probabilistic forecasting

This paper addresses the degradation of probabilistic forecast calibration in dynamic data streams caused by distributional shift, feedback loops, and adversarial perturbations. We propose the first general online calibration framework grounded in Blackwell approachability—a theoretically rigorous foundation for sequential decision-making under uncertainty. Our method provides strong calibration guarantees in compact output spaces (e.g., classification and bounded regression) and enables lossless post-hoc recalibration of arbitrary pre-trained predictors. Technically, it unifies insights from Blackwell approachability theory, online optimization, and gradient-based updates, and introduces task-specific efficient algorithms for both classification and regression. Empirical evaluation demonstrates substantial improvements in calibration quality for energy system forecasting, with marked gains in robustness and practical utility for downstream decision-making tasks.

This work addresses the interpretability of predictive models—such as binary neural networks and Boolean networks—under multivariate Bernoulli inputs. Method: We propose an L² oblique projection analysis framework grounded in Hoeffding decomposition. Theoretically, we establish, for the first time, the explicit structure of Hoeffding decomposition under Bernoulli distributions: all higher-order interaction terms are orthogonal to the one-dimensional main subspace, enabling exact reverse engineering and closed-form solutions. This structure permits explicit derivation of global sensitivity metrics, including Sobol’ indices and Shapley effects. Computationally, the framework integrates Hoeffding decomposition, L² oblique projection, and variance attribution theory. Results: Numerical experiments demonstrate its effectiveness and scalability in high-dimensional, sparse binary input settings. To our knowledge, this is the first unified framework for model interpretation under discrete, finite-support inputs that simultaneously ensures theoretical rigor and computational feasibility.

This paper addresses the conceptual ambiguity, incomparability, and heterogeneous objectives plaguing calibration in predictive systems. We propose a unified distributional calibration framework. Methodologically, we introduce— for the first time—two semantic motivations: predictor self-realization (Γ-calibration) and decision-oriented accurate loss estimation; we then construct a formal semantic map leveraging properties of outcome distributions (Γ), swap regret, omniprediction, and multi-granularity grouping generalization. Theoretical contributions include: (i) proving Γ-calibration is equivalent to a specific swap-regret condition; (ii) unifying binary and high-dimensional calibration definitions; (iii) revealing the fundamental role of grouping in both calibration paradigms; and (iv) establishing deep connections to multicalibration and actuarial fairness. Our work provides the first systematic, interpretable, and designable theoretical foundation for calibration in trustworthy AI.

This work addresses the limitation of conformal prediction—its reliance on strictly valid conformity scores, which restricts model compatibility. We propose a conformity-score-free approach that models residuals as random variables and directly learns their distribution via split-sample or full-sample nonparametric statistics, enabling construction of prediction distributions with out-of-sample calibration guarantees. Our method applies to any point-estimate regression model: it treats model residuals as stochastic quantities and estimates their empirical distribution without assuming parametric forms or structural constraints (e.g., independence, symmetry, or homoscedasticity). We prove finite-sample cross-calibration—that is, marginal coverage guarantees hold uniformly across test samples. Empirically, our method achieves calibration performance comparable to standard conformal prediction while being inherently compatible with arbitrary regression models, including deep neural networks and ensemble methods. This significantly broadens the applicability and flexibility of calibrated prediction systems.

This work addresses the challenge of entangled uncertainty sources and the difficulty of disentangling pointwise statistical risk in predictive modeling. We propose a unified generative framework based on approximate Bayesian inference that, for the first time, establishes an explicit, interpretable decomposition linking pointwise statistical risk to two fundamental uncertainty types: aleatoric uncertainty (arising from inherent data noise) and epistemic uncertainty (stemming from model ignorance). The framework jointly generates multiple uncertainty measures while ensuring semantic consistency across them. Experiments on image benchmarks demonstrate significant improvements in out-of-distribution detection and misclassification identification, achieving higher AUROC scores compared to existing methods. Our approach thus provides robust, quantifiable uncertainty estimates essential for downstream uncertainty-aware tasks such as active learning, safe decision-making, and model debugging.

This study addresses the unification of calibration concepts across classification and regression tasks, aiming to ensure consistency between predicted distributions and observed outcomes for diverse data types—continuous, discrete, nominal, and binary. The work introduces modal calibration for nominal outcomes and establishes a hierarchical framework distinguishing full, partial, and average calibration. It proposes a generalized definition of calibration based on predictive distribution functionals—such as means, quantiles, and event probabilities—and leverages probability integral transforms alongside constructive algorithms for analysis. Key contributions include demonstrating the logical independence between dual probability integral transform (PIT) calibration and existing discrete calibration notions, clarifying implication and independence relationships among various calibration types, and providing reproducible methods for generating illustrative examples and counterexamples.

This study addresses the challenge of uncertainty quantification in aggregated time series forecasting, particularly for annual totals and year-over-year growth rates. It proposes a simulation-augmented multi-step split conformal prediction method (SA-MSCP), which generates future trajectories via block bootstrap resampling from cross-validated residuals and constructs calibrated prediction intervals using empirical quantiles. By innovatively integrating a simulation-augmentation mechanism into the multi-step split conformal prediction framework, the method significantly improves empirical coverage for both aggregate totals and their growth rates, yielding more reliable uncertainty estimates without compromising predictive accuracy.

This study addresses the challenge of modeling predictive distributions for nonlinear, multivariate time series by proposing a general generative representation framework grounded in measure-theoretic probability, which is, to the authors’ knowledge, the first to be integrated with conditional generative adversarial networks (CGANs). Under a mild temporal dependence assumption, the method establishes estimation consistency in the Hausdorff metric and enables efficient simulation and computation of conditional means, variances, and risk measures. Empirical results demonstrate that the model achieves strong predictive performance on tasks involving stock returns, realized variances, and covariances, delivering high accuracy with remarkable computational efficiency—requiring only about one minute for a single training run.

This work rigorously establishes that predictive Bayesian inference (PBI) suffers from severely miscalibrated posterior uncertainty in practice when the forward predictive model is misspecified, potentially yielding credible sets with coverage approaching zero. We prove for the first time that the posterior concentrates precisely on the target dictated solely by the chosen forward predictive model, and that calibration of inference is guaranteed only when this model fully encompasses the true data-generating mechanism. By integrating predictive recursion algorithms, Bayesian nonparametric theory, and posterior concentration analysis, we demonstrate the fundamental role of the predictive model in determining inferential reliability and delineate the necessary conditions under which PBI can deliver valid uncertainty quantification.

This work addresses the limitation of existing safety-critical systems, which typically evaluate only predictive accuracy while lacking rigorous validation of the overall calibration of predicted probability distributions. To bridge this gap, the authors propose a modular calibration testing framework that decouples the calibration process into four interchangeable components: data model, scoring rule, hypothesis formulation, and statistical test procedure. Built upon formal statistical hypothesis testing, the framework provides a single accept/reject decision for the entire predictive distribution. Crucially, it rejects only overly confident predictions while tolerating reasonable deviations, thereby balancing practicality with flexibility. Empirical evaluations on weather forecasting and robotic pose estimation tasks demonstrate that the framework effectively supports reliable deployment in safety-critical applications.