Papers

A targeted learning (TL) framework is developed to estimate the difference in the restricted mean survival time (RMST) for a clinical trial with time-to-event outcomes. The approach starts by defining the target estimand as the RMST difference between investigational and control treatments. Next, an efficient estimation method is introduced: a targeted minimum loss estimator (TMLE) utilizing pseudo-observations. Moreover, a version of the copy reference (CR) approach is developed to perform a sensitivity analysis for right-censoring. The proposed TL framework is demonstrated using a real data application.

We introduce Ising-Hüsler-Reiss processes, a new class of multivariate Lévy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability indices. The underlying conditional independence graph is encoded as zeroes in a suitable precision matrix. An Ising-type parametrization of the weights for each orthant of the Lévy measure allows for data-driven modeling of asymmetry of the jumps while retaining an arbitrary sparse graph. We develop consistent estimators for the graphical structure and asymmetry parameters, relying on a new uniform small-time approximation for Lévy processes. The methodology is illustrated in simulations and a real data application to modeling dependence of stock returns.

Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an established model that accounts for the heterogeneity of node degrees. However, inference methods are computationally costly and highly sensitive to initialization, while cheaper alternatives, such as spectral or modularity-based approaches, are restricted to detecting specific structures, typically assortative. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem. Leveraging this insight, we propose a novel method for community detection and a theoretically well-grounded initialization strategy that provides an initial estimate of communities for inference algorithms. Our approach is agnostic to any specific network structure and applies to graphs with any structure representable by a DCBM. Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference while being faster; for instance, it processes a graph with 100,000 nodes and 1,000,000 edges in approximately 4 minutes. Moreover, the proposed initialization strategy significantly improves solution quality and reduces the number of iterations required by all tested inference algorithms. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.

We study the discrete-to-continuum consistency of the training of shallow graph convolutional neural networks (GCNNs) on proximity graphs of sampled point clouds under a manifold assumption. Graph convolution is defined spectrally via the graph Laplacian, whose low-frequency spectrum approximates that of the Laplace-Beltrami operator of the underlying smooth manifold, and shallow GCNNs of possibly infinite width are linear functionals on the space of measures on the parameter space. From this functional-analytic perspective, graph signals are seen as spatial discretizations of functions on the manifold, which leads to a natural notion of training data consistent across graph resolutions. To enable convergence results, the continuum parameter space is chosen as a weakly compact product of unit balls, with Sobolev regularity imposed on the output weight and bias, but not on the convolutional parameter. The corresponding discrete parameter spaces inherit the corresponding spectral decay, and are additionally restricted by a frequency cutoff adapted to the informative spectral window of the graph Laplacians. Under these assumptions, we prove $\Gamma$-convergence of regularized empirical risk minimization functionals and corresponding convergence of their global minimizers, in the sense of weak convergence of the parameter measures and uniform convergence of the functions over compact sets. This provides a formalization of mesh and sample independence, and hence of transferability across discretizations, for the training of such networks.

As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent positions" are often estimated via embeddings, whereby the nodes of a network are mapped to points in Euclidean space so that "similar" nodes are mapped to nearby points. Under certain model assumptions, these embeddings are consistent estimates of the latent positions, but most such results require that the embedding dimension be chosen correctly, typically equal to the dimension of the latent space. Methods for estimating this correct embedding dimension have been studied extensive in recent years, but there has been little work to date characterizing the behavior of embeddings when this embedding dimension is misspecified. In this work, we provide theoretical descriptions of the effects of misspecifying the embedding dimension of the adjacency spectral embedding under the random dot product graph, a class of latent space network models that includes a number of widely-used network models as special cases, including the stochastic blockmodel. We consider both the case in which the dimension is chosen too small, where we prove estimation error lower-bounds, and the case where the dimension is chosen too large, where we show that consistency still holds, albeit at a slower rate than when the embedding dimension is chosen correctly.A range of synthetic data experiments support our theoretical results. Our main technical result, which may be of independent interest, is a generalization of earlier work in random matrix theory, showing that all non-signal eigenvectors of a low-rank matrix subject to additive noise are delocalized.

