{"id":1071438,"date":"2025-01-08T11:07:19","date_gmt":"2025-01-08T03:07:19","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1071438.html"},"modified":"2025-01-08T11:07:21","modified_gmt":"2025-01-08T03:07:21","slug":"%e7%94%a8python%e5%a6%82%e4%bd%95%e5%81%9a%e9%80%90%e6%ad%a5%e5%9b%9e%e5%bd%92-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1071438.html","title":{"rendered":"\u7528python\u5982\u4f55\u505a\u9010\u6b65\u56de\u5f52"},"content":{"rendered":"

\"\u7528python\u5982\u4f55\u505a\u9010\u6b65\u56de\u5f52\"<\/p>\n

\u9010\u6b65\u56de\u5f52\u662f\u4e00\u79cd\u7edf\u8ba1\u65b9\u6cd5\uff0c\u7528\u4e8e\u9009\u62e9\u6700\u6709\u610f\u4e49\u7684\u53d8\u91cf\u8fdb\u884c\u56de\u5f52\u6a21\u578b\u7684\u6784\u5efa\u3002\u5176\u4e3b\u8981\u76ee\u7684\u662f\u901a\u8fc7\u9010\u6b65\u589e\u52a0\u6216\u51cf\u5c11\u53d8\u91cf\uff0c\u627e\u5230\u6700\u4f18\u7684\u6a21\u578b\u3002\u5728Python\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528statsmodels<\/code>\u5e93\u6765\u5b9e\u73b0\u9010\u6b65\u56de\u5f52\u3002\u4ee5\u4e0b\u662f\u5982\u4f55\u7528Python\u8fdb\u884c\u9010\u6b65\u56de\u5f52\u7684\u6b65\u9aa4\u548c\u8be6\u7ec6\u89e3\u91ca\u3002<\/p>\n<\/p>\n

\u9010\u6b65\u56de\u5f52\u5b9e\u73b0\u7684\u6838\u5fc3\u6b65\u9aa4\u5305\u62ec\uff1a\u9009\u62e9\u521d\u59cb\u6a21\u578b\u3001\u5411\u524d\u9009\u62e9\u53d8\u91cf\u3001\u5411\u540e\u6d88\u9664\u53d8\u91cf\u3001\u6700\u7ec8\u6a21\u578b\u9009\u62e9<\/strong>\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u9009\u62e9\u521d\u59cb\u6a21\u578b<\/h3>\n<\/p>\n

\u5728\u9010\u6b65\u56de\u5f52\u4e2d\uff0c\u9996\u5148\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u521d\u59cb\u6a21\u578b\u3002\u521d\u59cb\u6a21\u578b\u53ef\u4ee5\u662f\u4e00\u4e2a\u7a7a\u6a21\u578b\uff08\u6ca1\u6709\u72ec\u7acb\u53d8\u91cf\uff09\uff0c\u4e5f\u53ef\u4ee5\u662f\u5305\u542b\u6240\u6709\u72ec\u7acb\u53d8\u91cf\u7684\u6a21\u578b\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u9010\u6b65\u56de\u5f52\u6709\u4e09\u79cd\u7b56\u7565\uff1a\u5411\u524d\u9009\u62e9\uff08Forward Selection\uff09\u3001\u5411\u540e\u6d88\u9664\uff08Backward Elimination\uff09\u548c\u9010\u6b65\u56de\u5f52\uff08Stepwise Regression\uff09\u3002<\/p>\n<\/p>\n

\u5411\u524d\u9009\u62e9<\/h4>\n<\/p>\n

\u5411\u524d\u9009\u62e9\u4ece\u4e00\u4e2a\u7a7a\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u6dfb\u52a0\u53d8\u91cf\uff0c\u6bcf\u6b21\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u6a21\u578b\u7684\u89e3\u91ca\u80fd\u529b\u6700\u5f3a\u3002\u6dfb\u52a0\u53d8\u91cf\u7684\u6807\u51c6\u901a\u5e38\u662f\u57fa\u4e8eAI<\/a>C\uff08Akaike\u4fe1\u606f\u51c6\u5219\uff09\u6216BIC\uff08\u8d1d\u53f6\u65af\u4fe1\u606f\u51c6\u5219\uff09\u3002<\/p>\n<\/p>\n

