This article proposes an improved rank based regression estimator obtained by replacing the ordinary integer ranks in the Wilcoxon rank-score regression procedure with smoothed ranks derived from a smoothed empirical cumulative distribution function. The smoothed ranks are computed via a continuous, nondecreasing kernel distribution function H that provides a differentiable approximation to the classical indicator function used in standard rank regression. Substituting these smoothed ranks into the Wilcoxon score function yields a new estimator for the slope parameter(s) of the simple and multiple linear regression model. We show that the proposed estimator inherits the robustness properties of classical rank regression while providing improved efficiency under heavy tailed error distributions and better handling of tied observations. A Wald type hypothesis test for the regression coefficients is derived and its asymptotic normality is established. A Monte Carlo simulation study compares new estimator with the ordinary least-squares (OLS) estimator, the classical Wilcoxon rank regression estimator, and the Theil and Sen estimator under several error distributions including the normal, Laplace, Cauchy, and contaminated normal. The proposed estimator achieves relative efficiencies at or above those of classical rank regression uniformly across all scenarios considered, with notable gains in the presence of outliers and heavy-tailed errors.

We give a principled derivation of the Soft-Min-SNR weight of Crowson et al. (2024). The spread divergence of Zhang et al. (2018) convolves both compared distributions with a Gaussian kernel before taking the Kullback-Leibler (KL) divergence; applied to the per-sample local matched-Gaussian surrogate at each timestep, it yields the closed-form weight w(t,lambda) = sigma^2 / (sigma^2 + lambda). Three consequences follow. First, for variance-preserving schedules, w(t,lambda) equals a constant multiple of Soft-Min-SNR with gamma' = (1+lambda)/lambda, deriving a validated heuristic rather than introducing a new weight. Second, the same weight matches Min-SNR-gamma at leading order under gamma approximately 1/lambda, giving a cross-walk between the soft and hard reweighting families. Third, a local-geometry analysis scales an SGD-difficulty proxy by w^3 at high-SNR timesteps. Complementary to the objective-level account of Kingma & Gao (2023), who unified monotonic-in-log-SNR weightings as ELBOs of noise-augmented data, ours smooths both compared distributions rather than only the data side. Empirically, the matching rule holds on CIFAR-10 (linear and cosine) and CelebA-64 (cosine), with trajectory-wide confirmation on the cross-dataset cut: |Ours - Min-SNR| averages 0.45 FID across seven intermediate checkpoints on the seed-42 CelebA-64 trajectory, roughly 3x tighter than either reweighter's gap to DDPM. The local-geometry prediction is partially borne out: Ours converges about 21% earlier than DDPM at mid-training FID thresholds on CIFAR-10's linear schedule, where high-SNR damping headroom is largest, but this iteration-efficiency advantage does not transfer to cosine or CelebA-64, where all three methods reach similar final FIDs. Overall: final-FID parity with dataset-dependent iteration efficiency, plus a principled matching rule across the Min-SNR family.

We study robust parameter estimation in sinusoidal regression models within a least absolute deviations (LAD) framework. While classical approaches rely predominantly on least-squares formulations, they are known to be sensitive to heavy-tailed noise and outliers. We formulate the estimation problem as direct minimization of the LAD objective and propose a simple, modular coordinate descent algorithm that exploits the partial convexity of the objective: amplitude parameters are updated via weighted median computations, leading to substantial computational improvements over traditional simplex-based optimization methods, while frequency parameters are estimated via a periodogram-inspired grid search with local refinement. We establish strong consistency and asymptotic normality of the proposed estimator under mild regularity conditions. Empirically, we demonstrate the method's effectiveness on both synthetic datasets and real-world time series, including the Mauna Loa atmospheric CO2 data, air passenger data, and UK drivers' deaths data, where robustness to non-Gaussian noise is essential. The proposed approach provides a simple, interpretable, and robust alternative to least-squares-based methods for sinusoidal signal estimation.

The monomial parameterization of finite-memory Volterra identification is ill-conditioned under non-Gaussian input, and the Wiener--Hermite expansion removes this ill-conditioning only for Gaussian white-noise input. We construct the distribution-matched Volterra--Wiener--Kunchenko (VWK) basis by oriented Gram--Schmidt orthogonalization of monomials in $L^2(P)$ and use it as an arbitrary-polynomial-chaos coordinate system for finite-memory Volterra identification from data, following the generalized polynomial chaos of Xiu and Karniadakis (2002) and the data-driven arbitrary polynomial chaos of Oladyshkin and Nowak (2012). The basis itself is classical; the contribution is the Volterra-estimation reading. First, an order-2 misspecification-penalty theorem shows that a self-normalized diagonal estimator in the variance-matched Gaussian basis incurs an excess $L^2(P)$ risk governed by the skew coefficient $\delta=\mu_3/\sigma^2$, vanishing exactly for symmetric inputs. Second, conditioning experiments separate the constructional fact that the population matched Gram is the identity from the finite-sample design Gram: at $n=2000$, the centered-exponential empirical VWK Gram remains far better conditioned than the power Gram, although it degrades with degree. Third, a machine-checked Lean 4 proof establishes the Binomial$(N,p)$ Krawtchouk row for arbitrary $N$. Full least squares over a fixed span is basis-invariant, so VWK stabilizes diagonal cross-correlation and regularized coordinate fits rather than claiming universal prediction superiority. The analysis is moment-based, finite-memory, and restricted to product input laws.

A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance. However, beyond simple cases such as conditional sampling, the target distribution is often left implicit, defined only through a sampling rule or a heuristic energy function. To address this, we propose Jeffrey guidance, a principled framework that extends diffusion-model control to applications beyond what standard guidance can express. It leverages Jeffrey's rule of conditioning to update marginal distributions towards a prescribed target, preserving the conditional structure and minimally perturbing the joint distribution. We first demonstrate Jeffrey guidance by targeting a prescribed embedding distribution. With Inception embeddings as the target, this leads to substantial reductions in FID on both CIFAR-10 and FFHQ. We further apply Jeffrey guidance to fairness on CelebA-HQ, updating an unconditional diffusion model to enforce independence between attributes.

