Papers

Estimating endmember spectra and their corresponding abundances from hyperspectral images is a fundamental inverse problem in remote sensing. The standard linear mixing model relies on additive homoscedastic errors, which misspecifies the mean-variance relationship inherent to optical measurements for which the noise intensity might be proportional to the signal magnitude. This leads to confidence intervals with poor coverage. To address these limitations, we propose a hierarchical Bayesian multiplicative Errors-in-Variables (EIV) model. Motivated by the physics of light propagation, our formulation captures signal-dependent noise through a multivariate log-normal specification that naturally accommodates dependence across spectral bands. The EIV framework treats endmember signatures as random and allows for class-specific variance scaling, yielding a flexible and physically grounded data-generating process. We establish that the MLE of the abundance vector under the multiplicative model has a constant asymptotic multivariate coefficient of variation, implying that well-calibrated confidence intervals should scale proportionally with signal magnitude. The additive model, by contrast, produces intervals of constant width regardless of signal magnitude, leading to overcoverage at low abundance and undercoverage at high abundance when the true noise is multiplicative. Practical implementation and inference for the full hierarchical model is obtained from posterior distributions over the model parameters. Experiments on several real and simulated datasets demonstrate that confidence intervals derived from the proposed model achieve improved coverage across abundance levels compared to those from a standard additive model, with widths that scale proportionally with signal magnitude, while achieving comparable or superior signal reconstruction error.

We study the convergence properties of the random-sweep Gibbs sampler for Gaussian graphical models with a thin-membrane prior. We demonstrate that the convergence rate of the Gibbs sampler is significantly accelerated in the dual model, which is obtained by applying the Fourier transform to the local factors of the normal factor graph representing the original model. In both domains, we derive the exact convergence rates for homogeneous $k$-regular graphs. We prove that, for all homogeneous models whose graphical representations contain cycles, the convergence rate in the dual domain is universal and independent of the underlying graph topology. Moreover, we show that the effective convergence rate in the dual domain is governed by the algebraic connectivity of the graph, providing an additional acceleration without increasing the computational complexity per sweep. We further establish an explicit algebraic relation between the covariance structures of the primal and dual models, enabling marginal statistics of the primal model to be recovered directly from those of the dual model. Finally, numerical experiments on several graph families confirm our theoretical results and demonstrate substantial improvements in the convergence rates in various settings.

We address the problem of passive localisation of a stationary, ground-level IoT radio emitter using Doppler frequency measurements collected by low-Earth orbit (LEO) satellites during an observation window. The problem is challenging because radio emission from low-cost IoT devices is affected by various compounding sources of measurement error, that collectively render the likelihood function intractable in a closed form. Hence, we apply and investigate the performance of Approximate Bayesian Computation (ABC) methods for this task. Numerical results demonstrate the statistical and computational performance of two ABC methods, rejection sampling ABC and sequential Monte Carlo ABC.

Longitudinal causal studies often record histories as irregular functional fragments: laboratory values, physiologic signals, sensor streams, and image-derived summaries measured at unequal and informative times. Standard doubly robust estimators usually require scalar summaries, whereas sequence learners optimize prediction losses that need not stabilize the efficient influence function. We propose Doubly Robust Functional Representation Learning (DR-FRL), a cross-fitted workflow that turns irregular histories into estimand-targeted states for observed-history regimes. Functional and temporal encoders map point clouds and prior histories into states; nuisance heads estimate outcome, treatment, and censoring functions; and EIF-targeted validation, calibration, overlap, tail, and ablation diagnostics assess whether the state supports the estimating equation. If the selected state preserves the nuisance information needed by the EIF, representation error enters the same second-order product remainder as ordinary nuisance error, and the mean estimator is asymptotically linear under explicit rate, overlap, calibration, and stability conditions. Catoni aggregation is treated separately as a bounded-influence point estimator, not a replacement for Wald inference. Simulations show gains when functional confounding is high-dimensional, measurement is informative, support is weak, or pseudo-outcomes are heavy-tailed. A VitalDB audit shows that DR-FRL can use irregular laboratory point clouds and deliver a useful negative finding: for this ICU-disposition endpoint, scalar laboratory summaries already carry much endpoint-relevant information.