\u5411\u540e\u6d88\u9664<\/h4>\n<\/p>\n

\u5411\u540e\u6d88\u9664\u4ece\u5305\u542b\u6240\u6709\u53d8\u91cf\u7684\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u5220\u9664\u53d8\u91cf\uff0c\u6bcf\u6b21\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u6a21\u578b\u7684\u89e3\u91ca\u80fd\u529b\u6700\u5f3a\u3002\u5220\u9664\u53d8\u91cf\u7684\u6807\u51c6\u540c\u6837\u662f\u57fa\u4e8eAIC\u6216BIC\u3002<\/p>\n<\/p>\n

\u9010\u6b65\u56de\u5f52<\/h4>\n<\/p>\n

\u9010\u6b65\u56de\u5f52\u7ed3\u5408\u4e86\u5411\u524d\u9009\u62e9\u548c\u5411\u540e\u6d88\u9664\u7684\u65b9\u6cd5\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u5148\u5c1d\u8bd5\u5411\u6a21\u578b\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u7136\u540e\u5c1d\u8bd5\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u76f4\u5230\u6a21\u578b\u8fbe\u5230\u6700\u4f18\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u5411\u524d\u9009\u62e9\u53d8\u91cf<\/h3>\n<\/p>\n

\u5728\u5411\u524d\u9009\u62e9\u4e2d\uff0c\u6211\u4eec\u4ece\u4e00\u4e2a\u7a7a\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u6dfb\u52a0\u53d8\u91cf\u3002\u6bcf\u6b21\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u5f97\u6a21\u578b\u7684AIC\u6216BIC\u503c\u6700\u5c0f\u3002<\/p>\n<\/p>\n