We study the large sample asymptotic behaviour of the Maximum Likelihood Estimator of the discount and strength parameters $(\alpha,\theta)$ in the Ewens--Pitman model for random partitions, under mild assumptions on the data-generating mechanism. We show that four distinct regimes arise, depending on the limiting behaviour of the frequency spectrum. In particular, in contrast with previous work, we find that $\theta$ may play a crucial role asymptotically. We further show that the existing literature implicitly focuses on only two of these regimes, and we relate this restriction to the constraints imposed by infinite exchangeability. Under the latter, indeed, the number of distinct blocks and the frequency spectrum are necessarily tied by a rigid structural relation. We prove that this lack of flexibility can be overcome through what we call the scaled Ewens--Pitman model, in which $\theta$ is allowed to grow with the sample size $n$. Finally, we provide empirical evidence from real-world data showing that such extensions are needed to capture frequency spectra that fall outside the classical Ewens--Pitman framework.

We argue that dependent versions of McDiarmid's inequality are a useful but underutilized tool in mathematical statistics, learning theory and theoretical computer science. To make this point, we first highlight that approximate tensorization of entropy (ATE) implies McDiarmid's via the Entropy Method. Second, we derive McDiarmid's inequality for non-isotropic Gaussian random vectors $X \sim \mathcal N(\mu, \Sigma)$ through ATE with a constant of the order of the condition number of $\Sigma$. We both independently obtain this ATE through a simple application of stochastic localization and also discuss how a more general ATE for the Gibbs sampler due to Ascolani et al., 2026 generalizes McDiarmid's-like concentration to strongly log-concave and log-smooth probability measures. We then apply the resulting concentration inequalities to resolve a question on the concentration of $\operatorname{sign}(X)$ posed by Simone Bombari, investigate Erdős-Rényi graphs under dependence and prove a Dvoretzky-Kiefer-Wolfowitz-type inequality for observations from a joint measure fulfilling ATE and continuous marginal CDFs. For the class of strongly log-concave and log-smooth measures, this result improves upon a prior Dvoretzky-Kiefer-Wolfowitz-type inequality for non-i.i.d. observations due to Bobkov and Götze, 2010, by establishing the expected $1/\sqrt{n}$-rate of convergence under weak dependence instead of $n^{-1/3}$.

Recurrent event data frequently arise in biomedical studies, where individuals may experience multiple recurrences of the same type of events, such as recurrent hospitalizations. This article introduces a nonparametric method for recurrent events under a Bayesian ensemble learning framework, called Soft Bayesian Additive Regression Trees (SBART), which combines multiple soft decision trees to achieve high predictive accuracy and a smooth estimator of the underlying intensity of the recurrent events. The proposed model represents the conditional intensity function of the non-homogeneous Poisson process as the product of a time-constant baseline, a subject-specific frailty random effect, and a nonparametric component capturing potentially nonlinear covariate effects and unknown interactions among covariates and time. A two-layer data augmentation scheme is employed to efficiently incorporate the SBART component within our computational algorithm. Simulation studies demonstrate that our method, called RecSBART in short, achieves superior accuracy in estimating cumulative intensity compared to existing approaches, even when our modeling assumptions are not true. With the Bayesian analysis of a study of recurrent hospitalizations of colorectal cancer patients, we further demonstrate our RecSBART method's ability to reveal and interpret the underlying complex relationships among covariates in a recurrent events study.

Small randomized controlled trials are often used to screen interventions before running larger follow-up studies. This is a critical phase of experimentation, as missing effective interventions or scaling up harmful ones can be very costly. A common proposal to mitigate these errors is to recruit samples that are representative of the target population, but this is often challenging in resource-constrained pilots. We challenge the narrative that representative samples are always superior by showing that when statistical significance testing determines whether interventions receive further study, the pilot trial composition that maximizes the downstream expected improvement in outcomes depends critically on its budget size. In the large-budget limit, the optimal pilot design converges to a sample that is representative of the target population. However, in the small-budget regime, the pilot designer maximizes expected impact by sampling only from a single homogeneous sub-population, chosen in a manner that depends on sampling costs and the designer's prior beliefs about heterogeneous treatment effects. Our proof of the small-budget result applies more generally when an RCT and significance test are used to decide whether to receive any non-adaptive downstream payoff, a result that may be applicable to other settings with constrained experimentation budgets.

Cluster randomized trials (CRTs) are frequently used to evaluate interventions, yet conducting causal mediation analysis in these settings remains challenging, particularly when the mediator is measured at the cluster level and the number of clusters is small. Standard inference methods often rely on asymptotic assumptions that fail in finite-sample settings, leading to biased variance estimation and invalid confidence intervals. In this paper, we propose a robust inference framework for causal mediation analysis in CRTs. We utilize parametric Bayesian models for the outcome and mediator to ensure computational efficiency and interpretability. Crucially, to quantify uncertainty, we specify a novel similarity-weighted Bayesian bootstrap (SWBB) with a `distance' metric between clusters; this avoids the need for restrictive parametric assumptions and allows the model to borrow more information from `closer' clusters. By combining observed data models with causal assumptions, our approach accurately estimates natural direct and indirect effects even with limited clusters. Simulation studies demonstrate that our method achieves nominal coverage probability across diverse scenarios. We illustrate the practical utility of our approach by assessing mediation in a CRT in Kenya.

Causal discovery aims to identify causal relationships among variables from observational or interventional data, typically represented by a directed acyclic graph (DAG). The causal invariance principle enables the identification of the causal parents of target variables by exploiting the stability of causal effects across different experimental settings. When some parents are unobserved, however, the induced graph over the observed variables may no longer be a DAG, and it may not be unique, complicating causal inference. For relevant configurations of latent parents, we characterize the induced graph and formalize the conditions under which causal invariance is preserved for the identification of the observed parents. Necessary and sufficient conditions for testing such invariance are formally established for a multivariate Gaussian target.

