—<\/p>\n
type: note<\/p>\n
title: \u51b3\u7b56\u6811\u7f16\u7a0b\u4f5c\u4e1a<\/p>\n
date: 2026-08-27<\/p>\n
description: C2W4 \u4ece\u96f6\u9020\u4e00\u68f5\u51b3\u7b56\u6811\u8ba4\u8611\u83c7：\u71b5\u91cf"\u6709\u591a\u4e71"\u3001\u5206\u88c2\u63b0\u4e24\u62e8\u3001\u4fe1\u606f\u589e\u76ca=\u5207\u524d\u71b5\u2212\u5207\u540e\u52a0\u6743\u71b5\u3001\u9009\u589e\u76ca\u6700\u5927\u7279\u5f81\u3002\u5751：0log\u2082(0) \u8981 else \u515c\u5e95（np.log2(0)\u2192-inf\u2192nan）；get_best_split \u5360\u4f4d\u6570\u4e0d\u80fd\u649e\u771f\u5b9e\u4e0b\u6807\u3002<\/p>\n
—<\/p>\n
\u00a0<\/p>\n
# 2026-08-27 \u5b66\u4e60\u7b14\u8bb0<\/p>\n
\u00a0<\/p>\n
## \u7b14\u8bb0\u533a（\u5b66\u7684\u65f6\u5019\u968f\u624b\u8bb0）<\/p>\n
\u00a0<\/p>\n
### \u6838\u5fc3\u89c2\u70b9<\/p>\n
\u00a0<\/p>\n
**\u9020\u4e00\u68f5\u51b3\u7b56\u6811，\u8ba9\u5b83\u81ea\u5df1\u5b66\u4f1a\u8ba4\u8611\u83c7\u3002** \u6570\u636e：10 \u6735\u8611\u83c7\u30013 \u4e2a\u7279\u5f81（\u68d5\u8272\u83cc\u76d6 \/ \u7ec6\u957f\u83cc\u67c4 \/ \u72ec\u751f），\u6807\u7b7e\u662f**\u53ef\u98df(1) \/ \u6709\u6bd2(0)**\u3002\u8fd9\u68f5\u6811\u7684\u6d3b\u513f\u5c31\u662f：**\u6bcf\u6b21\u95ee\u4e00\u4e2a\u95ee\u9898，\u628a\u8611\u83c7\u5207\u5f97\u66f4\u5e72\u51c0，\u5207\u5230\u5206\u4e0d\u52a8\u4e3a\u6b62\u3002**<\/p>\n
\u00a0<\/p>\n
\u9020\u6811\u4e0d\u9760\u80cc，\u9760 4 \u5757\u79ef\u6728（\u4f5c\u4e1a\u5c31\u662f\u8865\u8fd9 4 \u4e2a\u51fd\u6570）：<\/p>\n
\u00a0<\/p>\n
| \u79ef\u6728 | \u5e72\u4ec0\u4e48 | \u4eba\u8bdd |<\/p>\n
| ———————————– | ——————– | ———————- |<\/p>\n
| \u71b5 `compute_entropy` | \u91cf\u8fd9\u4e00\u62e8"\u6709\u591a\u4e71" | \u4e00\u56e2\u7cca vs \u5206\u5f97\u6e05 |<\/p>\n
| \u5206\u88c2 `split_dataset` | \u6309\u67d0\u7279\u5f81\u63b0\u6210\u5de6\u53f3\u4e24\u62e8 | \u4e00\u4e2a\u95ee\u9898\u628a\u8611\u83c7\u5206\u5f00 |<\/p>\n
| \u4fe1\u606f\u589e\u76ca `compute_information_gain` | \u8fd9\u4e00\u5200\u5212\u4e0d\u5212\u7b97 | \u5207\u5b8c\u6bd4\u5207\u524d\u5e72\u51c0\u591a\u5c11 |<\/p>\n
| \u9009\u6700\u4f73 `get_best_split` | \u6311\u589e\u76ca\u6700\u5927\u7684\u7279\u5f81 | \u8bd5\u904d\u95ee\u9898，\u6311\u6700\u80fd\u5206\u5f00\u7684 |<\/p>\n
\u00a0<\/p>\n
### \u5173\u952e\u65b9\u6cd5\/\u6d41\u7a0b<\/p>\n
\u00a0<\/p>\n