We study how a player's execution error affects the optimal location at which to aim a serve in tennis. Aiming near the service-box boundaries makes a serve harder to return but increases the probability of a fault, creating a trade-off that depends on the player's execution error. Match-play data provide limited information about execution error because players' intended targets are unobserved. We conducted an experiment with Brigham Young University men's tennis players in which players explicitly identified targets they believed to be optimal for their serves. Players then served repeatedly toward their chosen targets, and we recorded the bounce locations. Using these data, we estimate player-specific execution error via a Bayesian hierarchical model that accounts for serves censored by net contact. These distributions define the transition dynamics of a two-period Markov decision process (MDP) representing a point in tennis, where the decision variables are the first- and second-serve aim locations. We solve the MDP for each posterior draw of the execution error distributions, yielding a posterior distribution over each player's optimal aim location. We find that players' stated targets are generally more aggressive than optimal, whereas their realized serve centers are more conservative and markedly closer to the optima.

The Atlantic Meridional Overturning Circulation is monitored and emulated through reduced indices, but such projections discard thermohaline structure and may require either explicit physical state or memory of the observed index. We compare these strategies in 30 branch-consistent CMIP6 trajectories from eight model families using leave-one-family-out validation. Salinity, temperature and density information improves direct 20-year forecasts, whereas compact scalar memory is top-ranked at every recursive horizon and yields the lowest case-averaged Brier score. A matched ablation confirms that feedback from memory improves long-horizon prediction. Physical state and recent trends also predict future ocean-state changes beyond the emissions pathway, most robustly at five years. NorESM under SSP5–8.5 identifies a forcing-dependent limit of scalar compression, while MIROC shows negative long-horizon transfer. A resolvent analysis explains why stable memory components do not guarantee stability of the complete learned model. Physical augmentation and memory compression therefore serve different AMOC prediction tasks.

Many wildlife surveys of species with individually identifiable animals are based on the analysis of the capture histories of individual animals. However, not many of these take account of both the animals' capture times and their capture locations. In this work, we develop a maximum likelihood estimator for surveys of individually identifiable animals using proximity detectors, multi-catch traps, single-catch traps, and traps that remove animals from the population, when capture times are known. We do this using the counting process theory at the foundation of event history (or survival) analysis. The work provides a unifying framework for such surveys, resolves open problems for single-catch traps and removal surveys, and introduces a new statistical method for multi-catch traps. We test the new methods by simulation and we present an analysis of possums in New Zealand caught with single-catch traps.

Let $\mu(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $\kappa=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start. For total-variation error $\varepsilon$, the expected query counts are $O(\kappa^{1/2}d\,(d\log\kappa+\log\frac1\varepsilon))$ gradient queries for the bouncy particle sampler and $O(\kappa d^{1/4}(d\log\kappa+\log\frac1\varepsilon))$ full-gradient equivalents for Zigzag, where $d$ coordinate-partial queries count as one equivalent.

This thesis studies policy learning in interactive systems where an agent observes a context, selects an action from a very large set, and receives partial feedback. The main framework is contextual bandits, with two paradigms: on-policy learning, where the agent interacts sequentially with the environment and minimizes regret, and off-policy learning, where it learns from logged data collected by a logging policy. In large action spaces, both settings face major challenges: inefficient exploration, sparse data coverage, high-variance importance weights, extrapolation bias, and difficult optimization landscapes. The first part develops structured Bayesian methods for on-policy learning. We introduce meTS, a mixed-effect extension of Thompson sampling, and dTS, which leverages diffusion-inspired priors to model dependencies between actions. These methods share information across actions and yield regret guarantees depending on an effective number of actions. The second part addresses off-policy learning. We propose sDM, a structured direct method based on latent variables, show that optimization error can dominate estimation error in large action spaces, and introduce concave, efficiently optimizable policy-weighted log-likelihood objectives. Finally, we develop differentiable pessimistic methods based on exponential smoothing and PAC-Bayesian bounds to control the bias-variance trade-off of regularized importance-sampling estimators.

