Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spaces

• URL: http://arxiv.org/abs/2506.08325v1
• Date: Tue, 10 Jun 2025 01:25:37 GMT
• Title: Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spaces
• Authors: Marcos Matabuena, Rahul Ghosal, Pavlo Mozharovskyi, Oscar Hernan Madrid Padilla, Jukka-Pekka Onnela,
• Abstract summary: We propose a model-free uncertainty quantification algorithm based on conditional depth measures and an integrated depth measure.<n>New algorithms can be used to define prediction and tolerance regions when predictors and responses are defined in separable Hilbert spaces.<n>We demonstrate the practical relevance of our approach through a digital health application related to physical activity.
• Score: 9.504740492278003
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties, the integration of depth measures into regression modeling to provide prediction regions remains a largely underexplored area of research. To address this gap, we propose a novel, model-free uncertainty quantification algorithm based on conditional depth measures--specifically, conditional kernel mean embeddings and an integrated depth measure. These new algorithms can be used to define prediction and tolerance regions when predictors and responses are defined in separable Hilbert spaces. The use of kernel mean embeddings ensures faster convergence rates in prediction region estimation. To enhance the practical utility of the algorithms with finite samples, we also introduce a conformal prediction variant that provides marginal, non-asymptotic guarantees for the derived prediction regions. Additionally, we establish both conditional and unconditional consistency results, as well as fast convergence rates in certain homoscedastic settings. We evaluate the finite--sample performance of our model in extensive simulation studies involving various types of functional data and traditional Euclidean scenarios. Finally, we demonstrate the practical relevance of our approach through a digital health application related to physical activity, aiming to provide personalized recommendations

Related papers

• Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces [3.637162892228131]
  We develop a conformal prediction algorithm that offers finite-sample coverage guarantees and fast convergence rates of the oracle estimator.<n>In heteroscedastic settings, we forgo these non-asymptotic guarantees to gain statistical efficiency.<n>We demonstrate the practical utility of our approach in personalized--medicine applications involving random response objects.
  arXiv  Detail & Related papers  (2025-07-21T15:54:13Z)
• Epistemic Uncertainty in Conformal Scores: A Unified Approach [2.449909275410288]
  Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture uncertainty.<n>We introduce $texttEPICSCORE$, a model-agnostic approach that enhances any conformal score by explicitly integrating uncertainty.<n>$texttEPICSCORE$ adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant.
  arXiv  Detail & Related papers  (2025-02-10T19:42:54Z)
• 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)
• A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models [6.647819824559201]
  We study the large-sample properties of a likelihood-based approach for estimating conditional deep generative models. Our results lead to the convergence rate of a sieve maximum likelihood estimator for estimating the conditional distribution.
  arXiv  Detail & Related papers  (2024-10-02T20:46:21Z)
• 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)
• 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)
• Validation Diagnostics for SBI algorithms based on Normalizing Flows [55.41644538483948]
  This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. This work should help the design of better specified models or drive the development of novel SBI-algorithms.
  arXiv  Detail & Related papers  (2022-11-17T15:48:06Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Bayesian Spatial Predictive Synthesis [8.66529877559667]
  spatial dependence is a prevalent and critical issue in spatial data analysis and prediction.<n>We propose a novel Bayesian ensemble methodology that captures spatially-varying model uncertainty.<n>We show that our method provides a finite sample theoretical guarantee for its predictive performance.
  arXiv  Detail & Related papers  (2022-03-10T07:16:29Z)
• Dense Uncertainty Estimation [62.23555922631451]
  In this paper, we investigate neural networks and uncertainty estimation techniques to achieve both accurate deterministic prediction and reliable uncertainty estimation. We work on two types of uncertainty estimations solutions, namely ensemble based methods and generative model based methods, and explain their pros and cons while using them in fully/semi/weakly-supervised framework.
  arXiv  Detail & Related papers  (2021-10-13T01:23:48Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Efficient Ensemble Model Generation for Uncertainty Estimation with Bayesian Approximation in Segmentation [74.06904875527556]
  We propose a generic and efficient segmentation framework to construct ensemble segmentation models. In the proposed method, ensemble models can be efficiently generated by using the layer selection method. We also devise a new pixel-wise uncertainty loss, which improves the predictive performance.
  arXiv  Detail & Related papers  (2020-05-21T16:08:38Z)

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.