2, 1, 2]])
Z1 = Z.transpose()
print Z1

y_predict = clf.predict(Z1)
print y_predict

Answer 1

为什么它会匹配训练数据？您的 X->Y 关系显然是非线性的，并且仅适用于完美的线性关系，这意味着 Y = AX + b，您可以期望线性回归能够完美地拟合训练数据。否则，您可以随意远离解决方案 - 例如参见 Anscombe 的四重奏（来自 wiki 的下图）。

线性回归预测与训练数据不匹配

Linear regression prediction not matching training data

python

numpy

machine-learning

scikit-learn