We propose a Riemannian factor model (RFM), a novel framework for analyzing potentially high-dimensional time series data observed on Riemannian manifolds. Such time series are encountered in various applications, including economics, finance, medical imaging, and genomics and microbiome research. The proposed model is geometry-aware and accounts for the inherent nonlinearity in the data. In a high-dimensional asymptotic regime, where the manifold dimension is allowed to diverge with the sample size $n$, we establish convergence rates for the estimated loading space. In particular, under short-memory and strong factor conditions, we obtain a dimension-free $n^{-1/2}$ rate, which matches the convergence rate of the high-dimensional linear factor model. Finite-sample performance of the proposed RFM is demonstrated with simulated time series on the Bures–Wasserstein manifolds and products of spheres, as well as an application to monthly realized covariances of selected U.S. stock returns—modeled as time series in the Bures–Wasserstein manifold, where the RFM provides demonstrably interpretable factors and yields competitive predictive performance.

Clustered Federated Learning (CFL) addresses data heterogeneity in federated settings by grouping clients with similar data distributions to enable effective training. Existing methods face a trade-off between privacy preservation, communication cost, and computational efficiency. We formalize this as the CFL trilemma, according to which improving two of these dimensions comes at the expense of the third. A prominent paradigm relies on metadata (i.e., low-dimensional representations of client datasets shared with the server) to enable communication- and computation-efficient clustering. However, such approaches are not compatible with standard FL privacy-preserving mechanisms. To address this limitation, we propose FLAMECHE, which reformulates metadata-based CFL as a distributed Expectation-Maximization (EM) procedure, restricting server updates to additive operations while preserving efficiency. This design enables compatibility with practical secure FL schemes. We conducted extensive experiments on multiple datasets under various heterogeneous scenarios. Results show that FLAMECHE improves the effectiveness of client models. It enables encryption-compatible metadata-based clustering, enhancing its positioning within the CFL trilemma.

We study the problem of sequential change detection over a general class of probability distributions ($\mathcal P$), where both the pre-change and post-change distributions are unknown and belong to $\mathcal P$. We do not assume a pre-specified partition of $\mathcal P$ into pre- and post-change families. We propose a general class of sequential change detectors obtained by aggregating point-null e-processes over possible changepoints and taking an infimum over candidate no-change distributions. The weights in the aggregation scheme determine whether they attain average run length (ARL) control and probability-of-false-alarm (PFA) control. Under suitable assumptions, we prove that our methods achieve first-order asymptotically optimal detection delay. Concrete examples include sub-Gaussian and bounded mean changes, Gaussian mean changes with unknown variance, as well as changes in Markov transition matrices.

For empirical studies, social and health scientists give background characteristics of their sample and summarize them in the famous "Table 1". When treatment/ control groups are present, this table gives summary statistics by group to see whether the background characteristics differ by group. We propose snapshot plots — parallel univariate plots with consistent highlighting — to visualize such tables. Compared to "Table 1", such plots are designed to facilitate comparisons of background characteristics — in particular among groups — and give more detail on numerical variables. We provide a web app as well as a python implementation of snapshot plots. Snapshot plots arise as edge cases of hammock plots (parallel coordinate plots for mixed categorical/ numerical data). We demonstrate the usefulness of snapshot plots for two "Table 1"s.

