Minimum Volume Conformal Sets for Multivariate Regression

• URL: http://arxiv.org/abs/2503.19068v1
• Date: Mon, 24 Mar 2025 18:54:22 GMT
• Title: Minimum Volume Conformal Sets for Multivariate Regression
• Authors: Sacha Braun, Liviu Aolaritei, Michael I. Jordan, Francis Bach,
• Abstract summary: Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity.<n>We propose an optimization-driven framework based on a novel loss function that directly learns minimum-conformity covering sets.<n>Our approach optimize over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid geometric assumptions or rely on flexible but computationally expensive approaches that do not explicitly optimize prediction set volume. We propose an optimization-driven framework based on a novel loss function that directly learns minimum-volume covering sets while ensuring valid coverage. This formulation naturally induces a new nonconformity score for conformal prediction, which adapts to the residual distribution and covariates. Our approach optimizes over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations. Additionally, by jointly optimizing both the predictive model and predictive uncertainty, we obtain prediction sets that are tight, informative, and computationally efficient, as demonstrated in our experiments on real-world datasets.

Related papers

• Rectifying Conformity Scores for Better Conditional Coverage [75.73184036344908]
  We present a new method for generating confidence sets within the split conformal prediction framework.<n>Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage.
  arXiv  Detail & Related papers  (2025-02-22T19:54:14Z)
• Optimal Transport-based Conformal Prediction [8.302146576157497]
  Conformal Prediction (CP) is a principled framework for uncertainty in blackbox learning models.<n>We introduce a novel CP procedure handling prediction score functions through a lens.<n>We then adapt our method for quantifying multi-output regression and multiclass classification.
  arXiv  Detail & Related papers  (2025-01-31T09:48:28Z)
• Multi-model Ensemble Conformal Prediction in Dynamic Environments [14.188004615463742]
  We introduce a novel adaptive conformal prediction framework, where the model used for creating prediction sets is selected on the fly from multiple candidate models. The proposed algorithm is proven to achieve strongly adaptive regret over all intervals while maintaining valid coverage.
  arXiv  Detail & Related papers  (2024-11-06T05:57:28Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation [18.928543069018865]
  Conformal prediction is one approach that avoids distributional assumptions.<n>Merging prediction regions directly, however, sacrifices structures present in the conformal scores that can further reduce conservatism.<n>We show that a novel framework can be efficiently leveraged in both classification and predict-then-optimize regression settings.
  arXiv  Detail & Related papers  (2024-05-25T14:11:01Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Variational Inference with Coverage Guarantees in Simulation-Based Inference [18.818573945984873]
  We propose Conformalized Amortized Neural Variational Inference (CANVI) CANVI constructs conformalized predictors based on each candidate, compares the predictors using a metric known as predictive efficiency, and returns the most efficient predictor. We prove lower bounds on the predictive efficiency of the regions produced by CANVI and explore how the quality of a posterior approximation relates to the predictive efficiency of prediction regions based on that approximation.
  arXiv  Detail & Related papers  (2023-05-23T17:24:04Z)
• Adaptive Selection of the Optimal Strategy to Improve Precision and Power in Randomized Trials [2.048226951354646]
  We show how to select the adjustment approach -- which variables and in which form -- to maximize precision. Our approach maintains Type-I error control (under the null) and offers substantial gains in precision. When applied to real data, we also see meaningful efficiency improvements overall and within subgroups.
  arXiv  Detail & Related papers  (2022-10-31T16:25:38Z)
• Efficient and Differentiable Conformal Prediction with General Function Classes [96.74055810115456]
  We propose a generalization of conformal prediction to multiple learnable parameters. We show that it achieves approximate valid population coverage and near-optimal efficiency within class. Experiments show that our algorithm is able to learn valid prediction sets and improve the efficiency significantly.
  arXiv  Detail & Related papers  (2022-02-22T18:37:23Z)
• CovarianceNet: Conditional Generative Model for Correct Covariance Prediction in Human Motion Prediction [71.31516599226606]
  We present a new method to correctly predict the uncertainty associated with the predicted distribution of future trajectories. Our approach, CovariaceNet, is based on a Conditional Generative Model with Gaussian latent variables.
  arXiv  Detail & Related papers  (2021-09-07T09:38:24Z)
• Universal Prediction Band via Semi-Definite Programming [4.401255328572734]
  We propose a method to construct nonparametric, heteroskedastic prediction bands for uncertainty quantification. The data-adaptive prediction band is universally applicable with minimal distributional assumptions.
  arXiv  Detail & Related papers  (2021-03-31T16:30:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.