Does scikit-learn perform “real” multivariate regression (multiple dependent variables)?

Does scikit-learn perform “real” multivariate regression (multiple dependent variables)?

This question delves into the capabilities of the popular Python machine learning library, scikit-learn, in handling multivariate regression problems.

What is multivariate regression?

In multivariate regression, we aim to predict multiple dependent variables simultaneously using a single model. It contrasts with the more common univariate regression where we predict a single dependent variable.

Scikit-learn’s approach

Limitations of built-in methods

Scikit-learn primarily focuses on univariate regression methods. While you can find methods like LinearRegression, Ridge, or Lasso, these are designed to predict a single dependent variable at a time.

Workarounds and alternatives

• Multiple independent models: You can train separate models for each dependent variable. This approach is simple but ignores potential relationships between dependent variables.
• Vector Autoregression (VAR): While not directly in scikit-learn, VAR models can handle time series data with multiple dependent variables.
• Custom models: Advanced users can build their own multivariate regression models using scikit-learn’s flexibility and building blocks.

Example: Multivariate Linear Regression (custom model)

Code Example

 import numpy as np from sklearn.linear_model import LinearRegression # Sample data (X: features, Y: multiple dependent variables) X = np.array([[1, 2], [3, 4], [5, 6]]) Y = np.array([[7, 8], [9, 10], [11, 12]]) # Create a custom multivariate model model = LinearRegression() model.fit(X, Y) # Predict multiple outputs predictions = model.predict([[7, 8]]) print(predictions) 

 [[13. 14.]] 

Explanation

• We use a standard LinearRegression object.
• fit() is called with both the features X and all dependent variables in Y.
• The model learns a single set of coefficients for all dependent variables. This assumes they are linearly related to the independent variables.
• predict() produces a prediction for all dependent variables at once.

Conclusion

Scikit-learn’s core regression methods are designed for univariate regression. While it lacks direct support for “real” multivariate regression, workarounds like custom models and external libraries like VAR can be employed for handling multiple dependent variables.