In Differential GNSS (DGNSS) positioning, differencing measurements between a user and a reference station suppresses common-mode errors but also introduces reference-station noise, which fundamentally limits accuracy. This limitation is minor for high-grade stations but becomes significant when using reference infrastructure of mixed quality. This paper investigates how large-scale user cooperation can mitigate the impact of reference-station noise in conventional (non-cooperative) DGNSS systems. We develop a unified estimation framework for cooperative DGNSS (C-DGNSS) and cooperative real-time kinematic (C-RTK) positioning, and derive parameterized expressions for their Fisher information matrices as functions of network size, satellite geometry, and reference-station noise. This formulation enables theoretical analysis of estimation performance, identifying regimes where cooperation asymptotically restores the accuracy of DGNSS with an ideal (noise-free) reference. Simulations validate these theoretical findings.

We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems for continuous semimartingales, which correlates number $N_\varepsilon$ of excursions of magnitude at least $\varepsilon$ with the quadratic variation $[X]_T$ of the process. The scaling law holds universally for all continuous semimartingales with finite quadratic variation, including general Ito diffusions with nonlinear or state-dependent volatility, but fails sharply for deterministic systems – thereby providing a theoretically-certfied method of distinguishing between these dynamics, as opposed to the subjective entropy or recurrence based state of the art methods. We construct a robust data-driven diffusion test. The method compares the empirical excursion counts against the theoretical expectation. The resulting ratio $K(\varepsilon)=N_{\varepsilon}^{\mathrm{emp}}/N_{\varepsilon}^{\mathrm{theory}}$ is then summarized by a log-log slope deviation measuring the $\varepsilon^{-2}$ law that provides a classification into diffusion-like or not. We demonstrate the method on canonical stochastic systems, some periodic and chaotic maps and systems with additive white noise, as well as the stochastic Duffing system. The approach is nonparametric, model-free, and relies only on the universal small-scale structure of continuous semimartingales.

Hypothesis testing problems for circular data are formulated, where observations take values on the unit circle and may contain a hidden, phase-coherent structure. Under the null, the data are independent uniform on the unit circle; under the alternative, either (i) a planted subset of size K concentrates around an unknown phase (the flat setting), or (ii) a planted community of size k induces coherence among the edges of a complete graph (the community setting). In each of the two settings, two circular signal distributions are considered: a hard-cluster distribution, where correlated planted observations lie in an arc of known length and unknown location, and a von Mises distribution, where correlated planted observations follow a von Mises distribution with a common unknown location parameter. For each of the four resulting models, nearly matching necessary and sufficient conditions are derived (up to constants and occasional logarithmic factors) for detectability, thereby establishing information-theoretic phase transitions.

We propose DeePM (Deep Portfolio Manager), a structured deep-learning macro portfolio manager trained end-to-end to maximize a robust, risk-adjusted utility. DeePM addresses three fundamental challenges in financial learning: (1) it resolves the asynchronous "ragged filtration" problem via a Directed Delay (Causal Sieve) mechanism that prioritizes causal impulse-response learning over information freshness; (2) it combats low signal-to-noise ratios via a Macroeconomic Graph Prior, regularizing cross-asset dependence according to economic first principles; and (3) it optimizes a distributionally robust objective where a smooth worst-window penalty serves as a differentiable proxy for Entropic Value-at-Risk (EVaR) - a window-robust utility encouraging strong performance in the most adverse historical subperiods. In large-scale backtests from 2010-2025 on 50 diversified futures with highly realistic transaction costs, DeePM attains net risk-adjusted returns that are roughly twice those of classical trend-following strategies and passive benchmarks, solely using daily closing prices. Furthermore, DeePM improves upon the state-of-the-art Momentum Transformer architecture by roughly fifty percent. The model demonstrates structural resilience across the 2010s "CTA (Commodity Trading Advisor) Winter" and the post-2020 volatility regime shift, maintaining consistent performance through the pandemic, inflation shocks, and the subsequent higher-for-longer environment. Ablation studies confirm that strictly lagged cross-sectional attention, graph prior, principled treatment of transaction costs, and robust minimax optimization are the primary drivers of this generalization capability.

