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:

[(a)] We have incorporated additional deep learning–based probabilistic forecasting models, including Quantile GRU, Quantile TCN, and Quantile Transformer, as new baseline methods. Their performance has been compared with the SVM-based probabilistic forecasting models in Tables 12 and 13.

[(b)] The code and datasets used in our experiments have been provided through an anonymous GitHub repository.

[(c)] The revised manuscript now includes an explicit mapping of all claims to the corresponding empirical evidence.

[(d)] We have thoroughly reviewed the entire manuscript and performed comprehensive proofreading.

[(e)] All tables have been updated with detailed captions that define every acronym and unit used. Additionally, each caption now includes a brief one or two sentence summary highlighting the key insights from the numerical results to enhance reader comprehension.

[(f)] We have added Figures 3 and 4 to visually compare the performance of SSVQR and SVQR. All revisions are highlighted in blue in the updated manuscript.

Assigned Action Editor: ~Michele_Caprio1

Submission Number: 5744