一、回顾决策树算法
二、代码实践
from CART import DecisionTreeRegressor from CARTclassifier import DecisionTreeClassifier from sklearn.tree import DecisionTreeRegressor as dt from sklearn.tree import DecisionTreeClassifier as dc from sklearn.datasets import make_regression from sklearn.datasets import make_classification if __name__ == "__main__": # 模拟回归数据集 X, y = make_regression( n_samples=200, n_features=10, n_informative=5, random_state=0 ) # 回归树 my_cart_regression = DecisionTreeRegressor(max_depth=2) my_cart_regression.fit(X, y) res1 = my_cart_regression.predict(X) importance1 = my_cart_regression.feature_importances_ sklearn_cart_r = dt(max_depth=2) sklearn_cart_r.fit(X, y) res2 = sklearn_cart_r.predict(X) importance2 = sklearn_cart_r.feature_importances_ # 预测一致的比例 print(((res1-res2)<1e-8).mean()) # 特征重要性一致的比例 print(((importance1-importance2)<1e-8).mean()) # 模拟分类数据集 X, y = make_classification( n_samples=200, n_features=10, n_informative=5, random_state=0 ) # 分类树 my_cart_classification = DecisionTreeClassifier(max_depth=2) my_cart_classification.fit(X, y) res3 = my_cart_classification.predict(X) importance3 = my_cart_classification.feature_importances_ sklearn_cart_c = dc(max_depth=2) sklearn_cart_c.fit(X, y) res4 = sklearn_cart_c.predict(X) importance4 = sklearn_cart_c.feature_importances_ # 预测一致的比例 print(((res3-res4)<1e-8).mean()) # 特征重要性一致的比例 print(((importance3-importance4)<1e-8).mean())
# -*- coding: utf-8 -*- """ Created on Sun Oct 17 10:46:08 2021 @author: 86493 """ import numpy as np from collections import Counter def MSE(y): return ((y - y.mean())**2).sum() / y.shape[0] # 基尼指数 def Gini(y): c = Counter(y) return 1 - sum([(val / y.shape[0]) ** 2 for val in c.values()]) class Node: def __init__(self, depth, idx): self.depth = depth self.idx = idx self.left = None self.right = None self.feature = None self.pivot = None class Tree: def __init__(self, max_depth): self.max_depth = max_depth self.X = None self.y = None self.feature_importances_ = None def _able_to_split(self, node): return (node.depth < self.max_depth) & (node.idx.sum() >= 2) def _get_inner_split_score(self, to_left, to_right): total_num = to_left.sum() + to_right.sum() left_val = to_left.sum() / total_num * Gini(self.y[to_left]) right_val = to_right.sum() / total_num * Gini(self.y[to_right]) return left_val + right_val def _inner_split(self, col, idx): data = self.X[:, col] best_val = np.infty for pivot in data[:-1]: to_left = (idx==1) & (data<=pivot) to_right = (idx==1) & (~to_left) if to_left.sum() == 0 or to_left.sum() == idx.sum(): continue Hyx = self._get_inner_split_score(to_left, to_right) if best_val > Hyx: best_val, best_pivot = Hyx, pivot best_to_left, best_to_right = to_left, to_right return best_val, best_to_left, best_to_right, best_pivot def _get_conditional_entropy(self, idx): best_val = np.infty for col in range(self.X.shape[1]): Hyx, _idx_left, _idx_right, pivot = self._inner_split(col, idx) if best_val > Hyx: best_val, idx_left, idx_right = Hyx, _idx_left, _idx_right best_feature, best_pivot = col, pivot return best_val, idx_left, idx_right, best_feature, best_pivot def split(self, node): # 首先判断本节点是不是符合分裂的条件 if not self._able_to_split(node): return None, None, None, None # 计算H(Y) entropy = Gini(self.y[node.idx==1]) # 计算最小的H(Y|X) ( conditional_entropy, idx_left, idx_right, feature, pivot ) = self._get_conditional_entropy(node.idx) # 计算信息增益G(Y, X) info_gain = entropy - conditional_entropy # 计算相对信息增益 relative_gain = node.idx.sum() / self.X.shape[0] * info_gain # 更新特征重要性 self.feature_importances_[feature] += relative_gain # 新建左右节点并更新深度 node.left = Node(node.depth+1, idx_left) node.right = Node(node.depth+1, idx_right) self.depth = max(node.depth+1, self.depth) return idx_left, idx_right, feature, pivot def build_prepare(self): self.depth = 0 self.feature_importances_ = np.zeros(self.X.shape[1]) self.root = Node(depth=0, idx=np.ones(self.X.shape[0]) == 1) def build_node(self, cur_node): if cur_node is None: return idx_left, idx_right, feature, pivot = self.split(cur_node) cur_node.feature, cur_node.pivot = feature, pivot self.build_node(cur_node.left) self.build_node(cur_node.right) def build(self): self.build_prepare() self.build_node(self.root) def _search_prediction(self, node, x): if node.left is None and node.right is None: # return self.y[node.idx].mean() return self.y[node.idx].min() if x[node.feature] <= node.pivot: node = node.left else: node = node.right return self._search_prediction(node, x) def predict(self, x): return self._search_prediction(self.root, x) class DecisionTreeClassifier: """ max_depth控制最大深度,类功能与sklearn默认参数下的功能实现一致 """ def __init__(self, max_depth): self.tree = Tree(max_depth=max_depth) def fit(self, X, y): self.tree.X = X self.tree.y = y self.tree.build() self.feature_importances_ = ( self.tree.feature_importances_ / self.tree.feature_importances_.sum() ) return self def predict(self, X): return np.array([self.tree.predict(x) for x in X])
输出结果如下,可见在误差范围内,实现的分类树和回归树均和sklearn实现的模块近似。
1.0 1.0 1.0 1.0