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for the prediction of outstanding number of claims, which are particularly useful to account for overdispersion. We first assume independence of random variables and introduce appropriate notation. Later, we generalise the model to account for dependence across development years. In both cases, the marginal distributions are negative binomials. We study the properties of the models and carry out bayesian inference. We illustrate the performance of the models with simulated and real datasets.

Modern engineering and scientific workflows often require simultaneous predictions across related tasks and fidelity levels, where high-fidelity data is scarce and expensive, while low-fidelity data is more abundant. This paper introduces an Multi-Task Gaussian Processes (MTGP) framework tailored for engineering systems characterized by multi-source, multi-fidelity data, addressing challenges of data sparsity and varying task correlations. The proposed framework leverages inter-task relationships across outputs and fidelity levels to improve predictive performance and reduce computational costs. The framework is validated across three representative scenarios: Forrester function benchmark, 3D ellipsoidal void modeling, and friction-stir welding. By quantifying and leveraging inter-task relationships, the proposed MTGP framework offers a robust and scalable solution for predictive modeling in domains with significant computational and experimental costs, supporting informed decision-making and efficient resource utilization.

As machine learning models become increasingly embedded in societal infrastructure, auditing them for bias is of growing importance. However, in real-world deployments, auditing is complicated by the fact that model owners may adaptively update their models in response to changing environments, such as financial markets. These updates can alter the underlying model class while preserving certain properties of interest, raising fundamental questions about what can be reliably audited under such shifts. In this work, we study group fairness auditing under arbitrary updates. We consider general shifts that modify the pre-audit model class while maintaining invariance of the audited property. Our goals are two-fold: (i) to characterize the information complexity of allowable updates, by identifying which strategic changes preserve the property under audit; and (ii) to efficiently estimate auditing properties, such as group fairness, using a minimal number of labeled samples. We propose a generic framework for PAC auditing based on an Empirical Property Optimization (EPO) oracle. For statistical parity, we establish distribution-free auditing bounds characterized by the SP dimension, a novel combinatorial measure that captures the complexity of admissible strategic updates. Finally, we demonstrate that our framework naturally extends to other auditing objectives, including prediction error and robust risk.

Real-world data (RWD) gains growing interests to provide a representative sample of the population for selecting the optimal treatment options. However, existing complex black box methods for estimating individualized treatment rules (ITR) from RWD have problems in interpretability and convergence. Providing an interpretable and sparse ITR can be used to overcome the limitation of existing methods. We developed an algorithm using Adaptive LASSO to predict optimal interpretable linear ITR in the RWD. To encourage sparsity, we obtain an ITR by minimizing the risk function with various types of penalties and different methods of contrast estimation. Simulation studies were conducted to select the best configuration and to compare the novel algorithm with the existing state-of-the-art methods. The proposed algorithm was applied to RWD to predict the optimal interpretable ITR. Simulations show that adaptive LASSO had the highest rates of correctly selected variables and augmented inverse probability weighting with Super Learner performed best for estimating treatment contrast. Our method had a better performance than causal forest and R-learning in terms of the value function and variable selection. The proposed algorithm can strike a balance between the interpretability of estimated ITR (by selecting a small set of important variables) and its value.

Estimating the size of hidden populations using Multiple Systems Estimation (MSE) is a critical task in quantitative sociology; however, practical application is often hindered by imperfect administrative data and computational constraints. Real-world datasets frequently suffer from censoring and missingness due to privacy concerns, while standard inference methods, such as Maximum Likelihood Estimation (MLE) and Markov chain Monte Carlo (MCMC), can become computationally intractable or fail to converge when data are sparse. To address these limitations, we propose a novel simulation-based Bayesian inference framework utilizing Neural Bayes Estimators (NBE) and Neural Posterior Estimators (NPE). These neural methods are amortized: once trained, they provide instantaneous, computationally efficient posterior estimates, making them ideal for use in secure research environments where computational resources are limited. Through extensive simulation studies, we demonstrate that neural estimators achieve accuracy comparable to MCMC while being orders of magnitude faster and robust to the convergence failures that plague traditional samplers in sparse settings. We demonstrate our method on two real-world cases estimating the prevalence of modern slavery in the UK and female drug use in North East England.

