Uncertainty Quantification in SVM prediction

TMLR Paper5744 Authors

Abstract: This paper explores SVM models from the lens of uncertainty quantification (UQ), developed for regression and forecasting tasks. Unlike the Neural Network, the SVM solutions are typically more certain, stable, sparse, optimal and interpretable. However, there is only limited literature addressing uncertainty quantification (UQ) in SVM-based prediction. At first, We provide a comprehensive summary of existing Prediction Interval (PI) estimation and probabilistic forecasting methods developed in the SVM framework. Although SVMs offer globally optimal and stable solutions, the existing literature on UQ within the SVM framework still exhibits several critical gaps. In this work, we also address these gaps and extend contemporary UQ techniques to SVMs, for promoting their applicability across diverse domains for more reliable estimation. Our major contributions include the development of sparse SVM models for PI estimation and probabilistic forecasting, an investigation of the role of feature selection in PI estimation, and the extension of SVM regression to the Conformal Regression (CR) setting to construct more stable prediction sets with finite-sample guarantees. Extensive numerical experiments highlight that SVM-based UQ methods yield PIs and probabilistic forecasts that are less uncertain and comparable to, or even better than, those produced by modern complex deep learning and neural network models.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=qR4Bo43Bzk&noteId=s583W2ithS&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

Changes Since Last Submission:

The changes made since the last submission have been detailed in a separate document included in the supplementary material. We have carefully revised the manuscript to incorporate the reviewers’ reservations along with your suggestions and have provided a detailed point-by-point response to all queries and concerns. As part of the supplementary material, we have included a single PDF that first presents our point-by-point responses to the reviewers’ comments, followed by the revised manuscript with all changes highlighted in blue. For clarity, the key changes are summarized below:

(a) We have provided a clearer description of the derivation from problem (16) to problem (17) in the revised version by including the intermediate steps, thereby enhancing clarity and comprehension for readers.

(b) We have added a detailed clarification on the significance of sparsity and its interpretation in different contexts of SVM model for UQ tasks.

(c) We have revised our work in line with a survey-style paper so that it may serve as a roadmap for SVM models in UQ tasks for a broader audience.

Assigned Action Editor: ~Michele_Caprio1

Submission Number: 5744