Personalized medicine in acute ischemic stroke requires moving beyond average treatment effects (ATE) to individualized treatment effect (ITE) estimates to support treatment decisions. In acute ischemic stroke, mechanical thrombectomy has been shown to be more effective on average than lysis in randomized controlled trials (RCTs), such as the MR CLEAN study. We aim to identify which individual patients benefit most from mechanical thrombectomy compared to lysis. The outcome of interest is the modified Rankin Scale (mRS) at three months, an ordinal measure of functional disability (0: no symptoms, 6: death). We demonstrate that causal transformation models on directed acyclic graphs (TRAM-DAG) can be used for ITE estimation after being fitted on observational MAGIC multi-center stroke patient data. To ensure comparability with the MR CLEAN population, which we use for validation, we train the TRAM-DAG on a MAGIC sub-population with NIHSS at admission >= 6, corresponding to one inclusion criterion of MR CLEAN. The fitted model is then used to estimate ITEs for stroke patients in the MR CLEAN population. While these ITE estimates cannot be confirmed experimentally, we show that their average is consistent with the trial's reported ATE. Furthermore, the ITE estimates correctly rank trial patients by their observed frequency of a good outcome (mRS at three months <= 2). These findings support the use of causal models like TRAM-DAG for personalized decision-making in stroke care and highlight their ability to bridge the gap between observational evidence and clinical trials.

Machine learning models often degrade when they are deployed on a target distribution that differs from the source distributions they were trained on. Recent work in causality-based domain generalization has shown how shared causal structure between domains can induce invariant predictors, e.g., models on a subset of features which have stable risk across structured domain shifts. However, the extent to which such population-level causal invariances can lead to gains in finite-sample settings remains underexplored. In particular, in practice we often have access to a few labeled target samples, a setting called supervised domain adaptation (sDA). In this paper, we explore when (full or partial) causal knowledge can provably improve supervised domain adaptation. As a first step, we study linear regression, where full or partial causal knowledge specifies a collection of invariant or possibly invariant feature subsets, each yielding a source-trained candidate predictor. We derive matching upper and lower bounds showing that finite-sample gains are governed by the target-risk margins separating the candidates, together with the finite-source estimation error. When these margins are sufficiently large relative to $n_Q$, an adaptive aggregation procedure can match the best candidate predictor while avoiding negative transfer relative to target-only learning. On the other hand, when the margins are too small, no algorithm can reliably exploit the candidate collection to obtain faster finite-sample rates. We further connect these margins to structural shift magnitude in linear SCMs and validate the theory on real-world causal benchmarks.

This study investigates semiparametric efficient estimation of causal and structural parameters in a semi-supervised setting. In our setting, unlabeled auxiliary regressors are available in addition to labeled observations consisting of outcomes and regressors. Our goal is to construct estimators of causal and structural parameters whose asymptotic variances are smaller than those of estimators constructed using only labeled data. We refer to this framework as prediction-powered causal inference (PPCI). We first derive the efficient influence function and the efficiency bound, which imply that the use of auxiliary regressors can attain a smaller asymptotic variance than the efficiency bound attainable from labeled observations alone. Then, by combining the efficient influence function with the debiased machine learning (DML) framework, we propose methods that we call DML-PPCI. If we construct an estimating-equation estimator, we refer to the method as EE-DML-PPCI; if we construct a targeted-learning estimator, we refer to the method as TMLE-DML-PPCI. The asymptotic variances of both estimators match our derived efficiency bound. In the construction of the estimators, estimation of the efficient influence function plays an important role. In our study, the efficient influence function is also a Neyman orthogonal score, which depends on the Riesz representer and the regression function. For Riesz representer estimation, we develop semi-supervised generalized Riesz regression with convergence rate guarantees.

We study the problem of diffusion parameter estimation for stochastic differential equation (SDE) models in scenarios where data and model are compatible only on specific scales that have yet to be determined. We introduce a simple and efficient method for selecting suitable rates at which given time series data should be subsampled in order to ensure that the statistical structure of the subsampled data is consistent with the behavior of the SDE model on an infinitesimal scale. Our approach is based on analyzing the statistics of the lengths of monotonically increasing or decreasing segments in the subsampled data sequence, which we refer to as monotone runs. As an analytical foundation, we prove for a large class of SDEs with additive noise that the lengths of monotone runs at an infinitesimal scale are approximately geometrically distributed with success probability $1/2$. This universal characterization is employed to derive an automated method for selecting appropriate subsampling rates for given time series data that is directly applicable in real-world scenarios and does not rely on an asymptotic framework of multiscale diffusions. The approach is demonstrated using an application from industrial mathematics concerning surrogate models for fiber lay-down curves in production processes of nonwoven textiles.

Here we address the problem of estimating the dimensionality and nature of parametric variation in an unknown generative process directly from time-series data, without specifying or fitting a model. In particular we suppose that inter-instance variation in collections of time series is caused by parametric variation in the generating model. We hypothesize that, given a sufficiently large library of time-series features, low-dimensional parametric variation will manifest as low-dimensional structure in feature space, enabling interpretable estimators of the underlying degrees of freedom to be constructed. We test our hypothesis using a library of over 7000 diverse and interpretable time-series statistics and thirteen simulated systems with known parametric variation, spanning linear stochastic processes, nonlinear oscillators, and chaotic dynamics. Our unsupervised, data-driven approach often reconstructs the underlying parametric variation across this extensive range of simulated dynamical systems while also yielding interpretable estimators for each underlying dimension. Applied to the movement dynamics of 1143 fruit flies, we use this method to extract biologically meaningful components corresponding to sex and circadian rhythmicity. Our results pave the way for much-needed data-driven methods to bridge the gap between interpretable theoretical understanding of dynamics and the large and complex datasets that characterize modern scientific problems.

Vine copulas provide a flexible framework for modeling complex multivariate dependence structures using only bivariate building blocks. Their practical success relies heavily on the simplifying assumption, which restricts conditional pair copulas to be independent of the specific conditioning values. While this assumption greatly facilitates estimation, it may lead to model misspecification in applications with pronounced varying conditional dependence. We propose a novel calibration strategy for simplified vine copula models based on observation-specific correction factors. These factors are derived using noise contrastive estimation (NCE), a supervised learning technique for density estimation that reframes the problem as a binary classification task with an easily sampled noise distribution. Treating the fitted simplified vine copula as the noise model, the NCE approach yields corrected log-likelihood estimates for individual observations, thereby locally adjusting the simplified vine toward the underlying data-generating dependence structure. Simulation studies demonstrate that the proposed calibration provides sensible and effective adjustments, improving model accuracy when the simplifying assumption is violated while remaining neutral when the simplified model is adequate. Two real-data applications further illustrate the practical benefits of the method. The results highlight NCE-based calibration as a promising tool to enhance simplified vine copula models without abandoning their computational tractability.

