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

arXiv:2606.20191 · stat.ML, stat.ME · Submitted 2026-06-18 · Read on arXiv

Edgar Jaber, Vincent Chabridon, Mathilde Mougeot

CB,ENS Paris Saclay · EDF R\&D PRISME · CB,ENSIIE,ENS Paris Saclay

stat.ML, stat.ME

Submitted: 2026-06-18

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Empirical Coverage — 20× in this paper · explained in 2 episodes
• Conformal Prediction — 16× in this paper · explained in 11 episodes
• Benchmark — 15× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Surrogate Model — 7× in this paper · explained in 3 episodes
• Hyperparameters — 5× in this paper · explained in 2 episodes
• Uncertainty Quantification — 5× in this paper · explained in 9 episodes
• Calibration — 4× in this paper · explained in 9 episodes
• Covariate Shift — 4× in this paper · explained in 3 episodes
• Active Learning — 3× in this paper · explained in 6 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Robustness — 3× in this paper · explained in 6 episodes
• Surrogate Models — 3× in this paper · explained in 3 episodes
• Exchangeability — 2× in this paper · explained in 2 episodes
• Expected Feasibility Function — 2× in this paper
• Gaussian Process (GP) — 2× in this paper · explained in 2 episodes
• Absorb — 1× in this paper · explained in 1 episode
• Bayesian Optimization — 1× in this paper · explained in 3 episodes
• Conformal Prediction (CP) — 1× in this paper · explained in 3 episodes
• Conformity — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 4 episodes
• Expressivity — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generator — 1× in this paper · explained in 2 episodes
• Monte Carlo Sampling — 1× in this paper · explained in 2 episodes
• Surrogate Modeling — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 6 episodes

Sources

• A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification
• Conformal prediction for full and sparse polynomial chaos expansions

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