AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation

• URL: http://arxiv.org/abs/2606.20191v1
• Date: Thu, 18 Jun 2026 13:02:45 GMT
• Title: AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation
• Abstract summary: We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis.<n>The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models.<n>Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface.
• Score: 1.491109220586182
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

Related papers

• Conformal prediction for full and sparse polynomial chaos expansions [0.5735035463793009]
  Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling.<n>We present the integration of two conformal prediction methods, namely the full conformal and the Jackknife+ approaches, into both full and sparse PCEs.
  arXiv  Detail & Related papers  (2026-01-23T10:46:46Z)
• A robust and adaptive MPC formulation for Gaussian process models [2.6661512675766037]
  We present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems.<n>We derive robust predictions for GP models using metrics, which are incorporated in the MPC formulation.<n>We provide a numerical example of a planar quadrotor subject to difficult-to-model ground effects.
  arXiv  Detail & Related papers  (2025-07-02T19:27:14Z)
• 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)
• From Conformal Predictions to Confidence Regions [1.4272411349249627]
  We introduce CCR, which employs a combination of conformal prediction intervals for the model outputs to establish confidence regions for model parameters. We present coverage guarantees under minimal assumptions on noise and that is valid in finite sample regime. Our approach is applicable to both split conformal predictions and black-box methodologies including full or cross-conformal approaches.
  arXiv  Detail & Related papers  (2024-05-28T21:33:12Z)
• Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects [2.8927696200109527]
  We propose two novel methods to generate full predictive distributions of potential outcomes and individual treatment effects (ITEs)<n>Our approaches combine weighted conformal predictive systems with either analytic convolution of potential outcome distributions or Monte Carlo sampling.<n>In contrast to other approaches that allow the generation of potential outcome predictive distributions, our approaches are model agnostic, universal, and come with finite-sample guarantees of probabilistic calibration.
  arXiv  Detail & Related papers  (2024-02-07T14:35:25Z)
• CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networks [58.29502185344086]
  In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks. It is important to provide provable guarantees for deep learning models against semantically meaningful input transformations. We propose a new universal probabilistic certification approach based on Chernoff-Cramer bounds.
  arXiv  Detail & Related papers  (2021-09-22T12:46:04Z)
• Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes [0.0]
  We propose a methodology to quantify the sensitivity of the probability of failure estimator to two uncertainty sources. This analysis also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities.
  arXiv  Detail & Related papers  (2020-11-30T17:06:28Z)
• 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)
• Evaluating probabilistic classifiers: Reliability diagrams and score decompositions revisited [68.8204255655161]
  We introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. Corpor is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm.
  arXiv  Detail & Related papers  (2020-08-07T08:22:26Z)
• Providing reliability in Recommender Systems through Bernoulli Matrix Factorization [63.732639864601914]
  This paper proposes Bernoulli Matrix Factorization (BeMF) to provide both prediction values and reliability values. BeMF acts on model-based collaborative filtering rather than on memory-based filtering. The more reliable a prediction is, the less liable it is to be wrong.
  arXiv  Detail & Related papers  (2020-06-05T14:24:27Z)
• 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.