Gaussian processes are widely used for surrogate modeling in computer experiments, which often produce numerous intermediate variables that are not explicitly used in standard calibration frameworks. Calibration of imperfect models can be challenging without leveraging these variables, while fitting the emulator and the discrepancy models separately also poses identifiability issues. In this work, we propose a robust Gaussian process calibration framework that leverages intermediate variables for discrepancy modeling. The framework integrates a structured intermediate variable selection process, a discretized scaled Gaussian stochastic process (S-GaSP) to constrain the discrepancy term, and a space-filling design strategy for selecting constraint points. This enables joint modeling of the emulator and discrepancy, improving predictive performance, providing principled uncertainty quantification, and alleviating identifiability risks. We demonstrate its efficacy on a nuclear physics application involving binding energies, where it outperforms baseline approaches.

We extend the Prais-Winsten AR(k) generalized least squares (GLS) transformation to panel data within the Beck-Katz panel-corrected standard error (PCSE) framework and implement the method in the community-contributed Stata package xtpraisk. As the panel extension of Prais-Winsten, xtpraisk is the natural comparator to xtscc, the panel extension of Newey-West and implementation of the Driscoll-Kraay estimator. We conduct a Monte Carlo simulation to validate the statistical properties of xtpraisk and compare its finite-sample performance with xtscc. The simulation spans autoregressive orders 1-3, three autocorrelation scenarios, three panel sizes, six series lengths, and five effect sizes, with 2,000 replications per condition. Across all conditions, xtpraisk achieved higher power than xtscc while maintaining near-nominal Type I error rates, confidence interval coverage, and standard error calibration. In contrast, xtscc exhibited systematic standard error underestimation and inflated Type I error at short series lengths, with both deficiencies worsening as autoregressive order increased. Both estimators were essentially unbiased. Misspecification of the autoregressive order did not degrade xtpraisk's inferential performance, and cross-panel correlation and panel size had negligible effects on the relative performance of either estimator. The results indicate that xtpraisk is preferable when both statistical efficiency and valid inference are priorities, particularly under persistent higher-order autocorrelation and short to moderate series lengths.

We introduce a switching Hamiltonian Monte Carlo method for sampling from finite mixture Boltzmann-Gibbs distributions. We propose symmetric numerical integrators to approximate switching Hamiltonian dynamics interlaced with Poisson jumps, where the regime-switching chain is simulated using the uniformization technique or the stochastic simulation algorithm. We prove geometric ergodicity of the resulting Markov chain. We develop an approach based on the discrete Poisson equation associated with numerical schemes to estimate the error in computing ergodic averages. Using this approach we prove that the proposed numerical integrators have second-order bias. This approach is simple and can be generalized to other settings, for example, kinetic Langevin equations. Finally, we verify the convergence result via numerical experiment.

We give a simple, unified, and nearly tight bound for sampling arbitrary logconcave distributions from a warm start using the In-and-Out algorithm along with exponential lifting. The main new ingredient in the analysis is an improved bound on the Poincaré constant of a lifted distribution. As a consequence, the resulting convergence rate is nearly tight for both constrained settings (e.g., Gaussian restricted to a convex body) and well-conditioned settings (e.g., strongly logconcave and smooth densities).

Forecasting the evolution of complex dynamical systems remains a fundamentally challenging task, primarily due to pronounced nonlinear interactions, high-dimensional state spaces, and the concomitant requirement for rigorous and reliable uncertainty quantification. Contemporary reduced-order modelling (ROM) frameworks frequently exhibit inherent trade-offs among predictive accuracy, numerical stability, and interpretability, and thus often fail to achieve an optimal balance among these competing objectives. To address these limitations, we propose a framework for forecasting complex dynamical systems via a kernel autonomous ordinary differential equation approach based on Gaussian Processes and Quadratic Order Model Reduction. Our base method, the Gaussian Process Ordinary Differential Equations model, allows accurate short-term forecasting with uncertainty quantification, and it provably converges to the real autonomous equation in the smooth case. We integrate it with quadratic order reduced-order modelling and sphere projection for learning the latent dynamics efficiently while preserving stability. Numerical experiments demonstrate that our full model outperforms ROM forecasting methods such as Extended Dynamic Mode Decomposition, Bagging Optimised Dynamic Mode Decomposition and Linear and Nonlinear Disambiguation Optimisation in terms of accuracy or computational costs. These results demonstrate the potential of the framework as a robust and stable tool for forecasting complex dynamical systems with rigorous uncertainty quantification.

Multidisciplinary design analysis of coupled engineering systems requires the computation of equilibrium states in which all disciplinary coupling variables are mutually consistent. Conventional fixed-point iteration resolves this consistency problem separately at each design point, which can become expensive when disciplinary evaluations are costly and many analyses are required in outer-loop tasks such as multidisciplinary design optimization, uncertainty quantification, or digital twin updating. This paper introduces REMAL, a residual manifold surrogate modeling framework for coupled systems. Instead of approximating each discipline independently or directly learning converged coupling variables, the proposed method learns a surrogate model of the joint residual manifold via multitask Gaussian process models. An entropy-based active learning strategy selects additional residual evaluations near uncertain zero-contour regions, and equilibrium states for new design inputs are recovered by solving a nonlinear least squares optimization problem using only the trained surrogate. The method is evaluated on four engineering coupled system benchmarks: a satellite model, an aerostructural model, a finite-element gas-turbine heat-transfer and economics model, and a modified turbine model with added feedback coupling. Across these cases, REMAL consistently demonstrates the cost effectiveness when repeated evaluations of the fixed point across the design space are necessary. Theoretically, we show that, under mild assumptions, REMAL's predictive fixed point error is bounded.

