Papers

We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which flexibly incorporates sparse, multi-source observational data, including hydraulic head, solute concentration, and hard conductivity data, through conditional injection mechanisms. These conditioning inputs subsequently guide the generative inversion process during sampling. Bypassing iterative forward simulations, DIN leverages stochastic sampling and probabilistic modeling mechanisms to directly generate ensembles of posterior parameter fields by repeatedly executing the reverse denoising process. Two representative posterior scenarios, Gaussian and non-Gaussian, are investigated. The results demonstrate that DIN can produce multiple constraint-satisfying realizations under identical observational conditions, accurately estimate hydraulic-conductivity fields, and achieve reliable uncertainty quantification. The framework exhibits strong generalization capability across diverse data distributions, offering a robust and unified alternative to conventional multi-stage inversion methodologies.

We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror descent routine for convex optimization to provably obtain - after finitely many iterations - both an approximate least-favorable distribution and a nearly optimal test, in a sense we make precise. Our theoretical results yield concrete recommendations about the algorithm's implementation, including its initial condition, its step size, and the number of iterations. Importantly, our suggested algorithm can be viewed as a slight variation of the algorithm suggested by Elliott, Müller, and Watson (2015), whose theoretical performance guarantees are unknown.

Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal Bayes provides the most efficient prediction sets (smallest by expected volume) among all prediction sets that are valid at the $(1 - \alpha)$ level if the model is correctly specified. However, a critical issue arises when the Bayesian model itself may be mis-specified, resulting in prediction set that might be suboptimal, even though it still enjoys the frequentist coverage guarantee. To address this limitation, we propose an innovative solution that combines Bayesian model averaging (BMA) with conformal prediction. This hybrid not only leverages the strengths of Bayesian conformal prediction but also introduces a layer of robustness through model averaging. Theoretically, we prove that the resulting prediction set will converge to the optimal level of efficiency, if the true model is included among the candidate models. This assurance of optimality, even under potential model uncertainty, provides a significant improvement over existing methods, ensuring more reliable and precise uncertainty quantification.

As digital communication grows in importance when connecting with healthcare providers, traditional behavioral and content message features are imbued with renewed significance. If one is to meaningfully connect with them, it is crucial to understand what drives them to engage and respond. In this study, the authors analyzed several million text messages sent through the Impiricus platform to learn which factors influenced whether or not a doctor clicked on a link in a message. Several key insights came to light through the use of logistic regression, random forest, and neural network models, the details of which the authors discuss in this paper.

In unsupervised or weakly-supervised approaches for speech dereverberation, the target clean (dry) signals are considered to be unknown during training. In that context, evaluating to what extent information can be retrieved from the sole knowledge of reverberant (wet) speech becomes critical. This work investigates the role of the reverberant (wet) phase in the time-frequency domain. Based on Statistical Wave Field Theory, we show that late reverberation perturbs phase components with white, uniformly distributed noise, except at low frequencies. Consequently, the wet phase carries limited useful information and is not essential for weakly supervised dereverberation. To validate this finding, we train dereverberation models under a recent weak supervision framework and demonstrate that performance can be significantly improved by excluding the reverberant phase from the loss function.

The estimation of explosive yield from heterogeneous observational data presents fundamental challenges in inverse problems, particularly when combining traditional physical measurements with modern artificial intelligence-interpreted modalities. We present a novel Bayesian fractional posterior framework that fuses seismic waves, crater dimensions, synthetic aperture radar imagery, and vision-language model interpreted ground-level images to estimate the yield of the 2020 Beirut explosion. Unlike conventional approaches that may treat data sources equally, our method learns trust weights for each modality through a Dirichlet prior, automatically calibrating the relative information content of disparate observations. Applied to the Beirut explosion, the framework yields an estimate of 0.34–0.48 kt TNT equivalent, representing 12 to 17 percent detonation efficiency relative to the 2.75 kt theoretical maximum from the blast's stored ammonium nitrate. The fractional posterior approach demonstrates superior uncertainty quantification compared to single-modality estimates while providing robustness against systematic biases. This work establishes a principled framework for integrating qualitative assessments with quantitative physical measurements, with applications to explosion monitoring, disaster response, and forensic analysis.

