### `ValueError: All the 10 fits failed.` 错误
此错误表明在交叉验证的 10 次拟合过程中，所有的拟合都失败了。常见原因及解决办法如下：
- **数据问题**：数据中可能存在缺失值、无穷大值或数据类型不兼容等情况。可以通过以下代码检查并处理缺失值：
```python
import numpy as np
import pandas as pd
from sklearn.preprocessing import StandardScaler
# 假设 x_train 和 y_train 是训练数据
# 检查是否有缺失值
if np.isnan(x_train).any() or np.isnan(y_train).any():
# 可以选择删除包含缺失值的行
x_train = pd.DataFrame(x_train).dropna().values
y_train = pd.DataFrame(y_train).dropna().values
# 或者使用均值、中位数等填充缺失值
# from sklearn.impute import SimpleImputer
# imputer = SimpleImputer(strategy='mean')
# x_train = imputer.fit_transform(x_train)
# 检查是否有无穷大值
if np.isinf(x_train).any() or np.isinf(y_train).any():
x_train = np.nan_to_num(x_train)
y_train = np.nan_to_num(y_train)
# 数据标准化
scaler = StandardScaler()
x_train = scaler.fit_transform(x_train)
```
- **模型参数问题**：岭回归的 `alpha` 参数可能设置得不合理。可以尝试调整 `alpha` 的范围，例如选择更小的值。
```python
alpha_range = np.arange(0.1, 10, 0.1)
```
### `TypeError: solve() got an unexpected keyword argument 'sym_pos'` 错误
这个错误通常与符号计算相关，与当前比较线性回归和岭回归的代码并无直接关联。它可能是在其他代码中调用 `solve()` 函数时传入了不支持的参数 `sym_pos` 导致的。需要检查调用 `solve()` 函数的代码部分，移除 `sym_pos` 参数或者修改为支持的参数。例如：
```python
# 假设原来的代码是这样
# result = solve(equation, variables, sym_pos=True)
# 修改为
result = solve(equation, variables)
```
### 修正后的完整代码示例
```python
import numpy as np
from sklearn.linear_model import Ridge, LinearRegression
from sklearn.model_selection import cross_val_score, train_test_split
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
# 生成示例数据
x, y = make_regression(n_samples=100, n_features=10, random_state=42)
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=42)
# 数据预处理
scaler = StandardScaler()
x_train = scaler.fit_transform(x_train)
alpha_range = np.arange(0.1, 10, 0.1)
re, lr = [], []
for i in alpha_range:
ridge = Ridge(alpha=i)
linear = LinearRegression()
r2_ridge = cross_val_score(ridge, x_train, y_train, scoring='r2', cv=10)
r2_linear = cross_val_score(linear, x_train, y_train, scoring='r2', cv=10)
re = np.append(re, [np.mean(r2_ridge)])
lr = np.append(lr, [np.mean(r2_linear)])
plt.figure()
plt.plot(alpha_range, re, c='black', label='ridge')
plt.plot(alpha_range, lr, c='red', label='linear')
plt.legend()
plt.show()
```
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