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Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Data Science](https://towardsdatascience.com/category/data-science/) # How To Perform Feature Selection for Regression Problems In this article I explain what feature selection is and how to perform it before training a regression model in Python. [Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/) August 8, 20206 min read ![](../images/000.png) ## 1. Introduction ### What is **feature selection** ? > **Feature selection** is the procedure of selecting a **subset** (some out of all available) of the **input** **variables** that are most relevant to the target variable (that we wish to predict). **Target variable** here **** refers to the** variabl**e that we wish to** predic**t. For this article we will assume that we only have numerical input variables and a numerical target for regression predictive modeling. Assuming that, we can easily estimate the **relationship** between each **input** variable and the **target** variable. This relationship can be established by calculating a metric such as the correlation value for example. * * * * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the "[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\))" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning. * * * Learn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps. ## 2. The main numerical feature selection methods The 2 most famous feature selection techniques that can be used for numerical input data and a numerical target variable are the following: * Correlation (Pearson, spearman) * Mutual Information (MI, normalized MI) **Correlation** is a measure of how two variables change together. The most widely used correlation measure is the Pearson's correlation that assumes a Gaussian distribution of each variable and detects linear relationship between numerical variables. This is done in 2 steps: 1. The **correlation** between each regressor and the target is computed, that is, ((X[:, i] - mean(X[:, i])) _(y - mean_y)) / (std(X[:, i])_ std(y)). 2. It is converted to an **F score** then to a **p-value**. * * * **Mutual information** originates from the field of information theory. The idea is that the information gain (typically used in the construction of decision trees) is applied in order to perform the feature selection. Mutual information is calculated between two variables and measures as the reduction in uncertainty for one variable given a known value of the other variable. * * * ## 3. The dataset We will use the **boston** **house** -**prices** **dataset**. This dataset contains information collected by the U.S Census Service concerning housing in the area of Boston Mass. The dataset consists of the following variables: 1. CRIM - per capita crime rate by town 2. ZN - proportion of residential land zoned for lots over 25,000 sq.ft. 3. INDUS - proportion of non-retail business acres per town. 4. CHAS - Charles River dummy variable (1 if tract bounds river; 0 otherwise) 5. NOX - nitric oxides concentration (parts per 10 million) 6. RM - average number of rooms per dwelling 7. AGE - proportion of owner-occupied units built prior to 1940 8. DIS - weighted distances to five Boston employment centres 9. RAD - index of accessibility to radial highways 10. TAX - full-value property-tax rate per $10,000 11. PTRATIO - pupil-teacher ratio by town 12. B - 1000(Bk - 0.63)² where Bk is the proportion of blacks by town 13. LSTAT - % lower status of the population 14. MEDV - Median value of owner-occupied homes in $1000's * * * ## 4. Python Code & Working Example Let's load and split the dataset into training (70%) and test (30%) sets. text ``` from sklearn.datasets import load_boston from sklearn.model_selection import train_test_split from sklearn.feature_selection import SelectKBest from sklearn.feature_selection import f_regression import matplotlib.pyplot as plt from sklearn.feature_selection import mutual_info_regression ``` text ``` # load the data X, y = load_boston(return_X_y=True) ``` text ``` # split into train and test sets X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=0) ``` We will use the well known scikit-learn machine library. ### Case 1: Feature selection using the Correlation metric For the **correlation statistic** we will use the [f_regression() function](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.f_regression.html). This function can be used in a feature selection strategy, such as selecting the top k most relevant features (largest values) via the [SelectKBest class](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.SelectKBest.html). text ``` # feature selection f_selector = SelectKBest(score_func=f_regression, k='all') ``` text ``` # learn relationship from training data f_selector.fit(X_train, y_train) ``` text ``` # transform train input data X_train_fs = f_selector.transform(X_train) ``` text ``` # transform test input data X_test_fs = f_selector.transform(X_test) ``` text ``` # Plot the scores for the features plt.bar([i for i in range(len(f_selector.scores_))], f_selector.scores_) ``` text ``` plt.xlabel("feature index") plt.ylabel("F-value (transformed from the correlation values)") plt.show() ``` **Reminder** : For the correlation statistic case: 1. The correlation between each regressor and the target is computed, that is, ((X[:, i] - mean(X[:, i])) _(y - mean_y)) / (std(X[:, i])_ std(y)). 2. It is converted to an **F score** then to a **p-value**. ![Feature Importance plot](../images/001.png) Feature Importance plot **The plot above shows that feature 6 and 13 are more important than the other features. The y-axis represents the F-values that were estimated from the correlation values.** * * * ### Case 2: Feature selection using the Mutual Information metric The scikit-learn machine learning library provides an implementation of **mutual information** for feature selection with numeric input and output variables via the [mutual_info_regression() function](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.mutual_info_regression.html). text ``` # feature selection f_selector = SelectKBest(score_func=mutual_info_regression, k='all') ``` text ``` # learn relationship from training data f_selector.fit(X_train, y_train) ``` text ``` # transform train input data X_train_fs = f_selector.transform(X_train) ``` text ``` # transform test input data X_test_fs = f_selector.transform(X_test) ``` text ``` # Plot the scores for the features plt.bar([i for i in range(len(f_selector.scores_))], f_selector.scores_) ``` text ``` plt.xlabel("feature index") plt.ylabel("Estimated MI value") plt.show() ``` ![Feature Importance plot](../images/002.png) Feature Importance plot **The y-axis represents the estimated mutual information between each feature and the target variable. Compared to the correlation feature selection method we can clearly see many more features scored as being relevant. This may be because of the statistical noise that might exists in the dataset.** * * * ## 5. Conclusion In this article I have provided two ways in order to perform feature selection. **Feature selection** is the procedure of selecting a subset (some out of all available) of the input variables that are most relevant to the target variable. **Target variable** here **** refers to the** variabl**e that we wish to** predic**t. Using either the **Correlation** metric or the **Mutual** **Information** metric , we can easily estimate the **relationship** between each **input** variable and the **target** variable. **Correlation** **vs** **Mutual** **Information:** Compared to the correlation feature selection method we can clearly see many more features scored as being relevant. This may be because of the statistical noise that might exists in the dataset. * * * ### You might also like: > [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f) > [**Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-an-arima-model-2e3b3080bd70) * * * ## Stay tuned & support this effort If you liked and found this article useful, **follow** me to be able to see all my new posts. Questions? Post them as a comment and I will reply as soon as possible. * * * ## Latest posts > [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5) > [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c) > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e) > [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79) > [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832) * * * ## Get in touch with me * **LinkedIn** : * **ResearchGate** : * **EPFL** **profile** : * **Stack** **Overflow** : ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. 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