We introduce Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates (BITS for GAPS), a framework enabling information-theoretic experimental design of Gaussian process-based surrogate models. Unlike standard methods, which use fixed or point-estimated hyperparameters in acquisition functions, our approach propagates hyperparameter uncertainty into the sampling criterion through Bayesian hierarchical modeling. In this framework, a latent function receives a Gaussian process prior, while hyperparameters are assigned additional priors to capture the modeler's knowledge of the governing physical phenomena. Consequently, the acquisition function incorporates uncertainties from both the latent function and its hyperparameters, ensuring that sampling is guided by both data scarcity and model uncertainty. We further establish theoretical results in this context: a closed-form approximation and a lower bound of the posterior differential entropy. We demonstrate the framework's utility for hybrid modeling with a vapor-liquid equilibrium case study. Specifically, we build a surrogate model for latent activity coefficients in a binary mixture. We construct a hybrid model by embedding the surrogate into an extended form of Raoult's law. This hybrid model then informs distillation design. This case study shows how partial physical knowledge can be translated into a hierarchical Gaussian process surrogate. It also shows that using BITS for GAPS increases expected information gain and predictive accuracy by targeting high-uncertainty regions of the Wilson activity model. Overall, BITS for GAPS is a generalized uncertainty-aware framework for adaptive data acquisition in complex physical systems.

Penalty-based methods have become popular for solving bilevel optimization (BLO) problems, thanks to their effective first-order nature. However, they often require inner-loop iterations to solve the lower-level (LL) problem and small outer-loop step sizes to handle the increased smoothness induced by large penalty terms, leading to suboptimal complexity. This work considers the general BLO problems with coupled constraints (CCs) and leverages a novel penalty reformulation that decouples the upper- and lower-level variables. This yields an improved analysis of the smoothness constant, enabling larger step sizes and reduced iteration complexity for Penalty-Based Gradient Descent algorithms in ALTernating fashion (ALT-PBGD). Building on the insight of reduced smoothness, we propose PBGD-Free, a novel fully single-loop algorithm that avoids inner loops for the uncoupled constraint BLO. For BLO with CCs, PBGD-Free employs an efficient inner-loop with substantially reduced iteration complexity. Furthermore, we propose a novel curvature condition describing the "flatness" of the upper-level objective with respect to the LL variable. This condition relaxes the traditional upper-level Lipschitz requirement, enables smaller penalty constant choices, and results in a negligible penalty gradient term during upper-level variable updates. We provide rigorous convergence analysis and validate the method's efficacy through hyperparameter optimization for support vector machines and fine-tuning of large language models.

Composite endpoints are widely used in cardiovascular clinical trials to improve statistical efficiency while preserving clinical relevance. The win ratio (WR) measure and more general frameworks of win statistics have emerged as popular alternatives to traditional time-to-first-event analyses. Although analytic sample size formulas for WR have been developed, they rely on design parameters that are often not straightforward to specify. Consequently, sample size determination in clinical trials with WR for the primary analysis is most often based on simulations, which, however, can be computationally intensive. To address this challenge, we derive refined formulas to calculate the proportions of wins, losses, and ties for multiple prioritized time-to-event endpoints to assist with study planning. These formulas rely on familiar design inputs and become directly applicable when integrated with existing sample size methods. We conduct a comprehensive assessment of how correlation among endpoints affects sample size requirements across varying design features, and demonstrate the role of correlations through case studies to generate further insights.