– **\u71b5**：\u5168\u4e00\u79cd = 0，\u4e00\u534a\u4e00\u534a = 1\u3002\u516c\u5f0f `-p1\u00b7log\u2082(p1) – (1-p1)\u00b7log\u2082(1-p1)`，`p1` = \u53ef\u98df\u6bd4\u4f8b\u3002<\/p>\n
– **\u4fe1\u606f\u589e\u76ca** = \u5206\u88c2\u524d\u71b5 \u2212 \u5206\u88c2\u540e\u4e24\u62e8\u52a0\u6743\u71b5\u3002**\u8d8a\u5927 = \u6df7\u4e71\u51cf\u5c11\u8d8a\u591a = \u8d8a\u8be5\u5f80\u4e0b\u5206\u3002**<\/p>\n
– **\u52a0\u6743**：\u4e24\u62e8\u5927\u5c0f\u53ef\u80fd\u4e0d\u540c，\u8981\u6309\u5360\u6bd4\u52a0\u6743，\u4e0d\u80fd\u76f4\u63a5\u5e73\u5747\u71b5\u3002<\/p>\n
\u00a0<\/p>\n
### \u5b9e\u6218\u8bb0\u5f55<\/p>\n
\u00a0<\/p>\n
**\u2460 \u71b5\u91cc `0\u00b7log\u2082(0)=0` \u8981 else \u515c\u5e95**<\/p>\n
\u00a0<\/p>\n
> 0log\u2082(0)=0 \u662f\u4eba\u4e3a\u7ea6\u5b9a\u3002\u4f46\u8ba1\u7b97\u673a\u91cc np.log2(0) \u8fd4\u56de -inf，0 \u00d7 -inf = nan，\u6240\u4ee5 p1=0 \u6216 p1=1 \u65f6\u516c\u5f0f\u4f1a\u7b97\u51fa nan \u800c\u4e0d\u662f 0\u3002\u56e0\u6b64\u5fc5\u987b\u5199 `else: entropy = 0` \u624b\u52a8\u5b9a\u6b7b，\u5426\u5219\u8fc7\u4e0d\u4e86\u6d4b\u8bd5\u3002<\/p>\n
\u00a0<\/p>\n
**\u2461 `best_feature=-1` \u5360\u4f4d\u4e0d\u649e\u771f\u5b9e\u4e0b\u6807**<\/p>\n
\u00a0<\/p>\n
> \u5728 get_best_split \u4e2d\u7528 -1 \u505a\u5360\u4f4d，\u56e0\u4e3a -1 \u4e0d\u662f\u4efb\u4f55\u771f\u5b9e\u7279\u5f81\u4e0b\u6807（\u672c\u6570\u636e\u96c6\u4e0b\u6807\u662f 0\u30011\u30012），\u80fd\u5b89\u5168\u8868\u793a"\u8fd8\u6ca1\u9009\u5230"\u3002\u82e5\u7528 0 \u5f53\u521d\u59cb\u503c，0 \u672c\u8eab\u662f\u5408\u6cd5\u7279\u5f81\u4e0b\u6807，\u4e00\u65e6\u5faa\u73af\u6ca1\u627e\u5230\u66f4\u5927\u589e\u76ca，\u4f1a\u8bef\u8fd4\u56de\u7279\u5f81 0\u3002\u5173\u952e\u662f\u5360\u4f4d\u6570\u522b\u649e\u4e0a\u771f\u5b9e\u4e0b\u6807\u2014\u2014-1\u30013\u30014\u30015 \u90fd\u53ef\u4ee5，**2 \u4e0d\u884c**（2 \u662f"\u72ec\u751f"\u7279\u5f81\u7684\u4e0b\u6807）\u3002<\/p>\n
\u00a0<\/p>\n
## \u4ee3\u7801\u9010\u6bb5\u5c55\u5f00<\/p>\n
\u00a0<\/p>\n
### Ex1 `compute_entropy(y)` \u2014 \u7b97\u4e00\u62e8\u7684\u71b5<\/p>\n
\u00a0<\/p>\n
```python<\/p>\n
def compute_entropy(y):<\/p>\n
\u00a0 \u00a0 entropy = 0.<\/p>\n
