Conformal inference prediction regions for Multivariate response regression
This repository contains the R package conformalInference.multi (now available also on CRAN), which can produce valid prediction regions at levels 1-α or 1-2α under the basic assumption of i.i.d. regression data.
The package was developed as part of my MSc. final thesis in Mathematical Engineering at Politecnico di Milano, as a multivariate extension of the main methods for Conformal Prediction for regression in the univariate response case.
Code Structure
There are three main famililies of functions:
- Prediction methods
- Regression methods
- Plot methods
The central idea upon which the package is designed is the following: regression methods should not be included into the prediction methods themselves. Final users can pass as input to the prediction methods custom-coded regression algorithms, which may be more suitable for the prediction task at hand. Anyways the most common regression methods are implemented in the package.
Main Functions
| Syntax | Description |
|---|---|
| conformal.multidim.full | Computes Full Conformal prediction regions |
| conformal.multidim.jackplus | Computes Jackknife+ prediction regions |
| conformal.multidim.split | Computes Split Conformal prediction regions |
| conformal.multidim.msplit | Computes Multi Split Conformal prediction regions |
| elastic.funs | Build elastic net regression |
| lasso.funs | Build lasso regression |
| lm_multi | Build linear regression |
| mean_multi | Build regression functions with mean |
| plot_multidim | Plot the output of prediction methods |
| ridge.funs | Build elastic net regression |
Detailed description
A complete description of the theory underpinning the package, an analysis of all the main functions as well as a case study is presented in my final MSc. thesis paper, availble at the following link.
Acknownledgments
Prof. Simone Vantini - Politecnico di Milano
Dr. Jacopo Diquigiovanni
Dr. Matteo Fontana
Prof. Aldo Solari - Università Bicocca di Milano