In this paper, we introduce the Generalized Mixed Regularized Reduced Rank Regression model (GMR4), an extension of the GMR3 model designed to improve performance in high-dimensional settings. GMR3 is a regression method for a mix of numeric, binary and ordinal response variables, while also allowing for mixed-type predictors through optimal scaling. GMR4 extends this approach by incorporating regularization techniques, such as Ridge, Lasso, Group Lasso, or any combination thereof, making the model suitable for datasets with a large number of predictors or collinearity among them. In addition, we propose a cross-validation procedure that enables the estimation of the rank S and the penalty parameter lambda. Through a simulation study, we evaluate the performance of the model under different scenarios, varying the sample size, the number of non-informative predictors and response dimension. The results of the simulation study guide the choice of the penalty parameter lambda in the empirical application ISSP: Health and Healthcare I-II (2023), which includes mixed-type predictors and ordinal responses. In this application, the model results in a sparse and interpretable solution, with a limited set of influential predictors that provide insights into public attitudes toward healthcare.

In Structural Health Monitoring (SHM), the recovery of distributed mechanical parameters from sparse data is often ill-posed, raising critical questions about identifiability and the reliability of inferred states. While deterministic regularization methods such as Tikhonov stabilise the inversion, they provide little insight into the spatial limits of resolution or the inherent uncertainty of the solution. This paper presents a Bayesian inverse framework that rigorously quantifies these limits, using the identification of distributed flexural rigidity from rotation (tilt) influence lines as a primary case study. Fisher information is employed as a diagnostic metric to quantify sensor informativeness, revealing how specific sensor layouts and load paths constrain the recoverable spatial features of the parameter field. The methodology is applied to the full-scale openLAB research bridge (TU Dresden) using data from controlled vehicle passages. Beyond estimating the flexural rigidity profile, the Bayesian formulation produces credible intervals that expose regions of practical non-identifiability, which deterministic methods may obscure. The results demonstrate that while the measurement data carry high information content for the target parameters, their utility is spatially heterogeneous and strictly bounded by the experiment design. The proposed framework unifies identification with uncertainty quantification, providing a rigorous basis for optimising sensor placement and interpreting the credibility of SHM diagnostics.

We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a polynomial-time algorithm that achieves the minimax-optimal misclassification rate \begin{equation*} \exp \Bigl(-\bigl(1 \pm o(1)\bigr) \tfrac{C}{k}\Bigr), \quad \text{where } C = (\sqrt{pn} - \sqrt{qn})^2, \end{equation*} whenever $C \ge K\,k^2\,\log k$ for some universal constant $K$, matching the Kesten–Stigum (KS) threshold up to a $\log k$ factor. Notably, this rate holds even when an adversary corrupts an $\eta \le \exp\bigl(- (1 \pm o(1)) \tfrac{C}{k}\bigr)$ fraction of the nodes. To the best of our knowledge, the minimax rate was previously only attainable either via computationally inefficient procedures [ZZ15] or via polynomial-time algorithms that require strictly stronger assumptions such as $C \ge K k^3$ [GMZZ17]. In the node-robust setting, the best known algorithm requires the substantially stronger condition $C \ge K k^{102}$ [LM22]. Our results close this gap by providing the first polynomial-time algorithm that achieves the minimax rate near the KS threshold in both settings. Our work has two key technical contributions: (1) we robustify majority voting via the Sum-of-Squares framework, (2) we develop a novel graph bisection algorithm via robust majority voting, which allows us to significantly improve the misclassification rate to $1/\mathrm{poly}(k)$ for the initial estimation near the KS threshold.

This brief note clarifies that, in Generator Matching (which subsumes a large family of flow matching and diffusion models over continuous, manifold, and discrete spaces), both the Bregman divergence loss and the linear parameterization of the generator can depend on both the current state $X_t$ and the time $t$, and we show that the expectation over time in the loss can be taken with respect to a broad class of time distributions. We also show this for Edit Flows, which falls outside of Generator Matching. That the loss can depend on $t$ clarifies that time-dependent loss weighting schemes, often used in practice to stabilize training, are theoretically justified when the specific flow or diffusion scheme is a special case of Generator Matching (or Edit Flows). It also often simplifies the construction of $X_1$-predictor schemes, which are sometimes preferred for model-related reasons. We show examples that rely upon the dependence of linear parameterizations, and of the Bregman divergence loss, on $t$ and $X_t$.