Langevin dynamics on Riemannian manifolds is analyzed. Conditions ensuring the existence of a suitable logarithmic Sobolev inequality (rapid mixing to the Gibbs measure) are identified. These conditions involve the curvature of the manifold, the inverse temperature, escaping directions from saddle points, and exclude barren plateaus and spurious local minima. We show that when these conditions are met, mixing times polynomial in the dimension of the manifold are achievable. This result is obtained through a relation between Langevin processes in the domain and in the image of a Riemannian submersion. Such a relation can be of independent interest.

In the era of Explainable Artificial Intelligence, there is a renewed focus on single trees for their ease of interpretation. This paper introduces Simultaneous Latent Budget Trees, a probabilistic machine learning framework for classification trees in the presence of a stratification factor such as a temporal, spatial, or demographic variable, acting as a control variable or potential confounder. Standard tree growth procedures are not designed to optimize a conditional split rule. A model-based split rule is proposed in which child nodes are interpreted as latent components of a simultaneous mixture model, such as the Simultaneous Latent Budget Model and its constrained versions, fitted to the parent node. Mixing parameters drive the observations, differently for each group, to the child nodes whereas latent budgets parameters update the response classes profile of each level of the control variable. Parameters are estimated by least squares considering a neural network perspective of the model. An informative tree structure can be interactively visualized with interpretation aids on the node and the paths, including visual pruning and decision tree selection procedure. Suitable measures are proposed to handle an unbalanced response class distribution. The proposed methodology is applied to investigate gender-related differences in disease progression of Amyotrophic Lateral Sclerosis. The SLBT library with the various tree-based algorithms is available in the linked GitHub repository.

Recent advances in time series anomaly detection (TSAD) have highlighted the effectiveness of self-supervised classification-based approaches. These methods apply transformations to normal training samples, training a classifier to recognize transformation-specific patterns that help identify anomalies through increased classification errors. Despite their strong performance, a significant challenge is their lack of explainability, as they provide limited insight into the characteristics of flagged anomalies. To address this limitation, we propose ProtoX-AD, a prototype-based self-explainable framework for self-supervised TSAD. ProtoX-AD learns transformation-aware latent representations alongside interpretable prototypes, enabling both accurate anomaly detection and the identification of distinct anomalous profiles through prototype-based explanations. Additionally, it allows for systematic analysis of how transformation design impacts detection performance and explainability. Experimental results on synthetic and real-world datasets demonstrate that ProtoX-AD achieves detection performance comparable to its black-box counterparts while offering more consistent and semantically meaningful explanations than existing explainable baselines. Our code is publicly available at this https URL.

We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.

Klindt, LeCun, and Balestriero ( arXiv:2605.26379 ) proved that Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability, the linear recovery of the world's true latent variables, if and only if the world's latent dynamics follow a Gaussian, stationary process. This Gaussian boundary implies a fundamental limit on temporal consistency: for any non-Gaussian physical system, the representation error of a statistical World Model grows monotonically with time. We prove that this limit is an artifact of the statistical alignment mechanism, not a property of World Models in general. We introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three results: (1) a PGSA achieves exact linear identifiability for all physical regimes, regardless of the latent distribution; (2) the per-step error of a PGSA is bounded by numerical precision alone; and (3) as a direct consequence, a PGSA maintains temporal consistency for an unbounded number of transitions, a property we term near-infinite temporal consistency. We further prove that statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or the volume of training data. The algebraic cores of four of the theorems are formalized in Lean 4 with Mathlib4 v4.31.0 (zero sorry placeholders); the Klindt et al. converse is taken as an external premise. The contrast establishes that symbolic grounding in the causal generator of the world's dynamics is the sufficient condition and, in non-Gaussian regimes, the only condition for near-infinite temporal consistency.

Understanding the minimal assumptions necessary for generalization is the fundamental question in learning theory. Unfortunately, most results rely heavily on independence (or some proxy thereof) of the data-generating process, while results for strongly dependent data are far more limited. Towards addressing this gap, we introduce the framework of simulatable processes, where the learner has access to a simulator that approximates the distribution generating the data (which may be an arbitrarily complex and dependent process). Surprisingly, given access to such a simulator, we show that we can recover the same learning guarantees as in the classical setting with independent data, namely, error bounds that depend on the VC dimension. Further, we use this framework to study the power of conditional sampling and show strict statistical and computational advantages in this setting. As a highlight of our framework, we exhibit a single algorithm that simultaneously learns any given VC class under all processes samplable in bounded polynomial time, with regret controlled by the time-bounded Kolmogorov complexity of the process. This provides a significant conceptual broadening of the classical PAC model.

Speculative decoding speeds up LLM inference by using a draft model to generate tokens, with an acceptance-rejection scheme that ensures that the output matches the target distribution. Adapting this to continuous diffusions is difficult because speculative sampling requires drawing from a residual distribution. While straightforward in discrete spaces, efficiently sampling this residual in continuous space is non-trivial. Consequently, existing diffusion adaptations either use computationally inefficient sampling techniques or rely on an alternative scheme. In this work, we introduce a novel scheme that efficiently implements the original speculative sampling mechanism for diffusion models. Our approach offers a critical advantage over current methods: it enables us to adapt block verification from LLMs to diffusions -- which provably improves the acceptance rate of drafts. Furthermore, we formalize and analyze the Free Drafter, a heuristic self-speculative drafter for diffusions that requires no training. By enabling block verification, our Free Drafter yields up to a 6.3% speedup over existing speculative methods with no additional training and negligible overhead beyond the existing parallel verification pass.

Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

We give a short proof that the majority vote of three independent consistent classifiers is an optimal learner in the realizable PAC setting. This proves optimality for the simplest voting scheme, while simplifying both the algorithmic structure and the probabilistic analysis of previous voting learners, including the algorithm of S. Hanneke and the analysis of bagging by K. Green Larsen.

This paper studies a variation of the classic network alignment problem, named diffusion-network alignment. The goal is to align the vertices of a rooted diffusion tree to the vertices of a network, where the diffusion tree could be from a communication trace or contact tracing, and the network could be an online or offline social network. Different from the classic network alignment where both networks are fully observed, this model captures the information asymmetry of two networks. To solve this problem, this paper presents an efficient algorithm based on tree correlation tests to extract alignment information from local neighborhoods. We analyze the performance of the algorithm in the sparse graph regime and show that with high probability, all matched pairs are correct. Furthermore, for each vertex on the diffusion tree, this paper establishes an explicit lower bound on the probability that the vertex is correctly matched. These lower bounds are depth-dependent and increase as vertices get closer to the root.

Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an open theoretical question. In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering. In particular, we show that the learned hidden representation coincides, up to a similarity transformation, with the state estimates produced by the optimal (Kalman) filter, even though the model has no explicit knowledge of the underlying dynamics or state. The result follows from three main insights. First, we establish that the Kalman filter is well approximated by an auto-regressive model with bounded truncation error. Second, we show that despite non-convexity, the two-layer optimization landscape is benign, i.e., all stationary points are either strict saddles or global minima. Finally, as our main contributions, we provide finite-sample guarantees on prediction error, parameter estimation error, and latent state recovery. Numerical simulations support the theoretical results and demonstrate that the latent representations of auto-regressive models recover state estimates.

The standard taxonomy of predictive uncertainty defines epistemic uncertainty as the part removable by collecting more data, while the standard measure identifies it with a mutual-information term. We prove the definition and the measure are extensionally inconsistent. On an explicit construction, the measure assigns all uncertainty to the epistemic class, yet no quantity of training data reduces it. Reducibility is instead a property of the pair (uncertainty, acquisition class), and the dichotomy resolves into three parts: aleatoric, sample-reducible epistemic, and mechanism-reducible epistemic uncertainty. An exact identity for the value of an observation shows that in-distribution data never reduces mechanism-irreducible uncertainty and generically increases it. Ensemble disagreement, the deployed epistemic estimate, tracks the training procedure rather than the epistemic term. It collapses to zero beneath a positive truth under consistent training, and equals hyperparameter-scaled initialization noise under interpolation. A finite-sample falsification test and seed-swept experiments confirm the theory.

Two-dimensional magnets offer compelling platforms for spintronics and quantum technologies, yet predicting their magnetic ground states, moments, and anisotropy remains challenging. This limitation primarily arises because existing machine-learning representations encode chemical environments without capturing the symmetry or exchange physics that govern magnetism. In this work, we introduce the symmetry-electronic fingerprint (SEF), a physically interpretable representation that encodes crystallographic symmetry operations, Wyckoff-site geometry, together with site-resolved electronic structure. Combined with ensemble learning with random forests, the SEF accurately classifies magnetic ordering while regressing moments alongside anisotropy energies while simultaneously resolving the distinct regimes of itinerant Stoner ferromagnetism from localized superexchange. What sets the SEF-trained models apart is that regions of elevated model uncertainty are not a failure but a diagnostic, identifying materials where these mechanisms compete. First-principles calculations on Co- and Ni-based halides and oxides confirm that these regions correspond to genuine near-degenerate FM and AFM phases with magnetic frustration, suppressed anisotropy, and emergent non-collinear ordering. By encoding symmetry together with exchange physics directly into the representation unlike conventional descriptors, the SEF transforms model uncertainty into a compass pointing toward two-dimensional materials where small perturbations drive transitions between collinear, frustrated, or non-collinear magnetic phases.

We investigate limitations of learning $\tanh$ neural networks from point evaluations under finite-precision computations and $L^p$ accuracy guarantees, building on Berner, Grohs, and Voigtländer (2023). Our approach is based on a novel construction of sharply localized bump functions via iterated $\tanh$ activations. Using this mechanism, we show that, in a finite-precision setting, no adaptive randomized algorithm based on $m$ samples can achieve a convergence rate higher than the Monte Carlo rate $O(m^{-1/p})$ in the $L^p$ norm, unless the sampling budget grows exponentially with the size of the network parameters and architecture. The results reveal fundamental limitations imposed by finite precision on the learnability of classes containing localized bump functions, extending previous results for ReLU networks to the $\tanh$ setting.

Neural ordinary differential equations (neural ODEs) have rapidly gained prominence as a powerful and unifying framework for conceptualizing artificial neural networks, elegantly connecting the continuous-time modeling of dynamical systems with the discrete, data-driven paradigm of modern deep learning. Beyond their practical advantages they offer fresh theoretical insights into the training and generalization properties of neural networks. The distinctive feature of this framework is its dual dynamical nature: inference dynamics, which govern the ODE evolution during forward computation, and training dynamics, which control the optimization of model parameters. This makes neural ODEs a particularly well-suited theoretical framework for studying a large variety of settings such as multi-layer neural networks (ResNets for example), autoregressive models (with next-token generation dynamics), generative models, and recurrent neural networks in theoretical neuroscience. In this work, we introduce a theoretically grounded class of models for studying neural ODEs trained via online stochastic gradient descent. We solve the training dynamics of these models via dynamical mean field theory and derive learning curves in the high-dimensional limit.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at this https URL.

When modeling health events in small areas, the conditional autoregressive (CAR) framework of Besag, York, and Mollié (BYM) is widely used. For multiple outcomes, the multivariate CAR (MCAR) extension accommodates dependence among diseases that share risk factors, in addition to spatial dependence, and can also jointly model demographic subgroups for a single disease, allowing information to be borrowed across related populations. However, recent studies have shown that the BYM CAR model can be overly informative, leading to excessively precise estimates. While the MCAR model is expected to be more informative due to additional information shared across subgroups, its level of informativeness has not been previously quantified. We propose a framework to measure MCAR model informativeness as an extension of prior work and introduce a method to control it, ensuring the model contributes comparably to each subgroup. We achieve this through a reparameterization of the MCAR model within a computationally efficient framework. We demonstrate how the MCAR model compares with the BYM CAR model in terms of informativeness and oversmoothing and highlight the advantages of the restricted MCAR model using county-level heart disease death data stratified by race and sex.

