所有算法
回归和分类作为两种类型的算法，都出现回归（线性回归和逻辑回归）的算法，如何理解。
线性回归和逻辑回归的区别
线性回归：一个参数一个值（参数不断的变化，值不断的变化）。逻辑回归是基于先线性回归的基础上加一个sigmod函数的判断，得出最终的一个分类结果（0/1）. 这就是线性回归和逻辑回归的区别。
线性回归例子：
import numpy as np from sklearn.linear_model import LinearRegression # 准备数据 X = np.array([[50], [60], [70], [80], [90], [100]]) # 面积 y = np.array([150, 180, 210, 240, 270, 300]) # 房价 # 创建并训练模型 model = LinearRegression() model.fit(X, y) # 查看学到的参数 print("权重 w =", model.coef_[0]) # 3.0 print("偏置 b =", model.intercept_) # 0.0 # 预测 75 平米 pred = model.predict([[75]]) print("75 平米预测房价 =", pred[0], "万元") # 225.0逻辑回归例子：
import numpy as np from sklearn.linear_model import LogisticRegression # 准备数据 X = np.array([[1], [2], [3], [4], [5], [6], [7], [8]]) # 学习时长 y = np.array([0, 0, 0, 1, 1, 1, 1, 1]) # 是否通过 # 创建并训练模型 model = LogisticRegression() model.fit(X, y) # 查看学到的参数 print("权重 w =", model.coef_[0][0]) print("偏置 b =", model.intercept_[0]) # 预测 3.5 小时 prob = model.predict_proba([[3.5]])[0][1] pred = model.predict([[3.5]])[0] print(f"3.5 小时通过概率 = {prob:.3f}") print(f"预测类别 = {pred}")如何理解参数中的 [**]
prob和pred分别代表什么意思，为什么prob有两个值？
岭回归：
import numpy as np from sklearn.linear_model import Ridge, LinearRegression # 准备数据 X = np.array([[50, 1], [60, 2], [70, 3], [80, 4], [90, 5], [100, 6]]) # 面积, 房龄 y = np.array([150, 180, 210, 240, 270, 300]) # 房价 # 普通线性回归 ols = LinearRegression() ols.fit(X, y) print("普通线性回归:") print(" 权重 =", ols.coef_) print(" 偏置 =", ols.intercept_) # 岭回归 ridge = Ridge(alpha=1.0) # alpha 就是 λ ridge.fit(X, y) print("\n岭回归 (alpha=1.0):") print(" 权重 =", ridge.coef_) print(" 偏置 =", ridge.intercept_) X_new = np.array([[75, 3]]) print("普通线性回归预测:", ols.predict(X_new)[0]) print("岭回归预测:", ridge.predict(X_new)[0])Lasso回归：
import numpy as np from sklearn.linear_model import LinearRegression, Ridge, Lasso # 数据 X = np.array([[50, 2, 1, 3, 10], [60, 2, 2, 5, 9], [70, 3, 3, 8, 8], [80, 3, 4, 10, 7], [90, 4, 5, 12, 6], [100, 4, 6, 15, 5], [110, 5, 7, 18, 4], [120, 5, 8, 20, 3], [130, 6, 9, 22, 2], [140, 6, 10, 25, 1]]) y = np.array([150, 180, 210, 240, 270, 300, 330, 360, 390, 420]) # 普通线性回归 ols = LinearRegression() ols.fit(X, y) print("普通线性回归权重:", np.round(ols.coef_, 2)) # 岭回归 ridge = Ridge(alpha=1.0) ridge.fit(X, y) print("岭回归权重: ", np.round(ridge.coef_, 2)) # Lasso 回归 lasso = Lasso(alpha=0.1) lasso.fit(X, y) print("Lasso 权重: ", np.round(lasso.coef_, 2))删除冗余特征的例子：
import numpy as np import pandas as pd from sklearn.linear_model import Lasso, LassoCV, LinearRegression from sklearn.model_selection import train_test_split from sklearn.metrics import mean_squared_error np.random.seed(42) # ========== 1. 生成数据 ========== n = 200 X = pd.DataFrame({ "面积": np.random.rand(n) * 100 + 50, "房间数": np.random.randint(1, 6, n), "房龄": np.random.randint(0, 30, n), "楼层": np.random.randint(1, 30, n), "距离地铁": np.random.rand(n) * 10, "朝向": np.random.randint(0, 4, n), "装修年限": np.random.randint(0, 10, n), "绿化率": np.random.rand(n), "物业费": np.random.rand(n) * 5, "编号": np.arange(n), }) y = (3.0 * X["面积"] + 5.0 * X["房间数"] - 1.0 * X["房龄"] + 0.5 * X["楼层"] - 2.0 * X["距离地铁"] + np.random.randn(n) * 5) print("=" * 50) print("原始特征数:", X.shape[1]) # ========== 2. 手动粗筛：10 -> 8 ========== X_8 = X.drop(columns=["编号", "朝向"]) print("粗筛后特征数:", X_8.shape[1]) # ========== 3. Lasso 细筛 ========== X_train, X_test, y_train, y_test = train_test_split( X_8, y, test_size=0.2, random_state=42 ) lasso_cv = LassoCV(alphas=np.logspace(-3, 2, 50), cv=5, random_state=42) lasso_cv.fit(X_train, y_train) lasso = Lasso(alpha=lasso_cv.alpha_).fit(X_train, y_train) print("=" * 50) print("Lasso 最优 alpha:", lasso_cv.alpha_) print(pd.DataFrame({"特征": X_8.columns, "权重": lasso.coef_})) # ========== 4. 手动删除权重为 0 的特征 ========== selected_idx = np.where(lasso.coef_ != 0)[0] selected_features = X_8.columns[selected_idx] X_selected = X_8[selected_features] print("=" * 50) print("Lasso 保留特征:", list(selected_features)) print("最终特征数:", X_selected.shape[1]) # ========== 5. 重新训练最终模型 ========== X_train_sel, X_test_sel, y_train_sel, y_test_sel = train_test_split( X_selected, y, test_size=0.2, random_state=42 ) final_model = LinearRegression().fit(X_train_sel, y_train_sel) print("=" * 50) print("最终模型权重:") print(pd.DataFrame({"特征": selected_features, "权重": final_model.coef_})) print("偏置:", final_model.intercept_) # ========== 6. 评估 ========== mse_final = mean_squared_error(y_test_sel, final_model.predict(X_test_sel)) print("=" * 50) print(f"最终模型测试集 MSE: {mse_final:.4f}")
