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助教老师实现了Cart回归树，在老师代码的基础上，实现了Cart分类树，代码如下：
import numpy as npdef Gini(y):gn=1.0n=y.shape[0]for i in np.unique(y):gn=gn-(np.sum(y==i)/n)**2return gndef argmax(y):l=sorted([(np.sum(y==i),i) for i in np.unique(y)],reverse=True)return l[0][1]class Node:def __init__(self, depth, idx):self.depth = depthself.idx = idxself.left = Noneself.right = Noneself.feature = Noneself.pivot = Noneclass Tree:def __init__(self, max_depth):self.max_depth = max_depthself.X = Noneself.y = Noneself.feature_importances_ = Nonedef _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_valdef _inner_split(self, col, idx):data = self.X[:, col]best_val = np.inftyfor 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():continueHyx = self._get_inner_split_score(to_left, to_right)if best_val > Hyx:best_val, best_pivot = Hyx, pivotbest_to_left, best_to_right = to_left, to_rightreturn best_val, best_to_left, best_to_right, best_pivotdef _get_conditional_entropy(self, idx):best_val = np.inftyfor 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_rightbest_feature, best_pivot = col, pivotreturn best_val, idx_left, idx_right, best_feature, best_pivotdef 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, pivotdef build_prepare(self):self.depth = 0self.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, pivotself.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 argmax(self.y[node.idx])if x[node.feature] <= node.pivot:node = node.leftelse:node = node.rightreturn self._search_prediction(node, x)def predict(self, x):return self._search_prediction(self.root, x)class DecisionTreeClassification:"""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 = Xself.tree.y = yself.tree.build()self.feature_importances_ = (self.tree.feature_importances_ / self.tree.feature_importances_.sum())return selfdef predict(self, X):return np.array([self.tree.predict(x) for x in X])这篇关于DataWhale-树模型与集成学习-Task02-Cart分类树代码实现-202110的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！
