Welcome to the Conformal Inference Prediction Regions for Multivariate Response Regression package! This repository provides a Python implementation of a robust and versatile tool for constructing valid prediction regions at levels (1-�lpha) or (1-2�lpha) in multivariate response regression. The package extends the widely used Conformal Prediction methods to handle multivariate response data, accommodating a wide range of data distributions without relying on Gaussian assumptions.
Originally developed as part of a Master’s thesis in Mathematical Engineering at Politecnico di Milano, this package empowers analysts and researchers to make accurate predictions across diverse datasets while embracing the flexibility of a non-parametric approach.
- Handles Multivariate Response Regression: Extends conformal prediction methods to multivariate data.
- Distribution-Free: No assumptions of Gaussian data, making it suitable for diverse real-world scenarios.
- Customizable and Modular: Separates regression methods from prediction methods for enhanced flexibility.
- Visualization Support: Includes functions for plotting and interpreting prediction regions.
The package is structured into distinct function families to streamline the workflow:
-
Prediction Methods
Compute valid prediction regions using different conformal inference approaches. -
Regression Methods
Use built-in regression techniques or integrate your own models. Supported methods include linear regression, ridge, lasso, and elastic net. -
Plotting Methods
Visualize prediction regions and model outputs with specialized plotting functions.
This modular design provides maximum flexibility, allowing you to tailor the package to your specific regression analysis needs.
The package provides a rich set of functions to enable and enhance regression analysis. Here are the core functions:
| Function | Description |
|---|---|
conformal_multi_full |
Computes Full Conformal prediction regions |
conformal_multi_split |
Computes Split Conformal prediction regions |
conformal_multi_msplit |
Computes Multi-Split Conformal prediction regions |
get_prediction_model |
Creates and retrieves regression models for prediction |
plot_multi_full |
Visualizes Full Conformal prediction as scatter plots |
plot_multi_full_contour |
Visualizes Full Conformal prediction as contour plots |
plot_multi_split |
Custom visualizations for Split Conformal predictions |
plot_multi_msplit |
Plots Multi-Split Conformal prediction regions |
-
Install the Package
Clone this repository and install the package using:pip install . -
Import and Configure
Import the package and use its functions for your analysis:from conformal_inference import conformal_multidim_full, plot_multidim_full_scatter
-
Compute Prediction Regions
Fit your regression model, then use the conformal methods to compute prediction regions:prediction_region = conformal_multidim_full(model, X_train, Y_train, X_test, alpha=0.1)
-
Visualize Results
Use the plotting functions to explore your prediction regions:plot_multidim_full_scatter(prediction_region)
For a comprehensive understanding of the theoretical foundations, refer to the original thesis and supporting materials. A detailed analysis is available in this research paper.
We would like to thank the following contributors for their invaluable guidance and support:
- Prof. Simone Vantini - Politecnico di Milano
- Dr. Jacopo Diquigiovanni - Research collaborator
- Dr. Matteo Fontana - Research collaborator
- Prof. Aldo Solari - Università Bicocca di Milano
Their expertise and contributions were instrumental in shaping this package into a powerful tool for multivariate regression analysis.
Ready to explore the world of non-parametric multivariate regression? Clone the repository, explore the provided examples, and start building prediction regions with ease and confidence. With this package, you can embrace the flexibility of distribution-free regression and make accurate predictions across diverse datasets.