.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/inspection/plot_causal_interpretation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_inspection_plot_causal_interpretation.py: =================================================== 机器学习在推断因果效应方面的失败 =================================================== 机器学习模型在测量统计关联方面表现出色。 不幸的是，除非我们愿意对数据做出强假设，否则这些模型无法推断因果效应。 为了说明这一点，我们将模拟一种情况，在这种情况下，我们试图回答教育经济学中最重要的问题之一：**获得大学学位对小时工资的因果效应是什么？** 尽管这个问题的答案对政策制定者至关重要，但 `遗漏变量偏差 `_ (OVB) 阻止了我们识别这种因果效应。 .. GENERATED FROM PYTHON SOURCE LINES 13-17 数据集：模拟的小时工资 ----------------------------------- 数据生成过程在下面的代码中列出。工作经验（以年为单位）和能力测量值从正态分布中抽取；父母一方的小时工资从贝塔分布中抽取。然后，我们创建一个大学学位的指示变量，该变量受能力和父母小时工资的正向影响。最后，我们将小时工资建模为所有先前变量和一个随机成分的线性函数。注意，所有变量对小时工资都有正向影响。 .. GENERATED FROM PYTHON SOURCE LINES 17-50 .. code-block:: Python import numpy as np import pandas as pd n_samples = 10_000 rng = np.random.RandomState(32) experiences = rng.normal(20, 10, size=n_samples).astype(int) experiences[experiences < 0] = 0 abilities = rng.normal(0, 0.15, size=n_samples) parent_hourly_wages = 50 * rng.beta(2, 8, size=n_samples) parent_hourly_wages[parent_hourly_wages < 0] = 0 college_degrees = ( 9 * abilities + 0.02 * parent_hourly_wages + rng.randn(n_samples) > 0.7 ).astype(int) true_coef = pd.Series( { "college degree": 2.0, "ability": 5.0, "experience": 0.2, "parent hourly wage": 1.0, } ) hourly_wages = ( true_coef["experience"] * experiences + true_coef["parent hourly wage"] * parent_hourly_wages + true_coef["college degree"] * college_degrees + true_coef["ability"] * abilities + rng.normal(0, 1, size=n_samples) ) hourly_wages[hourly_wages < 0] = 0 .. GENERATED FROM PYTHON SOURCE LINES 51-55 模拟数据的描述 --------------------------------- 下图显示了每个变量的分布以及成对的散点图。我们OVB故事的关键是能力与大学学位之间的正相关关系。 .. GENERATED FROM PYTHON SOURCE LINES 55-69 .. code-block:: Python import seaborn as sns df = pd.DataFrame( { "college degree": college_degrees, "ability": abilities, "hourly wage": hourly_wages, "experience": experiences, "parent hourly wage": parent_hourly_wages, } ) grid = sns.pairplot(df, diag_kind="kde", corner=True) .. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_001.png :alt: plot causal interpretation :srcset: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 70-71 在下一节中，我们将训练预测模型，因此我们将目标列与其他特征分开，并将数据分为训练集和测试集。 .. GENERATED FROM PYTHON SOURCE LINES 71-78 .. code-block:: Python from sklearn.model_selection import train_test_split target_name = "hourly wage" X, y = df.drop(columns=target_name), df[target_name] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0) .. GENERATED FROM PYTHON SOURCE LINES 79-83 收入预测（完全观测变量） --------------------------- 首先，我们训练一个预测模型，即:class:`~sklearn.linear_model.LinearRegression` 模型。在这个实验中，我们假设真实生成模型使用的所有变量都是可用的。 .. GENERATED FROM PYTHON SOURCE LINES 83-95 .. code-block:: Python from sklearn.linear_model import LinearRegression from sklearn.metrics import r2_score features_names = ["experience", "parent hourly wage", "college degree", "ability"] regressor_with_ability = LinearRegression() regressor_with_ability.fit(X_train[features_names], y_train) y_pred_with_ability = regressor_with_ability.predict(X_test[features_names]) R2_with_ability = r2_score(y_test, y_pred_with_ability) print(f"R2 score with ability: {R2_with_ability:.3f}") .. rst-class:: sphx-glr-script-out .. code-block:: none R2 score with ability: 0.975 .. GENERATED FROM PYTHON SOURCE LINES 96-97 该模型很好地预测了时薪，正如高R2得分所示。