Papers

The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has mainly been used in a binary context, in which it has many equivalent reformulations such as the receiver operating characteristic (ROC) or the area under the curve (AUC). In the actuarial literature, this rank based score for binary responses has been extended to general real-valued random variables using Lorenz curves and concentration curves. While these initial concepts assume that the risk ranking is generated by a continuous distribution function, we discuss in this paper how the Gini score can be used in the case of ties in the risk ranking. Moreover, we adapt the Gini score to the common actuarial situation of having case weights.

Interactive fixed effects are routinely controlled for in linear panel models. While an analogous fixed effects (FE) estimator for nonlinear models has been available in the literature (Chen, Fernandez-Val and Weidner, 2021), it sees much more limited use in applied research because its implementation involves solving a high-dimensional non-convex problem. In this paper, we complement the theoretical analysis of Chen, Fernandez-Val and Weidner (2021) by providing a new computationally efficient estimator that is asymptotically equivalent to their estimator. Unlike the previously proposed FE estimator, our estimator avoids solving a high-dimensional non-convex optimization problem and can be feasibly computed in large nonlinear panels. Our proposed method involves two steps. In the first step, we convexify the optimization problem using nuclear norm regularization (NNR) and obtain preliminary NNR estimators of the parameters, including the fixed effects. Then, we find the global solution of the original optimization problem using a standard gradient descent method initialized at these preliminary estimates. To make our method readily applicable in practice, we also propose specific numerical algorithms for solving the involved optimization problems, establish their convergence, and provide their efficient implementation in our R package NNRPanel.

Watanabe's singular learning theory provides a framework for asymptotic analysis of Bayesian model selection for statistical models with singularities, where traditional statistical regularity assumptions fail. Learning coefficients, also known as real log canonical thresholds, play a central role in singular learning, as they govern the asymptotic behavior of Bayesian marginal likelihood integrals in settings where the Laplace approximations used for regular statistical models are not applicable. Learning coefficients are algebraic invariants that quantify the geometric complexity of a model and reveal how the singular structure impacts the model's generalization properties. In this paper, we apply algebraic methods to study the learning coefficients of factor analysis models, which are widely used latent variable models for continuously distributed data. Our main result provides exact formulas for learning coefficients of factor analysis models. Moreover, we study the singularity types of specific factor analysis models in detail.

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic consistency constraints. This framework gives rise to a family of forward-backward algorithms whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss–Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models, we close the recursions using generalized statistical linear regression and Fourier–Hermite moment matching.

We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_i$ be random variables, $Y_i \sim f(y|\theta_i)$, $i=1,...,n$, where $\theta_i \sim G$, and $\theta_i \in \Theta$ are independent. The variables $Y_i $ are conditionally independent given $\theta_i, \; i=1,...,n$. The mixing distribution $G$ is unknown and assumed to belong to a nonparametric class $\{G \}$. Let $\eta(\theta)$ be a function of $\theta$. We address the problem of consistently estimating $E_G \eta(\theta) \equiv \eta_G$. This problem becomes particularly challenging when $G$ cannot be consistently estimated from the observed data. We motivate this problem, especially in contexts involving nonresponse and missing data. For such cases, a consistent estimation method is suggested and its performance is demonstrated through simulations.

Random-effects meta-analyses are widely used for evidence synthesis in medical research. However, conventional methods based on large-sample approximations often exhibit poor performance in case of very few studies (e.g., 2 to 4), which is very common in practice. Existing methods aiming to improve small-sample performance either still suffer from poor estimates of heterogeneity or result in very wide confidence intervals. Motivated by meta-analyses evaluating surrogate outcomes, where units nested within a trial are often exploited when the number of trials is small, we propose an inference approach based on a common-effect estimator synthesizing data from the subgroup-level instead of the study-level. Two DerSimonian-Laird type heterogeneity estimators are derived using the subgroup-level data, and are incorporated into the Henmi-Copas type variance to adequately reflect variance components. We considered t-quantile based intervals to account for small-sample properties and used flexible degrees of freedom to reduce interval lengths. A comprehensive simulation is conducted to study the performance of our methods depending on various magnitudes of subgroup effects as well as subgroup prevalences. Some general recommendations are provided on how to select the subgroups, and methods are illustrated using two example applications.