import statsmodels.api as sm<\/p>\n
import pandas as pd<\/p>\n
import numpy as np<\/p>\n
from sklearn.datasets import load_boston<\/p>\n
\u52a0\u8f7d\u6570\u636e<\/strong><\/h2>\n
boston = load_boston()<\/p>\n
X = pd.DataFrame(boston.data, columns=boston.feature_names)<\/p>\n
y = boston.target<\/p>\n
\u5411\u524d\u9009\u62e9<\/strong><\/h2>\n
def forward_selection(X, y, significance_level=0.05):<\/p>\n
    initial_features = X.columns.tolist()<\/p>\n
    best_features = []<\/p>\n
    while len(initial_features) > 0:<\/p>\n
        remaining_features = list(set(initial_features) - set(best_features))<\/p>\n
        new_pval = pd.Series(index=remaining_features)<\/p>\n
        for new_column in remaining_features:<\/p>\n
            model = sm.OLS(y, sm.add_constant(X[best_features + [new_column]])).fit()<\/p>\n
            new_pval[new_column] = model.pvalues[new_column]<\/p>\n
        min_p_value = new_pval.min()<\/p>\n
        if min_p_value < significance_level:<\/p>\n
            best_features.append(new_pval.idxmin())<\/p>\n
        else:<\/p>\n
            break<\/p>\n
    return best_features<\/p>\n
selected_features = forward_selection(X, y)<\/p>\n
print(selected_features)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u5411\u540e\u6d88\u9664\u53d8\u91cf<\/h3>\n<\/p>\n
\u5728\u5411\u540e\u6d88\u9664\u4e2d\uff0c\u6211\u4eec\u4ece\u5305\u542b\u6240\u6709\u53d8\u91cf\u7684\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u5220\u9664\u53d8\u91cf\u3002\u6bcf\u6b21\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u5f97\u6a21\u578b\u7684AIC\u6216BIC\u503c\u6700\u5c0f\u3002<\/p>\n<\/p>\n
# \u5411\u540e\u6d88\u9664<\/p>\n
def backward_elimination(X, y, significance_level=0.05):<\/p>\n
    features = X.columns.tolist()<\/p>\n
    while len(features) > 0:<\/p>\n
        model = sm.OLS(y, sm.add_constant(X[features])).fit()<\/p>\n
        max_p_value = model.pvalues.max()<\/p>\n
        if max_p_value >= significance_level:<\/p>\n
            excluded_feature = model.pvalues.idxmax()<\/p>\n
            features.remove(excluded_feature)<\/p>\n
        else:<\/p>\n
            break<\/p>\n
    return features<\/p>\n
selected_features = backward_elimination(X, y)<\/p>\n
print(selected_features)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u9010\u6b65\u56de\u5f52<\/h3>\n<\/p>\n
\u9010\u6b65\u56de\u5f52\u7ed3\u5408\u4e86\u5411\u524d\u9009\u62e9\u548c\u5411\u540e\u6d88\u9664\u7684\u65b9\u6cd5\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u5148\u5c1d\u8bd5\u5411\u6a21\u578b\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u7136\u540e\u5c1d\u8bd5\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u76f4\u5230\u6a21\u578b\u8fbe\u5230\u6700\u4f18\u3002<\/p>\n<\/p>\n
# \u9010\u6b65\u56de\u5f52<\/p>\n
def stepwise_selection(X, y, initial_list=[], threshold_in=0.01, threshold_out=0.05):<\/p>\n
    included = list(initial_list)<\/p>\n
    while True:<\/p>\n
        changed=False<\/p>\n
        # forward step<\/p>\n
        excluded = list(set(X.columns) - set(included))<\/p>\n
        new_pval = pd.Series(index=excluded)<\/p>\n
        for new_column in excluded:<\/p>\n
            model = sm.OLS(y, sm.add_constant(X[included + [new_column]])).fit()<\/p>\n
            new_pval[new_column] = model.pvalues[new_column]<\/p>\n
        best_pval = new_pval.min()<\/p>\n
        if best_pval < threshold_in:<\/p>\n
            best_feature = new_pval.idxmin()<\/p>\n
            included.append(best_feature)<\/p>\n
            changed=True<\/p>\n
        # backward step<\/p>\n
        model = sm.OLS(y, sm.add_constant(X[included])).fit()<\/p>\n
        pvalues = model.pvalues.iloc[1:]<\/p>\n
        worst_pval = pvalues.max()<\/p>\n
        if worst_pval > threshold_out:<\/p>\n
            changed=True<\/p>\n
            worst_feature = pvalues.idxmax()<\/p>\n
            included.remove(worst_feature)<\/p>\n
        if not changed:<\/p>\n
            break<\/p>\n
    return included<\/p>\n
selected_features = stepwise_selection(X, y)<\/p>\n
print(selected_features)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8be6\u7ec6\u89e3\u91ca<\/h3>\n<\/p>\n
1. \u6570\u636e\u52a0\u8f7d\u548c\u9884\u5904\u7406<\/h4>\n<\/p>\n