Habitat selection and space use are fundamental to understanding animal distribution. Traditional methods for quantifying habitat preferences from telemetry data assume regular sampling and negligible measurement error. However, these assumptions are routinely violated in marine systems. Practitioners typically regularize and filter the data before fitting models, but these two-step procedures do not propagate uncertainty from the filtering stage and can yield biased estimates. Habitat-driven Langevin diffusion models offer an elegant alternative, naturally accommodating irregular sampling. However, incorporating measurement error via a state-space formulation is challenging because habitat covariates depend on the latent true locations. We address this using the Laplace approximation to simultaneously integrate over true locations and account for habitat covariates along latent paths, yielding a single-stage framework efficiently implemented in Template Model Builder (TMB). By doing so, we provide the first TMB implementation capable of handling covariates that depend on latent variables, allowing inference via fast and efficient maximum likelihood estimation. Simulations show that our approach outperforms the two-step method, recovering habitat-selection parameters even under substantial measurement error and missing data, with more accurate utilization distributions and trajectory reconstructions. Applied to narwhal (Monodon monoceros) telemetry data, the two-step method substantially shrinks the habitat selection coefficient towards zero, while our unified approach recovers a much stronger signal. Our framework offers a computationally efficient solution to long-standing challenges of measurement error and temporal irregularity in habitat selection inference, applicable across a wide range of taxa and environments.

Passive acoustic monitoring holds great promise for ecological inference, yet existing automated tools are typically narrowly trained and non-transferable. We address these limitations with PULSE, a semi-supervised, multi-task framework for Orthoptera bioacoustics, combining weakly-supervised species classification, self-supervised learning on unlabelled field audio, and knowledge distillation from a general-purpose bioacoustic model. Our domain-adapted specialist model outperforms a state-of-the-art general model across all metrics (macro F1: 0.21 vs. 0.07; AUC: 0.74 vs. 0.45; AP: 0.32 vs. 0.19), with active learning further raising F1 to 0.34 and AUC to 0.84. Beyond classification, the learned embeddings encode ecologically meaningful structure, exposed through an interactive visualisation tool for ecological discovery.

The ongoing electrification and integration of renewable energy sources in Denmark's distribution grids pose significant operational challenges, including insufficient reserve capacity, component degradation due to overload, voltage instability, and increasing infrastructure investment requirements. This article argues that implicit demand-side flexibility (DSF) incentivized through dynamic tariffs offers the most scalable and cost-effective approach to address these challenges in a modern distribution network. We demonstrate that while explicit flexibility mechanisms provide operational certainty, they cannot scale to address system-wide congestion across heterogeneous customer bases. Drawing on empirical consumption data showing strong price-responsive behavior, varying prices due to, e.g., regulatory frameworks including the Danish Market Model 3.0 and Tariff Model 3.0, and economic analysis, we demonstrate potential grid savings of 13--48 million DKK per constrained substation through deferred or avoided reinforcement. We argue that implicit DSF mechanisms represent the necessary pathway for revenue-neutral scalable flexibility solutions that can defer costly grid reinforcements while maintaining system reliability. Beyond direct grid savings, additional value streams include avoided peak generation costs, reduced connection delays, and lower outage risk, further strengthening the economic case. Critically, dynamic tariffs offer the mechanism through which real-time grid constraints can be communicated to consumers, enabling price signals that accurately reflect the actual state of the capacity of the distribution network at any given point in time and space.

In aerospace certification and other safety-critical domains, conservative quantile estimation such as A- and B-basis values is essential to guarantee reliability. While these metrics are traditionally derived from experimental campaigns, this work focuses on their estimation using a validated deterministic numerical model. The problem is formulated under mixed aleatory-epistemic uncertainty, accounting for limited material data, finite sampling effects, and surrogate modeling errors. We propose a methodology for estimating conservative design quantiles with statistical guarantees under mixed uncertainties. The proposed method leverages importance sampling and control variates to achieve accurate and efficient estimates within a fixed computational budget. One key point is the surrogate model's role solely as a variance reduction device, which guarantees unbiased and consistent quantile estimation. By explicitly integrating all sources of uncertainty, the proposed framework provides a numerical alternative to estimate A-basis and B-Basis. Furthermore, Sobol-based sensitivity indices are obtained at no additional cost, offering insight into the dominant epistemic sources. Numerical experiments on structural models demonstrate the method's reliability and computational efficiency. In particular, the application to large-scale industrial simulations confirms its suitability for aerospace certification workflows and highlights its relevance for real world engineering environments.

To enable a numerical handling of uncertainties in composite structures, this work presents a stochastic finite-element framework aimed at improving the reliability assessment of aerospace composites, with particular attention to stiffener debonding. By representing interface variability between laminate parts with spatially correlated random fields, the method aims at considering scattering effect at a higher scale of simulation and testing. A parametric study carried out on standardized Mode I and Mode II fracture tests reveals that the correlation length is the primary driver of observed variability, while the regularity of the covariance kernel has only a marginal impact. To guarantee industrial relevance, we demonstrate that this key parameter can be extracted from experimental fracture data using an Approximate Bayesian Computation approach. The proposed methodology therefore offers a robust route to high-fidelity virtual testing and to the predictive management of uncertainties in the design of damage-tolerant composite airframes.

Donald Trump won the 2024 US Presidential Election despite polls predicting a Democratic lead, echoing the polling miss in 2016. Using the data defect correlation framework, we revisit the 60,000-respondent Cooperative Election Study and find that non-response bias for Trump voters persists on the same order of magnitude ($\rho=-0.0030$ vs $-0.0045$ in 2016) even under sample-matching to the US adult population. We additionally find evidence of positive response bias for Harris voters after adjusting for turnout. Consistent with findings in 2016, polling errors scale with state population size, and larger samples produce greater departures from conventional confidence intervals, with reductions of effective sample size exceeding 99% in the largest states. We propose a pre-election bias correction estimator informed by historical data defect correlations and turnout rates that decreases RMSE from 0.13 to 0.05 using only prior election data, comparable to post-election weighting (RMSE 0.09).

Using thematic maps to publish statistical information has become a popular visualization. As is the case with all statistical publications, thematic maps also have to deal with the balance between disclosure risk and utility. However, most risk and utility measures do not take into account the spatial character of a map. Some of the proposed spatial risk measures suffer from the Modifiable Areal Unit Problem (MAUP): slightly changing regional classifications may influence the risk. Indeed, even a small translation of for example a grid may influence that risk. We propose a new risk measure that does not suffer from MAUP. Moreover, our risk is directly related to the local density of the (target) population and takes into account that often multiple units may be connected to a single location. We show the behavior of our risk measure using an example dataset of fake but realistic locations of enterprises. Our risk measure can be adapted to take into account the effect on the (perceived) risk of zooming in or out and the effect of the used resolution.

