Inductive Venn-Abers and related regressors

Problem
This paper addresses the limitation of Venn-Abers predictors, which are currently restricted to binary classification and bounded regression tasks. The authors identify a gap in the literature regarding the extension of Venn-Abers predictors to unbounded regression scenarios. This work is presented as a preprint, indicating that it has not yet undergone peer review.

Method
The authors propose a generalization of Venn-Abers predictors to accommodate unbounded regression by integrating conformal prediction techniques. The core technical contribution involves the development of inductive Venn-Abers regressors, which leverage the properties of validity inherent in Venn-Abers predictors while extending their applicability. The methodology includes the formulation of a new loss function tailored for regression tasks and the use of conformal prediction to ensure valid uncertainty quantification. The training process is not explicitly detailed in terms of compute resources, but the authors conduct extensive simulation and empirical studies to evaluate the performance of their proposed regressors against standard regression techniques.

Results
The empirical evaluation demonstrates that the inductive Venn-Abers regressors achieve improved predictive efficiency compared to traditional regression methods, particularly as the size of the training dataset increases. While specific numerical results are not provided in the abstract, the authors claim that their approach yields significant effect sizes, suggesting a meaningful enhancement in predictive performance. The benchmarks used for comparison include standard regression algorithms, although specific names of these baselines are not disclosed in the abstract.

Limitations
The authors acknowledge that their approach is primarily focused on the theoretical underpinnings of extending Venn-Abers predictors to unbounded regression and may require further empirical validation across diverse datasets and real-world applications. They do not address potential computational inefficiencies that may arise from the added complexity of conformal prediction. Additionally, the scalability of the proposed method in high-dimensional settings is not discussed, which could limit its applicability in certain contexts.

Why it matters
This work has significant implications for the field of probabilistic regression, particularly in scenarios where valid uncertainty quantification is crucial. By extending Venn-Abers predictors to unbounded regression, the authors provide a framework that could enhance the reliability of predictions in various applications, such as finance, healthcare, and environmental modeling. The integration of conformal prediction into the regression framework may also inspire further research into hybrid models that combine the strengths of different probabilistic approaches. Overall, this paper lays the groundwork for future exploration of inductive Venn-Abers methods and their potential to improve predictive performance in complex regression tasks.

Authors: Ivan Petej, Vladimir Vovk
Source: arXiv:2605.06646
URL: https://arxiv.org/abs/2605.06646v1