\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u52a0\u8f7d\u6570\u636e\u5e76\u8fdb\u884c\u9884\u5904\u7406\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u4f7f\u7528sklearn<\/code>\u5e93\u4e2d\u7684\u6ce2\u58eb\u987f\u623f\u4ef7\u6570\u636e\u96c6\u4f5c\u4e3a\u793a\u4f8b\u3002\u6570\u636e\u96c6\u52a0\u8f7d\u540e\uff0c\u72ec\u7acb\u53d8\u91cf\uff08\u7279\u5f81\uff09\u5b58\u50a8\u5728X<\/code>\u4e2d\uff0c\u76ee\u6807\u53d8\u91cf\uff08\u623f\u4ef7\uff09\u5b58\u50a8\u5728y<\/code>\u4e2d\u3002<\/p>\n<\/p>\n
2. \u5411\u524d\u9009\u62e9<\/h4>\n<\/p>\n
\u5411\u524d\u9009\u62e9\u4ece\u4e00\u4e2a\u7a7a\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u6dfb\u52a0\u53d8\u91cf\u3002\u6bcf\u6b21\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u5f97\u6a21\u578b\u7684AIC\u6216BIC\u503c\u6700\u5c0f\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u6bcf\u4e2a\u5269\u4f59\u53d8\u91cf\u7684p\u503c\uff0c\u5e76\u9009\u62e9p\u503c\u6700\u5c0f\u7684\u53d8\u91cf\u6dfb\u52a0\u5230\u6a21\u578b\u4e2d\u3002\u5982\u679c\u8be5\u53d8\u91cf\u7684p\u503c\u5c0f\u4e8e\u7ed9\u5b9a\u7684\u663e\u8457\u6027\u6c34\u5e73\uff08significance_level<\/code>\uff09\uff0c\u5219\u5c06\u5176\u6dfb\u52a0\u5230\u6a21\u578b\u4e2d\uff1b\u5426\u5219\uff0c\u505c\u6b62\u6dfb\u52a0\u53d8\u91cf\u3002<\/p>\n<\/p>\n
3. \u5411\u540e\u6d88\u9664<\/h4>\n<\/p>\n
\u5411\u540e\u6d88\u9664\u4ece\u5305\u542b\u6240\u6709\u53d8\u91cf\u7684\u6a21\u578b\u5f00\u59cb\uff0c\u9010\u6b65\u5220\u9664\u53d8\u91cf\u3002\u6bcf\u6b21\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u4f7f\u5f97\u6a21\u578b\u7684AIC\u6216BIC\u503c\u6700\u5c0f\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u6bcf\u4e2a\u53d8\u91cf\u7684p\u503c\uff0c\u5e76\u9009\u62e9p\u503c\u6700\u5927\u7684\u53d8\u91cf\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u3002\u5982\u679c\u8be5\u53d8\u91cf\u7684p\u503c\u5927\u4e8e\u7ed9\u5b9a\u7684\u663e\u8457\u6027\u6c34\u5e73\uff08significance_level<\/code>\uff09\uff0c\u5219\u5c06\u5176\u4ece\u6a21\u578b\u4e2d\u5220\u9664\uff1b\u5426\u5219\uff0c\u505c\u6b62\u5220\u9664\u53d8\u91cf\u3002<\/p>\n<\/p>\n
4. \u9010\u6b65\u56de\u5f52<\/h4>\n<\/p>\n
\u9010\u6b65\u56de\u5f52\u7ed3\u5408\u4e86\u5411\u524d\u9009\u62e9\u548c\u5411\u540e\u6d88\u9664\u7684\u65b9\u6cd5\u3002\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u5148\u5c1d\u8bd5\u5411\u6a21\u578b\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u53d8\u91cf\uff0c\u7136\u540e\u5c1d\u8bd5\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u4e00\u4e2a\u53d8\u91cf\uff0c\u76f4\u5230\u6a21\u578b\u8fbe\u5230\u6700\u4f18\u3002\u5728\u5411\u524d\u9009\u62e9\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u6bcf\u4e2a\u5269\u4f59\u53d8\u91cf\u7684p\u503c\uff0c\u5e76\u9009\u62e9p\u503c\u6700\u5c0f\u7684\u53d8\u91cf\u6dfb\u52a0\u5230\u6a21\u578b\u4e2d\u3002\u5982\u679c\u8be5\u53d8\u91cf\u7684p\u503c\u5c0f\u4e8e\u7ed9\u5b9a\u7684\u9608\u503c\uff08threshold_in<\/code>\uff09\uff0c\u5219\u5c06\u5176\u6dfb\u52a0\u5230\u6a21\u578b\u4e2d\u3002\u5728\u5411\u540e\u6d88\u9664\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u6bcf\u4e2a\u53d8\u91cf\u7684p\u503c\uff0c\u5e76\u9009\u62e9p\u503c\u6700\u5927\u7684\u53d8\u91cf\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u3002\u5982\u679c\u8be5\u53d8\u91cf\u7684p\u503c\u5927\u4e8e\u7ed9\u5b9a\u7684\u9608\u503c\uff08threshold_out<\/code>\uff09\uff0c\u5219\u5c06\u5176\u4ece\u6a21\u578b\u4e2d\u5220\u9664\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u4e0d\u65ad\u91cd\u590d\uff0c\u76f4\u5230\u6ca1\u6709\u53d8\u91cf\u53ef\u4ee5\u6dfb\u52a0\u6216\u5220\u9664\u4e3a\u6b62\u3002<\/p>\n<\/p>\n
\u603b\u7ed3<\/h3>\n<\/p>\n
\u901a\u8fc7\u4ee5\u4e0a\u6b65\u9aa4\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Python\u5b9e\u73b0\u9010\u6b65\u56de\u5f52\uff0c\u5e76\u9009\u62e9\u6700\u4f18\u7684\u53d8\u91cf\u6784\u5efa\u56de\u5f52\u6a21\u578b\u3002\u9010\u6b65\u56de\u5f52\u662f\u4e00\u79cd\u6709\u6548\u7684\u7279\u5f81\u9009\u62e9\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u4ece\u5927\u91cf\u53d8\u91cf\u4e2d\u9009\u62e9\u6700\u6709\u610f\u4e49\u7684\u53d8\u91cf\uff0c\u4ece\u800c\u6784\u5efa\u66f4\u597d\u7684\u56de\u5f52\u6a21\u578b\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u663e\u8457\u6027\u6c34\u5e73\u548c\u9608\u503c\uff0c\u4ee5\u83b7\u5f97\u6700\u4f18\u7684\u6a21\u578b\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u9010\u6b65\u56de\u5f52\u7684\u5b9a\u4e49\u662f\u4ec0\u4e48\uff1f<\/strong>
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