\u00a0 \u00a0 if len(y) != 0: # \u7a7a\u8282\u70b9\u8fd4\u56de 0<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 p1 = len(y[y == 1]) \/ len(y) # \u53ef\u98df\u6bd4\u4f8b<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 if p1 != 0 and p1 != 1:<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 entropy = -p1 * np.log2(p1) – (1-p1) * np.log2(1-p1)<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 else: # p1=0\/1 \u2192 0log\u2082(0) \u7ea6\u5b9a<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 entropy = 0.<\/p>\n
\u00a0 \u00a0 return entropy<\/p>\n
```<\/p>\n
\u00a0<\/p>\n
– `p1 = len(y[y == 1]) \/ len(y)`：\u6570\u53ef\u98df\u7684 \u00f7 \u603b\u6570 = \u6bd4\u4f8b\u3002<\/p>\n
– `p1` \u662f 0 \u6216 1 \u65f6 `np.log2` \u4f1a\u7b97\u51fa `-inf`，`0\u00d7-inf = nan`，\u5fc5\u987b `else` \u515c\u5e95\u7ed9 0\u3002<\/p>\n
– \u6839\u8282\u70b9 5 \u53ef\u98df 5 \u6709\u6bd2 \u2192 p1=0.5 \u2192 \u71b5 = 1.0（\u6700\u4e71），\u6d4b\u8bd5\u9884\u671f\u5c31\u662f 1.0\u3002<\/p>\n
\u00a0<\/p>\n
### Ex2 `split_dataset(X, node_indices, feature)` \u2014 \u6309\u7279\u5f81\u63b0\u4e24\u62e8<\/p>\n
\u00a0<\/p>\n
```python<\/p>\n
def split_dataset(X, node_indices, feature):<\/p>\n
\u00a0 \u00a0 left_indices = []<\/p>\n
\u00a0 \u00a0 right_indices = []<\/p>\n
\u00a0 \u00a0 for i in node_indices: # \u9010\u4e2a\u6837\u672c<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 if X[i][feature] == 1: # \u7279\u5f81=1 \u5de6<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 left_indices.append(i)<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 else: # \u7279\u5f81=0 \u53f3<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 right_indices.append(i)<\/p>\n
\u00a0 \u00a0 return left_indices, right_indices<\/p>\n
```<\/p>\n
\u00a0<\/p>\n
– \u53ea\u8bb0**\u4e0b\u6807**，\u4e0d\u642c\u6570\u636e\u3002\u6309"\u68d5\u8272\u83cc\u76d6"(feature=0)\u5206\u6839\u8282\u70b9：\u5de6 `[0,1,2,3,4,7,9]`，\u53f3 `[5,6,8]`\u3002<\/p>\n
\u00a0<\/p>\n
### Ex3 `compute_information_gain(…)` \u2014 \u8fd9\u5200\u5212\u4e0d\u5212\u7b97<\/p>\n
\u00a0<\/p>\n
```python<\/p>\n
def compute_information_gain(X, y, node_indices, feature):<\/p>\n
\u00a0 \u00a0 left_indices, right_indices = split_dataset(X, node_indices, feature)<\/p>\n
\u00a0 \u00a0 X_node, y_node = X[node_indices], y[node_indices]<\/p>\n