Poisson non-negative matrix factorization (NMF) is a widely used method to find interpretable "parts-based" decompositions of count data. While many variants of Poisson NMF exist, existing methods assume that the "parts" in the decomposition combine additively. This assumption may be natural in some settings, but not in others. Here we introduce Poisson NMF with the shifted-log link function to relax this assumption. The shifted-log link function has a single tuning parameter, and as this parameter varies the model changes from assuming that parts combine additively (i.e., standard Poisson NMF) to assuming that parts combine more multiplicatively. We provide an algorithm to fit this model by maximum likelihood, and also an approximation that substantially reduces computation time for large, sparse datasets (computations scale with the number of non-zero entries in the data matrix). We illustrate these new methods on a variety of real datasets. Our examples show how the choice of link function in Poisson NMF can substantively impact the results, and how in some settings the use of a shifted-log link function may improve interpretability compared with the standard, additive link.

High-dimensional time series phenotypic data is becoming increasingly common within plant breeding programmes. However, analysing and integrating such data for genetic analysis and genomic prediction remains difficult. Here we show how factor analysis with Procrustes rotation on the genetic correlation matrix of hyperspectral secondary phenotype data can help in extracting relevant features for within-trial prediction. We use a subset of Centro Internacional de Mejoramiento de Maíz y Trigo (CIMMYT) elite yield wheat trial of 2014-2015, consisting of 1,033 genotypes. These were measured across three irrigation treatments at several timepoints during the season, using manned airplane flights with hyperspectral sensors capturing 62 bands in the spectrum of 385-850 nm. We perform multivariate genomic prediction using latent variables to improve within-trial genomic predictive ability (PA) of wheat grain yield within three distinct watering treatments. By integrating latent variables of the hyperspectral data in a multivariate genomic prediction model, we are able to achieve an absolute gain of .1 to .3 (on the correlation scale) in PA compared to univariate genomic prediction. Furthermore, we show which timepoints within a trial are important and how these relate to plant growth stages. This paper showcases how domain knowledge and data-driven approaches can be combined to increase PA and gain new insights from sensor data of high-throughput phenotyping platforms.

We study the conditional Cauchy-Schwarz divergence (C-CSD) as a symmetric and density-free measure for time series analysis. We derive a practical kernel based estimator using radial basis function kernels on both the condition and output spaces, together with numerical stabilizations including a symmetric logarithmic form with an epsilon ridge and a robust bandwidth selection rule based on the interquartile range. Median heuristic bandwidths are applied to window vectors, and effective rank filtering is used to avoid degenerate kernels. We demonstrate the framework in two applications. In time series clustering, conditioning on the time index and comparing scalar series values yields a pairwise C-CSD dissimilarity. Bandwidths are selected on the training split, after which precomputed distance k-medoids clustering is performed on the test split and evaluated using normalized mutual information. In fraud detection, conditioning on sliding transaction windows and comparing the magnitude of value changes with categorical and merchant change indicators, each query window is scored by contrasting a global normal reference mixture against a same account local history mixture with recency decay and change flag weighting. Account level decisions are obtained by aggregating window scores using the maximum value. Experiments on benchmark time series datasets and a transactional fraud detection dataset demonstrate stable estimation and effective performance under a strictly leak free evaluation protocol.