This paper develops bootstrap methods for likelihood-based inference in autoregressive conditional duration (ACD) models, where the sample size is endogenously determined by durations observed over a fixed time span. This feature fundamentally shapes the asymptotic framework, particularly so when the durations do not have finite expectation. Building on recent limit theory for heavy-tailed and integrated ACD processes, we analyze recursive bootstrap schemes that either fix the time span (yielding a random sample size) or fix the number of durations (yielding a random time span). We establish a bootstrap theory for ACD models that links naturally to renewal theory with random sample sizes. For the fixedcount bootstrap, we prove first-order validity in the finite-mean and boundary cases and characterize the random limiting bootstrap distribution in the infinite-mean case. Although classical bootstrap consistency can fail when the durations have infinite expectation, we argue that the bootstrap remains valid and yields asymptotically normal t-statistics. Monte Carlo evidence shows that the proposed methods have good finite-sample properties in both finite- and infinite-mean settings, and are robust to distributional misspecification relative to the exponential likelihood. We conclude with an empirical application to cryptocurrency ETFs.

Instrumental-variable (IV) analyses can be undermined when some instruments violate the exclusion restriction through direct effects on the outcome. Existing robust IV methods, including sisVIVE and CIIV, rely on majority- or plurality-validity conditions. We propose TEAM-IV, which targets joint validity by identifying sets of instruments that appear valid together and aggregating them, allowing reliable estimation even when only a small number of candidate instruments are valid (potentially as few as two). TEAM-IV fits MCP-penalized models of the outcome on projected exposure over overlapping instrument subsets. Instruments whose estimated direct effects are frequently shrunk to zero together (suggesting concordant validity status) form candidate “teams” (instrument sets). Teams are ranked by their out-of-sample predictive performance; near-best teams are unioned and used as the instrument set for the IV estimate. Across simulations varying the number, magnitude, and signs of invalid direct effects, instrument correlation, and exposure endogeneity, TEAM-IV generally attains lower absolute estimation error than sisVIVE and CIIV. Relative gains are largest when invalid instruments are prevalent. TEAM-IV is demonstrated in an empirical Mendelian randomization application using the Multi-Ethnic Study of Atherosclerosis (MESA) concerning the effect of LDL cholesterol on carotid intima–media thickness. Two additional MESA-anchored validation studies demonstrate differences between TEAM-IV and sisVIVE under challenging invalid-instrument configurations.

Sensitivity analysis methods based on Sobol' total-order indices ($T_i$) are well-founded but computationally demanding. A recently proposed ersatz discrepancy measure offers a cheaper alternative by quantifying deviations from uniformity in input–output scatterplots, yet lacks theoretical grounding and has not been benchmarked against other data-given estimators. We introduce an adjusted ersatz discrepancy that rank-transforms the output before gridding and imputes isolated empty cells via a Moore-neighbourhood rule, substantially improving agreement with $T_i$. We prove, via a copula-theoretic argument, that the adjustment is a consistent screening statistic with a zero condition, an explicit full-support ceiling bounding its use as a magnitude estimator, and a documented failure mode for purely interaction-mediated dependencies. We benchmark the adjusted ersatz against three zero-extra-cost comparators – polynomial chaos expansion (PCE), PCE-derived Shapley effects, and a PAWN-type maximum Kolmogorov–Smirnov index – across seven benchmark functions and a real-world hydrological model. The adjusted ersatz is the only estimator achieving perfect rank agreement on a non-smooth hydrological output where PCE is misspecified. A joint sensitivity analysis of five algorithmic parameters shows grid resolution, not the imputation threshold or sampling method, drives performance variability.