\u00a0 \u00a0 X_left, y_left = X[left_indices], y[left_indices]<\/p>\n
\u00a0 \u00a0 X_right, y_right = X[right_indices], y[right_indices]<\/p>\n
\u00a0 \u00a0 information_gain = 0<\/p>\n
\u00a0 \u00a0 node_entropy = compute_entropy(y_node) # \u5206\u88c2\u524d\u591a\u4e71<\/p>\n
\u00a0 \u00a0 left_entropy = compute_entropy(y_left) # \u5de6\u62e8<\/p>\n
\u00a0 \u00a0 right_entropy = compute_entropy(y_right) # \u53f3\u62e8<\/p>\n
\u00a0 \u00a0 w_left = len(X_left) \/ len(X_node) # \u5de6\u5360\u6bd4<\/p>\n
\u00a0 \u00a0 w_right = len(X_right) \/ len(X_node) # \u53f3\u5360\u6bd4<\/p>\n
\u00a0 \u00a0 weighted_entropy = w_left * left_entropy + w_right * right_entropy<\/p>\n
\u00a0 \u00a0 information_gain = node_entropy – weighted_entropy<\/p>\n
\u00a0 \u00a0 return information_gain<\/p>\n
```<\/p>\n
\u00a0<\/p>\n
– \u5206\u88c2\u7528\u7684\u662f**\u4f60\u81ea\u5df1\u5199\u7684 Ex2**，\u71b5\u7528**\u4f60\u81ea\u5df1\u5199\u7684 Ex1**\u2014\u2014\u79ef\u6728\u4e92\u76f8\u62fc\u3002<\/p>\n
– \u4e24\u62e8\u5927\u5c0f\u4e0d\u4e00\u6837 \u2192 \u6309\u5360\u6bd4\u52a0\u6743，\u4e0d\u80fd\u76f4\u63a5\u5e73\u5747\u3002<\/p>\n
– \u9884\u671f：\u68d5\u8272 0.0349\u3001\u7ec6\u957f 0.1245\u3001\u72ec\u751f 0.2781 \u2192 **\u72ec\u751f\u6536\u76ca\u6700\u5927**\u3002<\/p>\n
\u00a0<\/p>\n
### Ex4 `get_best_split(…)` \u2014 \u6311\u589e\u76ca\u6700\u5927\u7684\u7279\u5f81<\/p>\n
\u00a0<\/p>\n
```python<\/p>\n
def get_best_split(X, y, node_indices):<\/p>\n
\u00a0 \u00a0 num_features = X.shape[1]<\/p>\n
\u00a0 \u00a0 best_feature = -1<\/p>\n
\u00a0 \u00a0 max_info_gain = 0<\/p>\n
\u00a0 \u00a0 for feature in range(num_features): # \u8bd5\u904d\u6bcf\u4e2a\u7279\u5f81<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 info_gain = compute_information_gain(X, y, node_indices, feature)<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 if info_gain > max_info_gain:<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 max_info_gain = info_gain<\/p>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 best_feature = feature<\/p>\n
\u00a0 \u00a0 return best_feature<\/p>\n
```<\/p>\n
\u00a0<\/p>\n
– `best_feature = -1`：**\u5360\u4f4d**，\u4e0d\u649e\u771f\u5b9e\u4e0b\u6807，\u5b89\u5168\u8868\u793a"\u8fd8\u6ca1\u9009\u5230"\u3002<\/p>\n