Non-probability data sources are increasingly considered in small area estimation, but inverse probability weighting (IPW) gives model-dependent domain estimators whose reliability may vary substantially across domains. Standard Fay-Herriot (FH) smoothing borrows strength across domains, yet it uses the supplied area-level variance estimates as if they fully described the uncertainty of the input estimators. This can be misleading when some domains have weak coverage, unstable weights, or poor auxiliary balance, since these features may indicate selection-bias risk not captured by the estimated variance alone. We propose a diagnostics-guided variance-inflated FH estimator for finite-population domain totals. The method starts from calibrated IPW domain estimators, summarizes their reliability through a small set of domain diagnostics, and introduces a mixture variance-inflation component in the FH observation equation. Domains whose diagnostics indicate weaker IPW information are thereby smoothed more strongly toward the area-level regression mean. A truth-known validation based on a pseudo-real population of Lithuanian business enterprises shows a substantial reduction in estimation error relative to calibrated IPW.

There is a proliferation of work arguing for the use of synthetic data in scientific research. For example, social scientists are arguing for the use of LLM-generated "silicon samples" in pilot studies; AI evaluations increasingly rely on "LLM-as-a-judge" outputs; and proteomics research is accelerated by generative models that produce synthetic protein structures. These developments raise an intriguing possibility: synthetic data may help researchers ask more questions, run more studies, and accelerate discovery. But they also raise a fundamental concern: synthetic data can be biased, noisy, and misspecified. In this work, we propose statistical principles for using synthetic data in scientific research with provable validity guarantees. The key insight is a new technical condition that we call task exchangeability. Informally, this is a requirement that the researcher can identify historical tasks, for which real data is available, such that their current task of interest is exchangeable with the historical tasks in an appropriate mathematical sense. We develop methods for valid inference under task exchangeability, together with extensions that provide guarantees even beyond exchangeability. We demonstrate the framework on public opinion surveys with silicon samples and AI evaluation with autoraters.

We develop a new, differentially private mean estimator called the balloon mean. The main features of the balloon mean are that it is computationally tractable and enjoys robustness to outlying observations. It is based on an iterative clipping procedure over expanding Mahalanobis balls, or ``balloons.'' The method satisfies zero-concentrated differential privacy and depends on a small number of interpretable tuning parameters. We provide theoretical guarantees under heavy-tailed and contaminated elliptical models, characterizing its statistical performance and robustness to outliers. Extensive simulations demonstrate that the balloon mean is robust to heavy-tailed and contaminated data, and outperforms existing differentially private mean estimators in contaminated settings.

In multi-class classification problems, classes often have a natural priority ordering (e.g., cancer stages, COVID-19 severity levels, or air-quality categories). In such settings, it is important to prioritize correct identification of more severe classes and to control under-classification errors, which occur when an observation from a higher-priority class is misclassified into a lower-priority one. The Hierarchical Neyman-Pearson (H-NP) framework of Wang et al. (2024) was developed for ordered multi-class settings to prioritize under-classification error control; its H-NP umbrella algorithm provides high-probability control of under-classification errors at user-specified levels. This paper introduces the R package HNPclassifier, which implements H-NP umbrella algorithms to construct H-NP classifiers using built-in learners such as logistic regression, random forests, and support vector machines, as well as user-supplied scoring functions, thereby enabling effective error control for ordered multi-class classification tasks.

The OSIRIS-REx mission acquired spatially resolved (2-10 m spot sizes) visible-near infrared (VNIR) and thermal infrared (TIR) spectra across four candidate sampling sites on asteroid (101955) Bennu: Nightingale, Osprey, Sandpiper, and Kingfisher. To quantify heterogeneity across a small body (about 500 m radius) like Bennu, we explore remotely observed spectral data to draw conclusions about the mineralogical composition and key physical processes that drive surface variability. We derive diagnostic band parameters from the OSIRIS-REx Visible and Infrared Spectrometer and the OSIRIS-REx Thermal Emission Spectrometer datasets to quantify compositional and physical variability across sites and assess their mineralogical context. The VNIR spectra exhibit similar overall reflectance shapes but systematic differences in spectral slopes and the 2.74 micron OH absorption. TIR emissivity spectra reveal modest but statistically significant shifts in the Christiansen Feature, silicate stretching, and bending band positions, indicating differences in silicate composition, hydration state, and Mg/Fe relative abundance. Principal component analysis separates each site into distinct clusters in multivariate band-parameter space, whereas K-means clustering identifies intra-site spectral sub-populations. Welch's Analysis of Variance and Hotelling's tests confirm that band-parameter variations between sites are significant. These results reveal that Bennu's surface preserves measurable spectral heterogeneity at 2-10 m scales, with site-to-site variations in hydration indicators and silicate band positions. The spectral properties of Nightingale encompass the full range observed across all four sites, establishing a remote sensing baseline for contextualizing laboratory analyses of the returned sample within Bennu's broader composition diversity and alteration history.

Assessing structural performance under seismic hazard requires accounting for both damage accumulation and post-event recovery. In current performance-based earthquake engineering (PBEE), recovery is generally treated as a post-processing attribute, while structural performance is modeled using Poissonian exceedance assumptions that imply renewability and memorylessness. These assumptions hinder a unified treatment of reliability and resilience under repeated seismic loading. This study proposes a generalized PBEE framework in which damage and recovery are embedded directly into the system dynamics through a continuous-time Markov chain. A single generator matrix governs state-dependent transitions, providing a unified description of structural reliability and resilience while remaining compatible with standard PBEE metrics. Time-dependent failure probabilities and reliability indices are derived from the transient system dynamics, whereas resilience is quantified through the expected fraction of operational time before collapse. The framework exploits the spectral properties of the generator matrix to compute both metrics efficiently and transparently. The methodology is illustrated on a three-state example and applied to two structural archetypes: a braced frame and a base-isolated system. Results show that recovery dynamics can strongly affect long-term resilience even when conventional reliability measures exhibit limited sensitivity, emphasizing the need to explicitly account for recovery in life-cycle seismic performance assessment.