The deployment of deep neural networks in safety-critical domains demands reliable estimates of predictive confidence, yet conventional architectures lack principled uncertainty quantification. This survey provides a structured, critical review of methods for Uncertainty Quantification (UQ) in deep learning, scoped to ensemble-based and approximate Bayesian approaches and the measures used to summarize their outputs. Relative to existing UQ surveys, our contribution is depth on efficient ensemble approximations and single-pass methods, and a unified treatment that separates the method producing a predictive distribution from the measure that summarizes its uncertainty. We organize methods into five families: Bayesian neural networks, Monte Carlo Dropout, deep ensembles, efficient ensemble approximations, and last-layer or single-pass approaches. We situate adjacent work on evidential and prior networks, conformal prediction, and post-hoc calibration, together with the decision-time tasks of out-of-distribution detection and selective prediction. For each, we examine theoretical motivation, implementation, empirical performance, and limitations. We then review ensemble diversity theory and uncertainty measures and their decompositions, contrasting the entropy decomposition with pairwise divergence measures, and consolidate evaluation methodology so that our qualitative comparisons share a common basis. We close with a brief treatment of uncertainty in large language models and open research directions, including efficient epistemic measures for classification, last-layer diversity, diversity and calibration under shift, and hybrid architectures.

Ensuring the accuracy and consistency of clinical trial Tables, Figures, and Listings (TFLs) remains a major challenge in regulatory reporting. Independent programming and manual review are essential quality-control practices, but cross-output verification still depends heavily on reviewer inspection and may miss structural, logical, or arithmetic discrepancies. Large language models (LLMs) can help interpret varied table language and navigate lengthy study documents, but they are not reliable substitutes for programmed statistical checks. We introduce PROVE (Programmatic Reporting and Output Verification Engine), an auditable framework that uses optional LLM and retrieval support for table interpretation while reserving numerical and logical decisions for programmed validators. PROVE links findings to source evidence, supports cross-output consistency checks, and allows LLM use to be enabled or disabled based on study requirements. We evaluated PROVE using ten replicated synthetic oncology reporting packages generated from raw data through SDTM, ADaM, and TFL outputs, with paired clean and discrepancy-injected packages; each replicate included 15 randomly injected discrepancies. We examined two table-label settings: exact labels matching the validator vocabulary and labels with similar clinical meaning but different wording. Within the implemented rule classes, all automated PROVE variants achieved perfect classification in the exact-label setting. In the label-variation setting, LLM-assisted semantic matching improved overall recall from 0.588 to 0.993 and overall F1 from 0.735 to 0.996 compared with exact-match, fuzzy lexical, and embedding-similarity variants. These findings suggest that LLMs are most useful for interpreting real-world variation in TFL wording and formatting, while executable checks should remain responsible for final numerical validation.

Probabilistic forecast evaluation is inherently multi-objective, yet existing proper scoring rules reduce predictive performance to a single scalar value, potentially obscuring the trade-off between forecast concentration and predictive accuracy. We introduce the Interval-Score Receiver Operating Characteristic (IS-ROC) Curve, a graphical framework that represents the complete family of interval forecasts generated by varying prediction tightness. We show that the IS-ROC Curve induced by the data generating process is Pareto optimal and convex, providing a geometric characterization of the optimal forecasting frontier. Building on these properties, we propose a geometry-based calibration procedure based on tangent optimization and convexification, together with an ensemble strategy that combines competing forecasters through convex hull construction. Finally, we provide a practical workflow and numerical examples illustrating forecast comparison, calibration, and ensemble construction within the proposed framework.

We investigate a bias correction procedure based on sieve bootstrapping to estimate the long-memory parameter d in stationary or nonstationary fractionally integrated processes. The resampling method implements a sieve bootstrap method on data prefiltered by a preliminary estimate of the long-memory parameter. For the initial estimate, we recommend the local polynomial Whittle with noise (LPWN) estimator in Frederiksen et al. (2012) to reduce bias, especially in the presence of a strong short-range autoregressive dependence. Through a series of simulation studies, we first highlight the issue of bias, using the local Whittle or detrended fluctuation analysis estimator. Then, we consider the LPWN estimator and show the potential improvement in bias achieved by its sieve bootstrap enhancement. As a byproduct, the sieve bootstrap can also provide confidence intervals of the memory parameter.