– \u5faa\u73af\u91cc `if info_gain > max_info_gain`：\u627e\u5230\u66f4\u5927\u7684\u5c31\u6362，\u6700\u540e\u7559\u6700\u5927\u7684\u3002<\/p>\n
– \u6839\u8282\u70b9：\u72ec\u751f(2) \u589e\u76ca 0.2781 \u6700\u5927 \u2192 \u7b2c\u4e00\u6b21\u5206\u88c2\u5c31\u9009"\u72ec\u751f"\u3002<\/p>\n
\u00a0<\/p>\n
## \u7ebf\u7d22\u533a（\u5b66\u5b8c\u540e\u5408\u4e0a\u6750\u6599，\u81ea\u95ee\u81ea\u7b54）<\/p>\n
\u00a0<\/p>\n
> \u5148\u770b\u95ee\u9898 \u2192 \u81ea\u5df1\u56de\u7b54 \u2192 \u5bf9\u7167\u3002\u7b54\u4e0d\u4e0a\u6765\u7684\u5c31\u662f\u6ca1\u5b66\u900f\u3002<\/p>\n
\u00a0<\/p>\n
**Q: \u71b5\u6700\u5927\u662f\u5565\u65f6\u5019？\u4e3a\u4ec0\u4e48？**<\/p>\n
A: p1=0.5（\u4e00\u534a\u4e00\u534a）\u65f6\u71b5=1 \u6700\u5927\u3002\u6700\u4e71\u5c31\u662f\u4e24\u79cd\u5404\u5360\u4e00\u534a，\u731c\u54ea\u8fb9\u90fd\u6ca1\u628a\u63e1；\u5168\u662f\u4e00\u79cd\u5219\u71b5=0，\u4e00\u70b9\u60ac\u5ff5\u6ca1\u6709\u3002<\/p>\n
\u00a0<\/p>\n
**Q: \u4fe1\u606f\u589e\u76ca\u8d8a\u5927\u8bf4\u660e\u4ec0\u4e48？**<\/p>\n
A: \u8fd9\u4e00\u5200\u628a\u6df7\u4e71\u524a\u51cf\u5f97\u8d8a\u591a，\u8d8a\u503c\u5f97\u5728\u8fd9\u91cc\u5f80\u4e0b\u5206\u3002\u672c\u8d28 = \u5206\u88c2\u524d\u71b5 \u2212 \u5206\u88c2\u540e\u52a0\u6743\u71b5\u3002<\/p>\n
\u00a0<\/p>\n
**Q: \u5360\u4f4d\u6570\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u7528 0 \u6216 2？**<\/p>\n
A: 0\u30012 \u90fd\u662f\u771f\u5b9e\u7279\u5f81\u4e0b\u6807\u3002\u5360\u4f4d\u6570\u82e5\u649e\u771f\u5b9e\u4e0b\u6807，\u5faa\u73af\u91cc\u4e00\u76f4\u6ca1\u627e\u5230\u66f4\u5927\u589e\u76ca\u65f6，\u4f1a\u628a"\u8fd8\u6ca1\u9009\u5230"\u8bef\u5f53\u6210"\u9009\u5230\u4e86\u90a3\u4e2a\u7279\u5f81"\u3002\u7528 -1（\u6216 3\u30014\u30015）\u624d\u5b89\u5168\u3002<\/p>\n
\u00a0<\/p>\n
**Q: \u4fe1\u606f\u589e\u76ca\u91cc\u4e3a\u4ec0\u4e48\u6309\u4eba\u6570\u52a0\u6743，\u800c\u4e0d\u662f\u4e24\u4e2a\u71b5\u76f4\u63a5\u5e73\u5747？**<\/p>\n
A: \u5de6\u62e8\u53f3\u62e8\u5927\u5c0f\u53ef\u80fd\u4e0d\u4e00\u6837\u3002\u76f4\u63a5\u5e73\u5747＝\u628a 10 \u4eba\u548c 1 \u4eba\u5f53\u7b49\u91cd，\u4e0d\u516c\u5e73\u3002\u6309\u5360\u6bd4\u52a0\u6743\u624d\u53cd\u6620"\u6570\u636e\u591a\u7684\u90a3\u8fb9\u8bf4\u4e86\u7b97"\u3002<\/p>\n