我们绘制了模型系数，以表明我们准确地恢复了真实生成模型的值。 .. GENERATED FROM PYTHON SOURCE LINES 97-111 .. code-block:: Python import matplotlib.pyplot as plt model_coef = pd.Series(regressor_with_ability.coef_, index=features_names) coef = pd.concat( [true_coef[features_names], model_coef], keys=["Coefficients of true generative model", "Model coefficients"], axis=1, ) ax = coef.plot.barh() ax.set_xlabel("Coefficient values") ax.set_title("Coefficients of the linear regression including the ability features") _ = plt.tight_layout() .. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_002.png :alt: Coefficients of the linear regression including the ability features :srcset: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 112-116 收入预测（部分观测） ------------------------------------------- 在实际操作中，智力能力并未被观察到，或者仅通过一些间接指标（例如智商测试）进行估计，而这些指标也无意中测量了教育水平。但是，在线性模型中省略“能力”特征会通过正向遗漏变量偏差（OVB）导致估计值膨胀。 .. GENERATED FROM PYTHON SOURCE LINES 116-125 .. code-block:: Python features_names = ["experience", "parent hourly wage", "college degree"] regressor_without_ability = LinearRegression() regressor_without_ability.fit(X_train[features_names], y_train) y_pred_without_ability = regressor_without_ability.predict(X_test[features_names]) R2_without_ability = r2_score(y_test, y_pred_without_ability) print(f"R2 score without ability: {R2_without_ability:.3f}") .. rst-class:: sphx-glr-script-out .. code-block:: none R2 score without ability: 0.968 .. GENERATED FROM PYTHON SOURCE LINES 126-127 我们的模型在省略能力特征时的预测能力在R2得分方面是相似的。我们现在检查模型的系数是否与真实生成模型不同。 .. GENERATED FROM PYTHON SOURCE LINES 127-141 .. code-block:: Python model_coef = pd.Series(regressor_without_ability.coef_, index=features_names) coef = pd.concat( [true_coef[features_names], model_coef], keys=["Coefficients of true generative model", "Model coefficients"], axis=1, ) ax = coef.plot.barh() ax.set_xlabel("Coefficient values") _ = ax.set_title("Coefficients of the linear regression excluding the ability feature") plt.tight_layout() plt.show() .. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_003.png :alt: Coefficients of the linear regression excluding the ability feature :srcset: /auto_examples/inspection/images/sphx_glr_plot_causal_interpretation_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 142-150 为了补偿被省略的变量，模型夸大了大学学位特征的系数。因此，将该系数值解释为真实生成模型的因果效应是不正确的。 经验教训 --------------- 机器学习模型并非用于估计因果效应。虽然我们用线性模型展示了这一点，但遗漏变量偏差（OVB）可以影响任何类型的模型。 在解释系数或由于某个特征的变化引起的预测变化时，重要的是要记住可能存在的未观察到的变量，这些变量可能与所讨论的特征和目标变量都相关。这些变量被称为 `混杂变量 `_ 。为了在存在混杂的情况下仍然估计因果效应，研究人员通常会进行实验，其中处理变量（例如大学学位）是随机的。当实验费用过高或不道德时，研究人员有时可以使用其他因果推断技术，例如 `工具变量 `_ (IV) 估计。 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.170 seconds) .. _sphx_glr_download_auto_examples_inspection_plot_causal_interpretation.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/inspection/plot_causal_interpretation.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_causal_interpretation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_causal_interpretation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_causal_interpretation.zip ` .. include:: plot_causal_interpretation.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_