# Conformalization of Sparse Generalized Linear Models

arXiv: https://arxiv.org/abs/2307.05109 · HTML: https://mlsanity.com/paper/2307.05109/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Fast Exact Conformalization of Lasso using Piecewise Linear Homotopy](https://mlsanity.com/paper/1708.00427/) (2017)
- [Computing Full Conformal Prediction Set with Approximate Homotopy](https://mlsanity.com/paper/1909.09365/) (2019)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [Conformal Prediction Intervals with Temporal Dependence](https://mlsanity.com/paper/2205.12940/) (2022)
- [Making learning more transparent using conformalized performance prediction](https://mlsanity.com/paper/2007.04486/) (2020)
- [Root-finding Approaches for Computing Conformal Prediction Set](https://mlsanity.com/paper/2104.06648/) (2021)
- [Continuation Path with Linear Convergence Rate](https://mlsanity.com/paper/2112.05104/) (2021)

## Built on by (most cited first, 4 of 4)

- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [A multiobjective continuation method to compute the regularization path of deep neural networks](https://mlsanity.com/paper/2308.12044/) (2023)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [Scaling Full Conformal Image Classifiers](https://mlsanity.com/paper/2609.37298/) (2026)

## Abstract (arXiv)

Given a sequence of observable variables (x1, y1), ldots, (xn, yn), the conformal prediction method estimates a confidence set for yn+1 given xn+1 that is valid for any finite sample size by merely assuming that the joint distribution of the data is permutation invariant. Although attractive, computing such a set is computationally infeasible in most regression problems. Indeed, in these cases, the unknown variable yn+1 can take an infinite number of possible candidate values, and generating conformal sets requires retraining a predictive model for each candidate. In this paper, we focus on a sparse linear model with only a subset of variables for prediction and use numerical continuation techniques to approximate the solution path efficiently. The critical property we exploit is that the set of selected variables is invariant under a small perturbation of the input data. Therefore, it is sufficient to enumerate and refit the model only at the change points of the set of active features and smoothly interpolate the rest of the solution via a Predictor-Corrector mechanism. We show how our path-following algorithm accurately approximates conformal prediction sets and illustrate its performance using synthetic and real data examples.