sklearn：SVR 无法泛化加法器函数

Question

这是我学习加法函数的 SVR (y=x1 + x2):

%reset -f

#Libs
from sklearn import svm;

#PROGRAMME ENTRY POINT==========================================================
#Data, addition
#Exp[I] = sum(Inp[I])
Inp = [[1,2],[3,4],[5,6],[7,8],[9,0]];
Exp = [ 3,    7,    11,   15,   9   ];

#Train
Model = svm.SVR(kernel="poly",degree=3);
Model.fit(Inp,Exp);

#Infer
print("Input values are those in the train data:");
print(f"1 + 2 = {Model.predict([[1,2]])[0]:.6f}");

print("\nInput values are those in the train data:");
print(f"5 + 6 = {Model.predict([[5,6]])[0]:.6f}");

print("\nInput values are those NOT in the train data, but in range:");
print(f"5 + 5 = {Model.predict([[5,5]])[0]:.6f}");

print("\nInput values are those NOT in the train data, and OUT of range:");
print(f"9 + 1 = {Model.predict([[9,1]])[0]:.6f}");
#EOF

但结果不是预期的结果：

Input values are those in the train data:
1 + 2 = 6.007171

Input values are those in the train data:
5 + 6 = 9.595818

Input values are those NOT in the train data, but in range:
5 + 5 = 8.533934

Input values are those NOT in the train data, and OUT of range:
9 + 1 = 9.170507

sklearn SVR是否可以泛化加法器函数？在上面的代码中应该更改什么以使 SVR 学习 x1+x2？

Answer 1

三阶多项式核的方差太大，无法正确预测如此简单的函数，尤其是在如此小的数据集上。这是基于 bias/variance 权衡。在这种情况下，您的模型在方差上有所损失，而在偏差方面几乎没有任何收获（您的函数过于复杂）。低阶多项式和径向基函数也是如此。

降低模型的方差就可以了。就用线性核。

Model = svm.SVR(kernel="linear")

具有线性核的 SVM 的结果是：

Input values are those in the train data:
1 + 2 = 3.100000

Input values are those in the train data:
5 + 6 = 10.966667

Input values are those NOT in the train data, but in range:
5 + 5 = 9.983333

Input values are those NOT in the train data, and OUT of range:
9 + 1 = 9.983333

sklearn：SVR 无法泛化加法器函数

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