We introduce a Bayesian quantile mixed-effects model for censored longitudinal outcomes based on the skew exponential power (SEP) error distribution. The SEP family separates tail behavior and skewness from the targeted quantile and includes the skew Laplace (SL) distribution as a special case. We derive analytic likelihood contributions for left, right, and interval censoring under the SEP model, so censored observations are handled within a single parametric framework without numerical integration in the likelihood. In simulation studies with varying censoring patterns and skewness profiles, the SEP-based quantile mixed-effects model maintains near-nominal bias and credible interval coverage for regression coefficients. In contrast, the SL-based model can exhibit bias and undercoverage when the data's skewness conflicts with the skewness implied by the target quantile. In an HIV-1 RNA viral load case study with left censoring at the assay limit, bridge-sampled marginal likelihoods and simulation-based residual diagnostics favor the SEP specification across quantiles and yield more stable estimates of treatment-specific viral load trajectories than the SL benchmark.

We propose ECPv2, a scalable and theoretically grounded algorithm for global optimization of Lipschitz-continuous functions with unknown Lipschitz constants. Building on the Every Call is Precious (ECP) framework, which ensures that each accepted function evaluation is potentially informative, ECPv2 addresses key limitations of ECP, including high computational cost and overly conservative early behavior. ECPv2 introduces three innovations: (i) an adaptive lower bound to avoid vacuous acceptance regions, (ii) a Worst-m memory mechanism that restricts comparisons to a fixed-size subset of past evaluations, and (iii) a fixed random projection to accelerate distance computations in high dimensions. We theoretically show that ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability. We further empirically validate these findings through extensive experiments and ablation studies. Using principled hyperparameter settings, we evaluate ECPv2 across a wide range of high-dimensional, non-convex optimization problems. Across benchmarks, ECPv2 consistently matches or outperforms state-of-the-art optimizers, while significantly reducing wall-clock time.

We provide counterexamples showing that uniform laws of large numbers do not hold for subdifferentials under natural assumptions. Our constructions are univariate random Lipschitz functions and bivariate random convex functions with two smooth pieces. Consequently, they resolve the questions posed by Shapiro and Xu [J. Math. Anal. Appl., 325 (2007), 1390-1399] in the negative. They also demonstrate the failure of certain graphical and pointwise laws for subdifferentials, revealing fundamental barriers to the consistency of sample-average approximation and subdifferential approximation.

Clinical trials face mounting challenges: fragmented patient populations, slow enrollment, and unsustainable costs, particularly for late phase trials in oncology and rare diseases. While external control arms built from real-world data have been explored, a promising alternative is the generation of synthetic control arms using generative AI. A central challenge is the generation of time-to-event outcomes, which constitute primary endpoints in oncology and rare disease trials, but are difficult to model under censoring and small sample sizes. Existing generative approaches, largely GAN-based, are data-hungry, unstable, and rely on strong assumptions such as independent censoring. We introduce a variational autoencoder (VAE) that jointly generates mixed-type covariates and survival outcomes within a unified latent variable framework, without assuming independent censoring. Across synthetic and real trial datasets, we evaluate our model in two realistic scenarios: (i) data sharing under privacy constraints, where synthetic controls substitute for original data, and (ii) control-arm augmentation, where synthetic patients mitigate imbalances between treated and control groups. Our method outperforms GAN baselines on fidelity, utility, and privacy metrics, while revealing systematic miscalibration of type I error and power. We propose a post-generation selection procedure that improves calibration, highlighting both progress and open challenges for generative survival modeling.

