# Conformalization of Sparse Generalized Linear Models

In collaboration with Georgia Institute of Technology

AuthorsEtash Kumar Guha, Eugene Ndiaye, Xiaoming Huo

content type paperpublished July 2023

In collaboration with Georgia Institute of Technology

AuthorsEtash Kumar Guha, Eugene Ndiaye, Xiaoming Huo

Given a sequence of observable variables $\{(x_1, y_1), \ldots, (x_n, y_n)\}$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ 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 $y_{n+1}$ 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.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals. Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to…

See paper detailsThis paper was accepted at the workshop on Regulatable ML at NeurIPS 2023.
Conformal Prediction (CP) is a method of estimating risk or uncertainty when using Machine Learning to help abide by common Risk Management regulations often seen in fields like healthcare and finance. CP for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a…

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