线性回归梯度计算出现KeyError(1)问题求助

问题概述 #

计算线性回归模型梯度时触发KeyError(1)，怀疑与维度相关，但无法定位具体原因。

梯度函数说明 #

计算线性回归的梯度

• 参数：
  • X (ndarray (m,n)): 数据集，包含m个样本，每个样本有n个特征
  • y (ndarray (m,)) : 样本对应的目标值
  • w (ndarray (n,)) : 模型权重参数
  • b (scalar) : 模型偏置参数
• 返回值：
  • dj_dw (ndarray (n,)): 代价函数关于权重w的梯度
  • dj_db (scalar): 代价函数关于偏置b的梯度

实现代码 #

import numpy as np
 
def gradient(X, y, w, b): 

    m,n = X.shape           #(样本数量, 特征数量)
    dj_dw = np.zeros((n,))
    dj_db = 0
    for i in range(m):                             
        err = (np.dot(X[i],w) + b) - y[i] 
        for j in range(n):                         
            dj_dw[j] = dj_dw[j] + err * X[i, j]    
        dj_db = dj_db + err                        
    dj_dw = dj_dw / m                                
    dj_db = dj_db / m                                
        
    return dj_db, dj_dw

b_init = 785.1811367994083
w_init = np.array([ 0.39133535, 18.75376741, -53.36032453, -26.42131618,-33.2342342])
tmp_dj_db, tmp_dj_dw = gradient(X_train, y_train, w_init, b_init)
print(f'dj_db at initial w,b: {tmp_dj_db}')
print(f'dj_dw at initial w,b: \n {tmp_dj_dw}')

报错信息 #

KeyError                                  Traceback (most recent call last)
/usr/local/lib/python3.7/dist-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)
   3360             try:
-> 3361                 return self._engine.get_loc(casted_key)
   3362             except KeyError as err:

6 frames
/usr/local/lib/python3.7/dist-packages/pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

/usr/local/lib/python3.7/dist-packages/pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.Int64HashTable.get_item()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.Int64HashTable.get_item()

KeyError: 1

The above exception was the direct cause of the following exception:

KeyError                                  Traceback (most recent call last)
<ipython-input-73-1f87825d3f02> in <module>
      1 b_init = 785.1811367994083
      2 w_init = np.array([ 0.39133535, 18.75376741, -53.36032453, -26.42131618,-33.2342342])
----> 3 tmp_dj_db, tmp_dj_dw = gradient(X_train, y_train, w_init, b_init)
      4 print(f'dj_db at initial w,b: {tmp_dj_db}')
      5 print(f'dj_dw at initial w,b: \n {tmp_dj_dw}')

<ipython-input-72-52811c00c1ad> in gradient(X, y, w, b)
     16     dj_db = 0
     17     for i in range(m):
---> 18         err = (np.dot(X.iloc[i,],w) + b) - y[i]
     19         for j in range(n):
     20             dj_dw[j] = dj_dw[j] + err * X.iloc[i, j]

/usr/local/lib/python3.7/dist-packages/pandas/core/series.py in __getitem__(self, key)
    940 
    941         elif key_is_scalar:
---> 942             return self._get_value(key)
    943 
    944         if is_hashable(key):

/usr/local/lib/python3.7/dist-packages/pandas/core/series.py in _get_value(self, label, takeable)
   1049 
   1050         # Similar to Index.get_value, but we do not fall back to positional
-> 1051         loc = self.index.get_loc(label)
   1052         return self.index._get_values_for_loc(self, loc, label)
   1053 

/usr/local/lib/python3.7/dist-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)
   3361                 return self._engine.get_loc(casted_key)
   3362             except KeyError as err:
-> 3363                 raise KeyError(key) from err
   3364 
   3365         if is_scalar(key) and isna(key) and not self.hasnans:

KeyError: 1

问题原因与解决方案 #

原因分析 #

从报错栈可以看出：

1. 代码实际使用X.iloc[i,]，说明X_train是Pandas DataFrame，但函数定义假设输入为numpy ndarray，两者索引逻辑存在差异。
2. y[i]是按标签索引取值，若y_train为Pandas Series且索引不是连续的0起始整数序列（比如数据筛选后未重置索引），循环到i=1时会因找不到标签为1的元素抛出KeyError。

解决方案 #

方案1：将输入数据转为numpy数组

在调用梯度函数前，把Pandas格式数据集转为numpy ndarray，匹配函数参数要求：

# 转换数据格式
X_train = X_train.to_numpy()
y_train = y_train.to_numpy()

# 调用梯度函数
tmp_dj_db, tmp_dj_dw = gradient(X_train, y_train, w_init, b_init)

方案2：修改梯度函数适配Pandas数据

若需保留Pandas格式，修改函数内索引方式，统一使用位置索引：

def gradient(X, y, w, b): 
    m,n = X.shape           
    dj_dw = np.zeros((n,))
    dj_db = 0
    for i in range(m):                             
        # 用iloc按位置取y元素，X转为numpy数组计算点积
        err = (np.dot(X.iloc[i].values, w) + b) - y.iloc[i] 
        for j in range(n):                         
            dj_dw[j] = dj_dw[j] + err * X.iloc[i, j]    
        dj_db = dj_db + err                        
    dj_dw = dj_dw / m                                
    dj_db = dj_db / m                                
    return dj_db, dj_dw

内容的提问来源于stack exchange，提问作者Arshdeep Singh