We study high-dimensional sparse regression under simultaneous heavy-tailed covariates and noise. Heavy-tailed data affect sparse optimization in two different ways: extreme covariates can destabilize the gradient field during global localization, while heavy-tailed noise limits the final statistical accuracy during local refinement. Motivated by this two-phase structure, we propose two-stage RIGHT, a robust sparse first-order method based on coordinate-wise median-of-means (MoM) gradient estimation and delayed sample splitting. The MoM gradient estimator is computationally simple, compatible with hard-thresholded updates, and admits phase-adaptive concentration bounds whose rates depend on the current localization radius. Delayed splitting reuses data during global localization and reserves fresh batches for the shorter refinement stage, reducing the sample-splitting cost. The theoretical results reveal a decoupled rate structure: the design-tail index controls gradient stability and sample complexity, whereas the noise-tail index controls the final statistical rate. We also provide phase-wise lower-bound benchmarks showing that the design-driven localization barrier is intrinsic. Extensive simulation experiments and real data analysis showcase the efficacy of the proposed method over existing competitors.

Neural networks have shown state-of-the-art performances in various classification and regression tasks. Rectified linear units (ReLU) are often used as activation functions for the hidden layers in a neural network model. In this article, we establish the connection between the Poisson hyperplane processes (PHP) and two-layer ReLU neural networks. We show that the PHP with a Gaussian prior is an alternative probabilistic representation to a two-layer ReLU neural network. In addition, we show that a two-layer neural network constructed by PHP is scalable to large-scale problems via the decomposition propositions. Finally, we propose an annealed sequential Monte Carlo algorithm for Bayesian inference. Our numerical experiments demonstrate that our proposed method outperforms the classic two-layer ReLU neural network. The implementation of our proposed model is available at https://github.com/ShufeiGe/Pois_Relu.git.

A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations without the need for a calculator. Several previous studies have used mixed-integer optimization (MIO) techniques to develop scoring systems for binary classification; however, they have not focused on directly maximizing AUC (i.e., area under the receiver operating characteristic curve), even though AUC is recognized as an essential evaluation metric for scoring systems. Our goal herein is to establish an effective MIO framework for constructing scoring systems that directly maximize the buffered AUC (bAUC) as the tightest concave lower bound on AUC. Our optimization model is formulated as a mixed-integer linear optimization (MILO) problem that maximizes bAUC subject to a group sparsity constraint for limiting the number of questions in the scoring system. Computational experiments using publicly available real-world datasets demonstrate that our MILO method can build scoring systems with superior AUC values compared to the baseline methods based on regularization and stepwise regression. This research contributes to the advancement of MIO techniques for developing highly interpretable classification models.

The global carbon market is fragmented and characterized by limited pricing transparency and empirical evidence, creating challenges for investors and policymakers in identifying carbon management opportunities. The European Union is among several regions that have implemented emissions pricing through an Emissions Trading System (EU ETS). While the EU ETS has contributed to emissions reductions, it has also raised concerns related to international competitiveness and carbon leakage, particularly given the strong integration of EU industries into global value chains. To address these challenges, the European Commission proposed the Carbon Border Adjustment Mechanism (CBAM) in 2021. CBAM is designed to operate alongside the EU ETS by applying a carbon price to selected imported goods, thereby aligning carbon costs between domestic and foreign producers. It will gradually replace existing carbon leakage mitigation measures, including the allocation of free allowances under the EU ETS. The initial scope of CBAM covers electricity, cement, fertilizer, aluminium, iron, and steel. As climate policies intensify under the Paris Agreement, CBAM-like mechanisms are expected to play an increasingly important role in managing carbon-related trade risks and supporting the transition to net zero emissions.

This paper establishes a rigorous theoretical foundation for the function class implicitly learned by XGBoost, bridging the gap between its empirical success and our theoretical understanding. We introduce an infinite-dimensional function class $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ that extends finite ensembles of bounded-depth regression trees, together with a complexity measure $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ that generalizes the $L^1$ regularization penalty used in XGBoost. We show that every optimizer of the XGBoost objective is also an optimizer of an equivalent penalized regression problem over $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ with penalty $V^{d, s}_{\infty-\text{XGB}}(\cdot)$, providing an interpretation of XGBoost as implicitly targeting a broader function class. We also develop a smoothness-based interpretation of $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ and $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ in terms of Hardy–Krause variation. We prove that the least squares estimator over $\{f \in \mathcal{F}^{d, s}_{\infty-\text{ST}}: V^{d, s}_{\infty-\text{XGB}}(f) \le V\}$ achieves a nearly minimax-optimal rate of convergence $n^{-2/3} (\log n)^{4(\min(s, d) - 1)/3}$, thereby avoiding the curse of dimensionality. Our results provide the first rigorous characterization of the function space underlying XGBoost, clarify its connection to classical notions of variation, and identify an important open problem: whether the XGBoost algorithm itself achieves minimax optimality over this class.

