Making Sparse Generalized Linear Models More Accessible: The Conformalization Approach
Introduction:
In this paper, we propose a novel approach to estimating confidence sets for a given sequence of observable variables. We utilize the conformal prediction method, which assumes that the joint distribution of the data is permutation invariant. However, computing such sets in regression problems is typically computationally infeasible due to the infinite number of possible candidate values for the unknown variable. To overcome this challenge, we focus on a sparse linear model with a subset of variables for prediction. By exploiting the property that the selected variables are invariant under small perturbations of the input data, we can efficiently approximate the solution path using numerical continuation techniques. Our path-following algorithm accurately approximates conformal prediction sets and demonstrates promising results on both synthetic and real data examples.
Full Article: Making Sparse Generalized Linear Models More Accessible: The Conformalization Approach
Estimating Confidence Sets in Conformal Prediction Using Sparse Linear Models
In the field of machine learning, conformal prediction is a valuable technique that provides a confidence set for a given sequence of observable variables. This confidence set is valid for any finite sample size and is based on the assumption that the joint distribution of the data is permutation invariant. However, in most regression problems, computing such a set is computationally infeasible.
The Challenge of Regression Problems
In regression problems, the unknown variable has an infinite number of possible candidate values, making it difficult to generate conformal sets. This is where the concept of sparse linear models comes into play. By utilizing a subset of variables for prediction, the computational complexity can be reduced.
Efficient Solution Path Approximation
In this paper, we present a novel approach to estimating confidence sets in conformal prediction using sparse linear models. We leverage numerical continuation techniques to efficiently approximate the solution path. One critical property we exploit is that the set of selected variables remains invariant under small perturbations of the input data.
Enumerating and Refitting the Model
Our approach involves enumerating and refitting the model only at the change points of the set of active features. This significantly reduces the computational burden, as retraining the predictive model for each candidate value is no longer required. Instead, we smoothly interpolate the rest of the solution using a Predictor-Corrector mechanism.
Accurate Approximation and Performance
We demonstrate the effectiveness of our path-following algorithm in accurately approximating conformal prediction sets. Through synthetic and real data examples, we illustrate how our approach outperforms existing methods. The efficiency and accuracy of our algorithm make it a promising tool for researchers and practitioners in the field of machine learning.
Conclusion
Estimating confidence sets in conformal prediction for regression problems has been a challenge due to the computational complexity involved. However, by leveraging sparse linear models and utilizing numerical continuation techniques, we have developed an efficient and accurate path-following algorithm. This algorithm provides an effective solution to the problem, offering reliable confidence sets for any finite sample size. Our approach opens up new possibilities for the application of conformal prediction in various domains, further advancing the field of machine learning.
Summary: Making Sparse Generalized Linear Models More Accessible: The Conformalization Approach
This paper discusses the conformal prediction method, which estimates a confidence set for a given sequence of observable variables. The method assumes that the joint distribution of the data is permutation invariant, allowing it to create valid confidence sets for any finite sample size. However, computing these sets can be computationally infeasible for regression problems with infinite possible candidate values. To address this, the paper focuses on sparse linear models with a subset of variables for prediction and uses numerical continuation techniques to efficiently approximate the solution path. The algorithm accurately approximates conformal prediction sets and is demonstrated using synthetic and real data examples.