Many modern outcomes, including images, point clouds, networks, and spatial fields, are structured objects for which \(Y^1-Y^0\) may be undefined or scientifically inadequate. We introduce Topological Causal Data Analysis (TCDA), a framework separating the observation space, causal-model class, topological representation, and causal query. Topology does not define interventions; it supplies stable, shape-sensitive summaries after causal assumptions have been specified. We distinguish outcome-level TCDA, which transforms individual potential outcomes, from distribution-level TCDA, which transforms interventional outcome laws, and characterize when outcome and distribution level contrasts agree. Building on recent outcome-level theory, we formulate identification and doubly robust representations for Banach-space-valued summaries. At the distribution level, we identify targets through the standard causal \(g\)-formula and derive stability-transfer bounds and plug-in consistency. We also place target-specific topological ignorability within the framework, clarifying when a covariate-standardized coarse effect can be identified without identifying the full interventional laws. Finally, we delimit the role of observational topology in causal discovery: it can assist diagnosis on restricted model classes but cannot by itself identify causal structure.

We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems. It is shown that the proposed extension - that we coin as Entropy-Optimal Manifold Regression (EOMR) - allows a robust learning with linearly-scaling iteration and memory complexities. EOMR is compared to the most complete set of state-of-the-art tools from the Artificial Intelligence (AI) and Machine Learning (ML) that is available to the author, on the very challenging problems from chaotic and fluid dynamics: (i) on predicting the Lorenz-96 systems dynamics in strongly- and very-strongly chaotic regimes (with forcing parameter being $F=8$ and $F=12$, respectively); and, (ii) on a data from the Hasegawa-Wakatani model on the edge of the tokamak plasma. It is demonstrated that the proposed benchmarks (i) and (ii), indeed, are the very challenging problems for the state of the art ML and AI tools - since both the general-purpose gradient boosted random forests and deep neuronal networks, as well as transformer-based AI tools like TabPFN v.03 (more spezialised for large-dimensional small data learning problems) - result in orders of magnitude inferior root mean squared prediction errors, and orders of magnitude larger model complexities, when compared to the EOMR. For a Hasegawa-Wakatani example, EOMR distills a very simple entropy-optimal and skilful description of the leading Essential Orthogonal Function (EOF) dynamics, given by linear, causal and weakly-stationary autoregressive process described by just 8 parameters.

Reconfigurable intelligent surfaces (RISs) are a promising technology for improving the spectral and energy efficiency of future wireless networks, which make use of metasurfaces. However, optimizing RIS configurations typically leads to large-scale, non-convex problems whose complexity grows significantly with the number of scattering elements and the adoption of advanced metasurface architectures. In this paper, we develop a stochastic optimization framework for RIS-aided wireless networks based on continuous versions of the ($a$) cross-entropy (CE) and ($b$) Metropolis-Hastings (MH) methods. Unlike existing stochastic approaches that mainly focus on discrete optimization, the proposed framework directly handles continuous variables and can be readily applied to discrete settings through relaxation and projection. We provide a theoretical characterization of the proposed algorithms, including convergence guarantees and efficiency analysis. The framework is applied to ($i$) achievable-rate maximization with nearly-passive RISs and ($ii$) energy-efficiency maximization with active RISs. Numerical results show that the proposed methods achieve performance comparable to, or better than, state-of-the-art deterministic algorithms, while reducing execution times up to 10 times in representative scenarios.