This brief note considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their relative importances or in their true relations based-on some aggregated information shared by the principal. Whereas, the principal, which is exerting an influence on the learning process of the agents in the aggregation, is primarily tasked to solve a high-level optimization problem posed as an empirical-likelihood estimator under conditional moment restrictions model that also accounts information about the agents' predictive performances on out-of-samples as well as a set of private datasets available only to the principal. In particular, we present a coherent mathematical argument which is necessary for characterizing the learning process behind this abstract principal-agent learning framework, although we acknowledge that there are a few conceptual and theoretical issues still need to be addressed.

The study aimed to evaluate the applicability of environmental indices in the monitoring of smouldering coal-waste dumps. A dump located in the Upper Silesian Coal Basin served as the research site for a multi-method analysis combining remote sensing and field-based data. Two UAV survey campaigns were conducted, capturing RGB, infrared, and multispectral imagery. These were supplemented with direct ground measurements of subsurface temperature and detailed vegetation mapping. Additionally, publicly available satellite data from the Landsat and Sentinel missions were analysed. A range of vegetation and fire-related indices (NDVI, SAVI, EVI, BAI, among others) were calculated to identify thermally active zones and assess vegetation conditions within these degraded areas. The results revealed strong seasonal variability in vegetation indices on thermally active sites, with evidence of disrupted vegetation cycles, including winter greening in moderately heated root zones - a pattern indicative of stress and degradation processes. While satellite data proved useful in reconstructing the fire history of the dump, their spatial resolution was insufficient for detailed monitoring of small-scale thermal anomalies. The study highlights the diagnostic potential of UAV-based remote sensing in post-industrial environments undergoing land degradation but emphasises the importance of field validation for accurate environmental assessment.

The aim of Active Learning is to select the most informative samples from an unlabelled set of data. This is useful in cases where the amount of data is large and labelling is expensive, such as in machine vision or medical imaging. Two particularities of machine vision are first, that most of the images produced are free of defects, and second, that the amount of images produced is so big that we cannot store all acquired images. This results, on the one hand, in a strong class imbalance in defect distribution and, on the other hand, in a potential label shift caused by limited storage. To understand how these two forms of imbalance affect active learning algorithms, we propose a simulation study based on two open-source datasets. Our contribution is not a new acquisition strategy but a controlled and reproducible protocol that synthetically constructs datasets in which the levels of class imbalance and label shift are fixed and vary independently. Four standard active learning selection strategies are compared: random sampling, entropy-based selection, core-set selection and an imbalance aware strategy called galaxy sampling. We empirically find that active learning, and in particular the entropy-based and core-set selections, remains competitive with and typically superior to random sampling even for highly imbalanced datasets, and we quantify the loss of efficiency that occurs under a strong label shift.

Large language models (LLMs) are increasingly used as automatic evaluators of generative AI outputs, a paradigm often referred to as "LLM-as-a-judge." In practice, LLM judges are imperfect predictions for the underlying truth and can exhibit systematic, non-random errors. Two main approaches have recently been proposed to address this issue: (i) direct measurementerror correction based on misclassification models such as Rogan-Gladen-style estimators, and (ii) surrogate-outcome approaches such as prediction-powered inference (PPI), which correct bias by calibrating prediction residuals on a small set of gold-standard human labels. In this paper, we systematically study the performance of these two approaches for estimating mean parameters (e.g., average benchmark scores or pairwise win rates). Leveraging tools from semiparametric efficiency theory, we unify the two classes of estimators by deriving explicit forms of efficient influence function (EIF)-based efficient estimators and characterize conditions under which PPI-style estimators attain strictly smaller asymptotic variance than measurement-error corrections. We verify our theoretical results in simulations and demonstrate the methods on real-data examples. We provide an implementation of the benchmarked methods and comparison utilities at https://github.com/yiqunchen/debias-llm-as-a-judge.