Ordering the expected outcomes across a collection of clusters after performing a covariate adjustment commonly arises in many applied settings, such as healthcare provider evaluation. Regression parameters in such covariate adjustment models are frequently estimated by maximum likelihood or through other criteria that do not directly evaluate the quality of the rankings resulting from using a particular set of parameter estimates. In this article, we propose both a novel empirical Bayes ranking procedure and an associated estimation approach for finding the regression parameters of the covariate adjustment model. By building our ranking approach around estimating approximate percentiles of the covariate-adjusted cluster-level means, we are able to develop manageable expressions for the expected ranking squared-error loss associated with any choice of the covariate-adjustment model parameters, and we harness this to generate a novel unbiased estimator for this expected loss. Minimization of this unbiased estimator directly leads to a novel ranking procedure that is often more robust than conventional empirical Bayes ranking methods. Through a series of simulation studies, we show that our approach consistently delivers improved ranking squared-error performance relative to competing methods, such as posterior expected ranks and ranking the components of the best linear unbiased predictor. Estimating rankings using our method is illustrated with an example from a longitudinal study evaluating test scores across a large group of schools.

We propose a flexible scenario-based regularized Sample Average Approximation (SBR-SAA) framework for stochastic optimization. This work is motivated by challenges in standard Wasserstein Distributionally Robust Optimization (WDRO), where out-of-sample performance, particularly tail risk, is sensitive to the choice of the p-norm, and formulations can be computationally intractable. Our method is inspired by the asymptotic expansion of the WDRO objective and introduces a regularizer that penalizes the (sub)gradient norm of the objective at a selected set of scenarios. This framework serves a dual purpose: (i) it provides a computationally tractable alternative to WDRO by using a representative subset of the data, and (ii) it can provide targeted robustness by incorporating user-defined adverse scenarios. We establish the theoretical properties of this framework by proving its equivalence to a decision-dependent WDRO problem, from which we derive finite sample guarantees and asymptotic consistency. We demonstrate the method's efficacy in two applications: (1) a multi-product newsvendor problem, where SBR-SAA serves as a tractable alternative to NP-hard WDRO, and (2) a mean-risk portfolio optimization problem, where it successfully uses historical crisis data to improve out-of-sample performance.

Explainable AI (XAI) is increasingly essential as modern models become more complex and high-stakes applications demand transparency, trust, and regulatory compliance. Existing global attribution methods often incur high computational costs, lack stability under correlated inputs, and fail to scale efficiently to large or heterogeneous datasets. We address these gaps with ExCIR (Explainability through Correlation Impact Ratio), a correlation-aware attribution score equipped with a lightweight transfer protocol that reproduces full-model rankings using only a fraction of the data. ExCIR quantifies sign-aligned co-movement between features and model outputs after robust centering (subtracting a robust location estimate, e.g., median or mid-mean, from features and outputs). We further introduce BlockCIR, a groupwise extension of ExCIR that scores sets of correlated features as a single unit. By aggregating the same signed-co-movement numerators and magnitudes over predefined or data-driven groups, BlockCIR mitigates double-counting in collinear clusters (e.g., synonyms or duplicated sensors) and yields smoother, more stable rankings when strong dependencies are present. Across diverse text, tabular, signal, and image datasets, ExCIR shows trustworthy agreement with established global baselines and the full model, delivers consistent top-$k$ rankings across settings, and reduces runtime via lightweight evaluation on a subset of rows. Overall, ExCIR provides computationally efficient, consistent, and scalable explainability for real-world deployment.

In ecology, photogrammetry is a crucial method for efficiently collecting non-destructive samples of natural environments. When estimating the spatial distribution of animals, detecting objects in large-scale images becomes crucial. Object detection models enable large-scale analysis but introduce uncertainty because detection probability depends on various factors. To address detection bias, we model the distribution of a species of benthic animals (holothurians) in an area of the Italian Tyrrhenian coast near Giglio Island using a Thinned Log-Gaussian Cox Process (LGCP). We assume that a "true" intensity function accurately describes the distribution, while the observed process, resulting from independent thinning, is represented by a degraded intensity. The detection function controls the thinning mechanism, influenced by the object's location and other detection-related features. We use manual identification of holothurians as our benchmark. We compare automatic detection with this benchmark, an unthinned LGCP, and the thinned model to highlight the improvements gained from the proposed approach.Our method allows researchers to use photogrammetry, automatically identify objects of interest, and correct biases and approximations caused by the observation process.

