机器学习基础算法

机器学习基础算法1. 技术分析1.1 机器学习概述机器学习是数据科学的核心机器学习类型 监督学习: 有标签数据 无监督学习: 无标签数据 半监督学习: 部分标签 强化学习: 交互学习 学习任务: 分类: 离散输出 回归: 连续输出 聚类: 分组1.2 监督学习算法监督学习算法 线性模型: 线性回归、逻辑回归 树模型: 决策树、随机森林 集成学习: XGBoost、LightGBM 支持向量机: SVM 神经网络: Deep Learning 算法选择: 数据规模 特征类型 任务类型1.3 算法对比算法适用任务复杂度可解释性线性回归回归低高逻辑回归分类低高决策树分类/回归中高随机森林分类/回归中中XGBoost分类/回归高中2. 核心功能实现2.1 线性回归import numpy as np class LinearRegression: def __init__(self, learning_rate0.01, iterations1000): self.learning_rate learning_rate self.iterations iterations self.weights None self.bias None def fit(self, X, y): n_samples, n_features X.shape self.weights np.zeros(n_features) self.bias 0 for _ in range(self.iterations): y_pred np.dot(X, self.weights) self.bias dw (1 / n_samples) * np.dot(X.T, (y_pred - y)) db (1 / n_samples) * np.sum(y_pred - y) self.weights - self.learning_rate * dw self.bias - self.learning_rate * db def predict(self, X): return np.dot(X, self.weights) self.bias def score(self, X, y): y_pred self.predict(X) ss_res np.sum((y - y_pred) ** 2) ss_tot np.sum((y - np.mean(y)) ** 2) return 1 - (ss_res / ss_tot)2.2 逻辑回归class LogisticRegression: def __init__(self, learning_rate0.01, iterations1000): self.learning_rate learning_rate self.iterations iterations self.weights None self.bias None def _sigmoid(self, z): return 1 / (1 np.exp(-z)) def fit(self, X, y): n_samples, n_features X.shape self.weights np.zeros(n_features) self.bias 0 for _ in range(self.iterations): z np.dot(X, self.weights) self.bias y_pred self._sigmoid(z) dw (1 / n_samples) * np.dot(X.T, (y_pred - y)) db (1 / n_samples) * np.sum(y_pred - y) self.weights - self.learning_rate * dw self.bias - self.learning_rate * db def predict_proba(self, X): z np.dot(X, self.weights) self.bias return self._sigmoid(z) def predict(self, X, threshold0.5): return (self.predict_proba(X) threshold).astype(int) def accuracy(self, X, y): predictions self.predict(X) return np.mean(predictions y)2.3 决策树class DecisionTree: def __init__(self, max_depthNone, min_samples_split2): self.max_depth max_depth self.min_samples_split min_samples_split self.tree None def _entropy(self, y): _, counts np.unique(y, return_countsTrue) probabilities counts / len(y) return -np.sum(probabilities * np.log2(probabilities)) def _information_gain(self, X, y, feature_idx, threshold): left_mask X[:, feature_idx] threshold right_mask ~left_mask if len(y[left_mask]) 0 or len(y[right_mask]) 0: return 0 parent_entropy self._entropy(y) left_entropy self._entropy(y[left_mask]) right_entropy self._entropy(y[right_mask]) weight_left len(y[left_mask]) / len(y) weight_right len(y[right_mask]) / len(y) return parent_entropy - (weight_left * left_entropy weight_right * right_entropy) def _best_split(self, X, y): best_gain -1 best_feature None best_threshold None for feature_idx in range(X.shape[1]): thresholds np.unique(X[:, feature_idx]) for threshold in thresholds: gain self._information_gain(X, y, feature_idx, threshold) if gain best_gain: best_gain gain best_feature feature_idx best_threshold threshold return best_feature, best_threshold, best_gain def _build_tree(self, X, y, depth0): if len(np.unique(y)) 1 or len(y) self.min_samples_split: return np.bincount(y).argmax() if self.max_depth is not None and depth self.max_depth: return np.bincount(y).argmax() feature, threshold, gain self._best_split(X, y) if gain 0: return np.bincount(y).argmax() left_mask X[:, feature] threshold right_mask ~left_mask left_tree self._build_tree(X[left_mask], y[left_mask], depth 1) right_tree self._build_tree(X[right_mask], y[right_mask], depth 1) return { feature: feature, threshold: threshold, left: left_tree, right: right_tree } def fit(self, X, y): self.tree self._build_tree(X, y) def _predict_sample(self, x, tree): if not isinstance(tree, dict): return tree if x[tree[feature]] tree[threshold]: return self._predict_sample(x, tree[left]) else: return self._predict_sample(x, tree[right]) def predict(self, X): return np.array([self._predict_sample(x, self.tree) for x in X])2.4 随机森林class RandomForest: def __init__(self, n_trees100, max_depthNone, min_samples_split2): self.n_trees n_trees self.max_depth max_depth self.min_samples_split min_samples_split self.trees [] def fit(self, X, y): n_samples X.shape[0] for _ in range(self.n_trees): indices np.random.choice(n_samples, n_samples, replaceTrue) X_sample X[indices] y_sample y[indices] tree DecisionTree(max_depthself.max_depth, min_samples_splitself.min_samples_split) tree.fit(X_sample, y_sample) self.trees.append(tree) def predict(self, X): predictions np.array([tree.predict(X) for tree in self.trees]) return np.array([np.bincount(preds).argmax() for preds in predictions.T])3. 性能对比3.1 监督学习算法对比算法训练速度预测速度精度线性回归快快中逻辑回归快快中决策树中快中随机森林慢中高XGBoost慢中很高3.2 算法选择指南数据规模推荐算法原因小数据(1万)决策树/RF稳定中等数据(1万-100万)XGBoost平衡大数据(100万)LightGBM高效3.3 模型评估指标任务指标说明分类准确率正确预测比例分类F1分数平衡精确率和召回率回归RMSE均方根误差回归R²解释方差比例4. 最佳实践4.1 算法选择流程def choose_algorithm(X, y, task_typeclassification): n_samples, n_features X.shape if n_samples 1000: if task_type classification: return LogisticRegression else: return LinearRegression elif n_samples 100000: return XGBoost else: return LightGBM4.2 模型训练流程def train_model(X_train, y_train, X_test, y_test, model): model.fit(X_train, y_train) y_pred_train model.predict(X_train) y_pred_test model.predict(X_test) if hasattr(model, predict_proba): train_proba model.predict_proba(X_train)[:, 1] test_proba model.predict_proba(X_test)[:, 1] print(f训练集准确率: {np.mean(y_pred_train y_train):.4f}) print(f测试集准确率: {np.mean(y_pred_test y_test):.4f}) return model5. 总结机器学习算法是数据科学的核心线性模型简单、可解释树模型处理非线性关系集成学习提高准确性算法选择根据数据规模和任务类型对比数据如下XGBoost是分类任务的首选线性模型可解释性最强随机森林稳定性好推荐从简单模型开始逐步尝试理解算法原理有助于更好地应用和调优模型。