\u00a0<\/p>\n
## \u603b\u7ed3（50 \u5b57\u4ee5\u5185）<\/p>\n
\u00a0<\/p>\n
C2W4 \u51b3\u7b56\u6811 = \u4ece\u96f6\u9020\u6811：\u71b5\u91cf\u591a\u4e71\u3001\u5206\u88c2\u63b0\u4e24\u62e8\u3001\u4fe1\u606f\u589e\u76ca=\u5207\u524d\u71b5\u2212\u5207\u540e\u52a0\u6743\u71b5\u3001\u9009\u589e\u76ca\u6700\u5927\u7279\u5f81\u3002\u5751：0log\u2082(0) \u8981 else \u515c\u5e95\u3001\u5360\u4f4d\u6570\u4e0d\u649e\u771f\u5b9e\u4e0b\u6807\u3002<\/p>\n
\u00a0<\/p>\n
—<\/p>\n
\u00a0<\/p>\n
## \u590d\u4e60\u5361\u7247<\/p>\n
\u00a0<\/p>\n
| \u6982\u5ff5 | \u4e00\u53e5\u8bdd | \u6211\u7684\u573a\u666f |<\/p>\n
| ——– | ———————————- | ————————— |<\/p>\n
| \u71b5 | \u91cf\u8fd9\u4e00\u62e8\u591a\u4e71；\u5168\u4e00\u79cd=0\u3001\u4e00\u534a\u4e00\u534a=1 | \u5224\u65ad\u8be5\u4e0d\u8be5\u7ee7\u7eed\u5207 |<\/p>\n
| \u4fe1\u606f\u589e\u76ca | \u5207\u524d\u71b5 \u2212 \u5207\u540e\u52a0\u6743\u71b5 | \u8d8a\u5927\u8d8a\u8be5\u5f80\u4e0b\u5206 |<\/p>\n
| \u52a0\u6743\u71b5 | \u6309\u5360\u6bd4\u52a0\u6743，\u4e0d\u76f4\u63a5\u5e73\u5747 | \u4e24\u62e8\u4eba\u6570\u4e0d\u4e00\u6837\u65f6 |<\/p>\n
| \u5360\u4f4d\u6570 | -1\/3\/4\/5 \u884c，0\u30012 \u4e0d\u884c | get_best_split \u7684"\u8fd8\u6ca1\u9009\u5230" |<\/p>\n
| 0log\u2082(0) | \u6570\u5b66\u7ea6\u5b9a=0，\u673a\u5668\u7b97 nan | np.log2(0) \u8981 else \u515c\u5e95 |<\/p>\n","protected":false},"excerpt":{"rendered":"
—type: notetitle: \u51b3\u7b56\u6811\u7f16\u7a0b\u4f5c\u4e1adate: 2026-08-27description: C2W4 \u4ece\u96f6\u9020\u4e00\u68f5\u51b3\u7b56\u6811\u8ba4\u8611\u83c7：\u71b5\u91cf\\”\u6709\u591a\u4e71\\”\u3001\u5206\u88c2\u63b0\u4e24\u62e8\u3001\u4fe1\u606f\u589e\u76ca\u5207\u524d\u71b5\u2212\u5207\u540e\u52a0\u6743\u71b5\u3001\u9009\u589e\u76ca\u6700\u5927\u7279\u5f81\u3002\u5751：0log\u2082(0) \u8981 else \u515c\u5e95（np.log2(0)\u2192-inf\u2192nan）；get_best_split \u5360\u4f4d\u6570\u4e0d\u80fd\u649e\u771f\u5b9e\u4e0b\u6807\u3002—# 2026-08-27 \u5b66\u4e60\u7b14\u8bb0## \u7b14\u8bb0\u533a&#<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[81,50,207],"topic":[],"class_list":["post-96621","post","type-post","status-publish","format-standard","hentry","category-server","tag-python","tag-50","tag-207"],"yoast_head":"\n