Bayesian posterior sampling is a ubiquitous paradigm for problems where a point estimate of parameters is not sufficient, such as risk analysis and uncertainty quantification. However, likelihoods may be misspecified, intractable, computationally expensive, or not representative of the discrepancy of interest. Generalized Bayes extends likelihood-based posterior updates by using other losses. Sinkhorn divergences have appealing geometric properties: they compare empirical measures directly and yield smooth gradients thanks to entropic regularization. In this work, we introduce Sinkhorn divergences as Generalized Bayes losses for Hamiltonian Monte Carlo (HMC) and No-U-Turn Sampler (NUTS). We also propose heuristics to set hyperparameters that affect the stability and calibration quality, such as the number of Sinkhorn iterations, the entropic regularization strength, and the marginal relaxation penalty. In regimes where the forward model relies on a stochastic simulator, we combine HMC/NUTS with a common-random-numbers strategy to obtain a deterministic surrogate objective that preserves gradients and Hamiltonian dynamics. We study both mass-preserving balanced and relaxed unbalanced settings. We evaluate our method empirically on (1) a simple Gaussian model as a sanity check; (2) a distribution supported on a noisy spiral manifold where a likelihood-based approach is a poor fit; (3) a Gaussian pulse model with misalignment due to errors-in-variables, emphasizing robustness to misspecification; and (4) CIFAR-10 image patch alignment under perturbations, highlighting differences between balanced and unbalanced regimes.

Although neural-based machine learning models have received a lot of attention recently, tree-based models such as gradient boosting are competitive for tabular data and therefore remain widely used in various applications of AI. As when using other machine learning predictive models, they can however yield discriminative predictions across demographic groups, due to so-called algorithmic biases. These undesirable phenomena have motivated the emergence of new regulatory frameworks and various AI fairness strategies. While several pre-and post-processing methodologies exist to mitigate such bias on gradient boosting models, only a few in-processing methods have been proposed. To bridge this gap, we introduce OT-FairBoost, a novel in-processing framework that incorporates a Wasserstein-2 distance penalty directly into the objective function of gradient-boosted trees. This OT-based mitigation strategy has been shown to efficiently optimize group fairness criteria such as Demographic Parity and Equalized Odds on neural-based predictions. To adapt this approach for gradient boosting, we extend the sample-wise gradient estimation of the Wasserstein-2 distance between group predictions to discrete distributions and hessian diagonals. We then integrate our approach into the LightGBM training procedure and evaluate it across binary classification, regression, and multi-group sensitive attribute settings. Experimental results in each of these settings demonstrate that OT-FairBoost achieves best accuracy-fairness trade-offs against alternatives.

Adversarial training can improve the robustness of predictive models to bounded perturbations, often at the cost of statistical efficiency. We study this trade-off in kernel regression over a reproducing kernel Hilbert space (RKHS). It is shown that, under squared loss, adversarial training in RKHS introduces a term involving the product of the function norm with the mean absolute value of the response noise, which we call the noise premium. Our analysis shows that the noise premium makes the prediction error of adversarial training converge strictly more slowly than the nonparametric minimax benchmark even after balancing approximation and estimation errors. Moreover, for a fixed perturbation budget, once the budget exceeds a certain threshold, the solution to adversarial training collapses to the zero function. To mitigate these effects of the noise premium, we propose noise-debiased adversarial training. The resulting noise-debiased estimator can attain the minimax optimal rate up to a logarithmic factor for the prediction error, raises the collapse threshold, and admits an explicit bound on the increase in adversarial loss. Numerical experiments on synthetic and real data support the theoretical findings and validate the effectiveness of the proposed noise-debiased method.

In spring 2026, an economics professor at Brown University gave a take-home midterm and, after unusually high scores, made the final exam proctored. Among the 59 students who completed the course, average scores fell from 95.7 out of 100 to 48.8. The instructor attributed the drop to unauthorized use of generative AI on the midterm; others proposed test anxiety, a harder final, student withdrawals, and regression to the mean. The publicly released scores, one midterm-final pair per student, show two striking patterns: the correlation between a student's two scores is only 0.06, and individual changes range from a 4-point gain to a 100-point loss. Permutation tests find no statistically detectable association between students' midterm and final scores, yet would detect association of the strength the alternative explanations predict more than 90 percent of the time. Once model complexity is accounted for, a model in which a student's midterm carries no information about that student's final describes the data as well as any model that permits an association. Neither result rules out a weak association, but together they show that the data do not require any. In simulated classes where each student's two scores remain linked through that student's own proficiency, as the alternative explanations imply, the two patterns almost never appear together; they appear together regularly only when that link is nearly severed. More than one mechanism could have severed it: midterm answers that were not the students' own work would have done so, and so would a final testing substantially different material, with no assistance involved. The scores cannot distinguish these possibilities or identify which students, if any, used unauthorized assistance. Our study offers a framework for evaluating statistical evidence in future disputes over generative AI use in academic assessment.