Multi-group classification arises in many prediction and decision-making problems, including applications in epidemiology, genomics, finance, and image recognition. Although classification methods have advanced considerably, much of the literature focuses on binary problems, and available extensions often provide limited flexibility for multi-group settings. Recent work has extended linear discriminant analysis to multiple groups, but more general methods are still needed to handle complex structures such as nonlinear decision boundaries and group-specific covariance patterns. We develop Multi-Group Quadratic Discriminant Analysis (MGQDA), a method for multi-group classification built on quadratic discriminant analysis. MGQDA projects high-dimensional predictors onto a lower-dimensional subspace, which enables accurate classification while capturing nonlinearity and heterogeneity in group-specific covariance structures. We derive theoretical guarantees, including variable selection consistency, to support the reliability of the procedure. In simulations and a gene-expression application, MGQDA achieves competitive or improved predictive performance compared with existing methods while selecting group-specific informative variables, indicating its practical value for high-dimensional multi-group classification problems. Supplementary materials for this article are available online.

As large language models (LLMs) transition from chat interfaces to integral components of stochastic pipelines and systems approaching general intelligence, the ability to faithfully sample from specified probability distributions has become a functional requirement rather than a theoretical curiosity. We present the first large-scale, statistically powered audit of native probabilistic sampling in frontier LLMs, benchmarking 11 models across 15 distributions. To disentangle failure modes, we employ a dual-protocol design: Batch Generation, where a model produces $N{=}1000$ samples within one response, and Independent Requests, comprising $N{=}1000$ stateless calls. We observe a sharp protocol asymmetry: batch generation achieves only modest statistical validity, with a 7% median pass rate, while independent requests collapse almost entirely, with 10 of 11 models passing none of the distributions. Beyond this asymmetry, we reveal that sampling fidelity degrades monotonically with distributional complexity and aggravates as the sampling horizon $N$ increases. Finally, we demonstrate how the propagation of these failures into downstream real-world application tasks introduces systematic biases: models fail to enforce uniform answer-position constraints in Multiple Choice Question generation and systematically violate demographic targets in attribute-constrained text-to-image prompt synthesis. These findings indicate that current LLMs lack a functional internal sampler, necessitating external tools for applications requiring statistical guarantees.

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the method embeds the variables that define the proximity to or from each object. It is straightforward to implement, and the quality of the resulting representation can be easily evaluated. The methodology is illustrated by visualizing the asymmetric relationships between the citing and cited profiles of journals on a common map. Two profiles that are far apart (or close together) in the h-plot, as measured by Euclidean distance, are different (or similar), respectively. This representation allows archetypoid analysis (ADA) to be calculated. ADA is used to find archetypal journals (or extreme cases). We can represent the dataset as convex combinations of these archetypal journals, making the results easy to interpret, even for non-experts. Comparisons with other methodologies are carried out, showing the good performance of our proposal. Code and data are available for reproducibility.

Injection molding is a critical manufacturing process, but controlling warpage remains a major challenge due to complex thermomechanical interactions. Simulation-based optimization is widely used to address this, yet traditional methods often overlook the uncertainty in model parameters. In this paper, we propose a data-driven framework to minimize warpage and quantify the uncertainty of optimal process settings. We employ polynomial regression models as surrogates for the injection molding simulations of a box-shaped part. By adopting a Bayesian framework, we estimate the posterior distribution of the regression coefficients. This approach allows us to generate a distribution of optimal decisions rather than a single point estimate, providing a measure of solution robustness. Furthermore, we develop a Monte Carlo-based boundary analysis method. This method constructs confidence bands for the zero-level sets of the response surfaces, helping to visualize the regions where warpage transitions between convex and concave profiles. We apply this framework to optimize four key process parameters: mold temperature, injection speed, packing pressure, and packing time. The results show that our approach finds stable process settings and clearly marks the boundaries of defects in the parameter space.