Compared to nonparametric estimators in the multivariate setting, kernel estimators for functional data models have a larger order of bias. This is problematic for constructing confidence regions or statistical tests since the bias might not be negligible. It stems from the fact that one sided kernels are used where already the first moment of the kernel is different from 0. It cannot be cured by assuming the existence of higher order derivatives. In the following, we propose bias corrected estimators based on the idea in \cite{Cheng2018} which still have an appealing structure, but have a bias of smaller order as in multiple regression settings while the variance is of the same order of magnitude as before. In addition we show asymptotic normality of such estimators and derive uniform rates. The performance of the estimator in finite samples is in addition checked in a simulation study.

We investigate how to optimally design local differential privacy (LDP) mechanisms that reduce data unfairness and thereby improve fairness in downstream classification. We first derive a closed-form optimal mechanism for binary sensitive attributes and then develop a tractable optimization framework that yields the corresponding optimal mechanism for multi-valued attributes. As a theoretical contribution, we establish that for discrimination-accuracy optimal classifiers, reducing data unfairness necessarily leads to lower classification unfairness, thus providing a direct link between privacy-aware pre-processing and classification fairness. Empirically, we demonstrate that our approach consistently outperforms existing LDP mechanisms in reducing data unfairness across diverse datasets and fairness metrics, while maintaining accuracy close to that of non-private models. Moreover, compared with leading pre-processing and post-processing fairness methods, our mechanism achieves a more favorable accuracy-fairness trade-off while simultaneously preserving the privacy of sensitive attributes. Taken together, these results highlight LDP as a principled and effective pre-processing fairness intervention technique.

Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization. Iterative approaches of approximating the GP posterior using solvers like conjugate gradients, stochastic gradient descent, or alternating projections avoid cubic costs, but often require many iterations to converge, limiting their efficacy when the posterior is updated frequently with new data. To address this, we introduce three warm-start strategies that exploit solutions of smaller linear systems to substantially speed-up convergence when updating the posterior with new data. Our methods are supported by theoretical analysis showing reduced initialization error in reproducing kernel Hilbert space (RKHS) distance, and by empirical results on regression benchmarks and Bayesian optimization tasks. Across solvers, warm-starting achieves speed-ups of up to 19x when solving to tolerance, and produces more accurate posterior estimates under fixed compute budgets, directly improving optimization performance. These results establish warm-starting as a simple, effective, and broadly applicable tool for scaling Gaussian processes in sequential settings.

Linear probes are widely used to interpret and evaluate neural representations, yet their reliability remains unclear, as probes may appear accurate in some regimes but collapse unpredictably in others. We uncover a spectral mechanism behind this phenomenon and formalize it as the Spectral Identifiability Principle (SIP), a verifiable Fisher-inspired condition for probe stability. When the eigengap separating task-relevant directions is larger than the Fisher estimation error, the estimated subspace concentrates and accuracy remains consistent, whereas closing this gap induces instability in a phase-transition manner. Our analysis connects eigengap geometry, sample size, and misclassification risk through finite-sample reasoning, providing an interpretable diagnostic rather than a loose generalization bound. Controlled synthetic studies, where Fisher quantities are computed exactly, confirm these predictions and show how spectral inspection can anticipate unreliable probes before they distort downstream evaluation.

The importance of Synthetic Data Generation (SDG) has increased significantly in domains where data quality is poor or access is limited due to privacy and regulatory constraints. One such domain is recruitment, where publicly available datasets are scarce due to the sensitive nature of information typically found in curricula vitae, such as gender, disability status, or age. This lack of accessible, representative data presents a significant obstacle to the development of fair and transparent machine learning models, particularly ranking algorithms that require large volumes of data to effectively learn how to recommend candidates. In the absence of such data, these models are prone to poor generalisation and may fail to perform reliably in real-world scenarios. Recent advances in Causal Generative Models (CGMs) offer a promising solution. CGMs enable the generation of synthetic datasets that preserve the underlying causal relationships within the data, providing greater control over fairness and interpretability in the data generation process. In this study, we present a specialised SDG method involving two CGMs: one modelling job offers and the other modelling curricula. Each model is structured according to a causal graph informed by domain expertise. We use these models to generate synthetic datasets and evaluate the fairness of candidate rankings under controlled scenarios that introduce specific biases.