At the July 2026 Johor state election, Barisan Nasional (BN) swept the state and nearly doubled its vote relative to 2022. We exploit geographic variation in the ethnic composition of polling stations and administration-induced variation in the age composition of polling streams to estimate turnout and coalition support by ethnicity and age for the three elections involving Johor since 2022, with five key findings. (1) Turnout is a first-order driver of outcomes, moving by up to 26 points within an ethnic group across elections and following a life-cycle profile. (2) BN's surge was a near one-for-one Perikatan Nasional (PN) collapse among Malay voters, robust to PN's stand-down in 23 of 56 seats. (3) The largest reversal towards BN was among young Malays, who had previously carried the `green wave' of 2022. (4) Two-thirds of Pakatan Harapan's (PH) decline among the Chinese electorate came through lower Chinese turnout; any crossover to BN was comparatively small. (5) The apparent youth gradient in BN's 2026 support is largely ethnic composition rather than within-group behaviour: by 2026, Malay support for every coalition was close to flat in age. More broadly, we provide what we believe are the first open and fully reproducible ecological estimates of voting behaviour for any Malaysian election, accompanied by estimand-specific validation errors measured against held-out behaviour.

We develop a selfnormalized approach to inference for relevant changes in functional time series measured by the supremum norm. The main difficulty is that the supremum norm is not Hadamard differentiable, so standard projection-based selfnormalization does not apply and the limiting distribution may depend on the geometry of the extremal set and the long-run covariance structure. We address this problem by replacing the supremum norm with a smooth log-sum-exp approximation and constructing a projected selfnormalizer from its derivative. The resulting statistic has an asymptotically pivotal distribution that is free of long-run covariance nuisance parameters and depends only on the break location. We derive explicit smoothing-bias expansions for both isolated nondegenerate extrema and extremal sets of positive measure. To avoid direct estimation of geometric quantities such as the number, curvature, or measure of the extrema, we combine several smoothing levels to cancel the leading bias terms. This yields an asymptotically exact test for relevant changes under mild regularity conditions. More generally, the proposed smoothing and bias-correction principles provide a framework for combining selfnormalization with supremum-type statistics in problems involving relevant hypotheses.

Local differential privacy (LDP) protocols are vulnerable to poisoning attacks. Existing research have proposed efficient defense strategies for single-item users. However, in practice, a user may possess multiple items. The defense against poisoning attacks for multi-item users is challenging, because due to larger output spaces, the adversary can conduct more powerful attacks without being detected. In this paper, we address the robust sparse vector mean estimation problem, in which each user has a vector with $m$ nonzero coordinates. We propose Randomized Projection with Clipping (RPC). Firstly, the server sends a random binary vector to each user. The user then projects its local data on the vector, and clip the value to restrict the attacker's capability. To handle clipping bias, we propose a correction method based on a careful analysis that gives an exact expression of the bias. As a result, bias-variance tradeoff is no longer needed, thus the clipping threshold can be further reduced to shrink the output space and enhance robustness. We provide a rigorous theoretical guarantee of the estimation error under all possible attacks. Numerical experiments show that under trusted environments, our new method achieves comparable or better performance than existing methods, indicating that our method is already an efficient estimator in its own right. Under untrusted environments, our method is also significantly more robust to poisoning attacks.