We propose constructing confidence sets for the emergence, collapse, and recovery dates of a bubble separately by inverting tests for the location of the break date. We examine both likelihood ratio-type tests and the Elliott-Muller-type (2007) tests for detecting break locations. The limiting distributions of these tests are derived under the null hypothesis, and their asymptotic consistency under the alternative is established. Finite-sample properties are evaluated through Monte Carlo simulations. The results indicate that combining different types of tests effectively controls the empirical coverage rate while maintaining a reasonably small length of the confidence set.

In a growing renewable based energy system, accurate and reliable wind power forecasts are crucial for grid stability, balancing supply and demand and market risk management. Even though short-term weather forecasts have been thoroughly used to provide up to 3 days ahead renewable power predictions, forecasts involving prediction horizons longer than a week still need investigations. Despite the recent progress in subseasonal-to-seasonal weather probabilistic forecasting, their use for wind power prediction usually involves both temporal and spatial aggregation to achieve reasonable skill. In this study, we present a lead time and numerical weather model agnostic forecasting pipeline which enables to transform ECMWF subseasonal-to-seasonal weather forecasts into wind power forecasts for France for lead times ranging from 1 day to 46 days at daily resolution. By leveraging a post-processing step of the resulting power ensembles we show that these forecasts improve the climatological baseline by 15% to 5% for the Continuous Ranked Probability Score and 20% to 5% for ensemble Mean Squared Error up to 16 days in advance, before converging towards the climatological skill. This improvement in skill is jointly obtained with near perfect calibration of the forecasts for every lead time. The results suggest that electricity market players could benefit from the extended forecast range up to two weeks to improve their decision making on renewable supply

Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. Inspired by the universal approximation property of classical neural networks, ensuring that every continuous function can be arbitrarily well approximated uniformly on a compact set of a Euclidean space, some recent works have established analogous results for QNNs, ranging from single-qubit to multi-qubit QNNs, and even hybrid classical-quantum models. In this paper, we study the approximation capabilities of QNNs for periodic functions with respect to the supremum norm. We use the Jackson inequality to approximate a given function by implementing its approximating trigonometric polynomial via a suitable QNN. In particular, we see that by restricting to the class of periodic functions, one can achieve a quadratic reduction of the number of parameters, producing better approximation results than in the literature. Moreover, the smoother the function, the fewer parameters are needed to construct a QNN to approximate the function.

Graph spectral representations are fundamental in graph signal processing, providing a rigorous frameworkforanalyzing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the graph Fourier transform (GFT) through a fractional-order parameter, enabling flexible spectral analysis with mathematical consistency. The angular graph Fourier transform (AGFT) further introduces angular control by rotating GFT eigenvectors; however, existing constructions may fail to reduce exactly to the GFT at zero angle, weakening theoretical consistency and interpretability. To address these complementary limitations, namely the lack of rotation-based basis control in GFRFT and the defective zero-angle degeneracy of AGFT, this paper proposes the rotation-parameterized graph fractional Fourier transform (RP-GFRFT), which unifies fractional order and rotation-parameterized spectral analysis. A degeneracy preserving rotation matrix family is constructed to guarantee exact GFT reduction at zero angle. TwoRP-GFRFTvariants,I-RP-GFRFTandII-RP-GFRFT,arethenformulated, with theoretical analyses confirming their unitarity, invertibility, reduction behavior, and smooth parameter dependence. The fractional order and rotation angle are jointly optimized for adaptive graph spectral filtering. Experiments on real-world signals, images, and point clouds demonstrate that RP-GFRFT improves denoising accuracy, reconstruction quality, and feature preservation over GFRFT, AGFT, and representative filtering baselines.