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed noise, potentially leading to unreliable model selection and biased estimates. To address this limitation, we introduce the Exponential Lasso, a novel robust method that integrates an exponential-type loss function within the Lasso framework. This loss function is designed to achieve a smooth trade-off between statistical efficiency under Gaussian noise and robustness against data contamination. Unlike other methods that cap the influence of large residuals, the exponential loss smoothly redescends, effectively downweighting the impact of extreme outliers while preserving near-quadratic behavior for small errors. We establish theoretical guarantees showing that the Exponential Lasso achieves strong statistical convergence rates, matching the classical Lasso under ideal conditions while maintaining its robustness in the presence of heavy-tailed contamination. Computationally, the estimator is optimized efficiently via a Majorization-Minimization (MM) algorithm that iteratively solves a series of weighted Lasso subproblems. Numerical experiments demonstrate that the proposed method is highly competitive, outperforming the classical Lasso in contaminated settings and maintaining strong performance even under Gaussian noise. Our method is implemented in the R package heavylasso available on Github: https://github.com/tienmt/heavylasso

Biological data sets are often high-dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g., motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accuracy, yet their black-box nature limits interpretability. We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for high-dimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large feature spaces. In extensive simulations, we can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology.

General Bayesian updating replaces the likelihood with a loss scaled by a learning rate, but posterior uncertainty can depend sharply on that scale. We propose a simple post-processing that aligns generalized posterior draws with their asymptotic target, yielding uncertainty quantification that is invariant to the learning rate. We prove total-variation convergence for generalized posteriors with an effective sample size, allowing sample-size-dependent priors, non-i.i.d. observations, and convex penalties under model misspecification. Within this framework, we justify and extend the open-faced sandwich adjustment (Shaby, 2014), provide general theoretical guarantees for its use within generalized Bayes, and extend it from covariance rescaling to a location–scale calibration whose draws converge in total variation to the target for any learning rate. In our empirical illustration, calibrated draws maintain stable coverage, interval width, and bias over orders of magnitude in the learning rate and closely track frequentist benchmarks, whereas uncalibrated posteriors vary markedly.

Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the famous upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB's regret bounds match those of the standard GP-UCB algorithm.

Most of researchers on testing a significance of coefficient $\ubeta$ in high-dimensional linear regression models consider the classical hypothesis testing problem $H_0^{c}: \ubeta=\uzero \mbox{ versus } H_1^{c}: \ubeta \neq \uzero$. We take a different perspective and study the testing problem with the null hypothesis of no relevant difference between $\ubeta$ and $\uzero$, that is, $H_0: \|\ubeta\|\leq \delta_0 \mbox{ versus } H_1: \|\ubeta\|> \delta_0$, where $\delta_0$ is a prespecified small constant. This testing problem is motivated by the urgent requirement to detect the transferability of source data in the transfer learning framework. We propose a novel test procedure incorporating the estimation of the largest eigenvalue of a high-dimensional covariance matrix with the assistance of the random matrix theory. In the more challenging setting in the presence of high-dimensional nuisance parameters, we establish the asymptotic normality for the proposed test statistics under both the null and alternative hypotheses. By applying the proposed test approaches to detect the transferability of source data, the unified transfer learning models simultaneously achieve lower estimation and prediction errors with comparison to existing methods. We study the finite-sample properties of the new test by means of simulation studies and illustrate its performance by analyzing the GTEx data.

High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and nested sampling, provide a strong classical baseline that matches or outperforms state-of-the-art neural samplers in sample quality and wall-clock time on standard scalar field theory benchmarks, while also estimating the partition function. Using only a single data-driven covariance for tuning, these methods achieve competitive performance without problem-specific structure, raising the bar for when learned proposals justify their training cost.

In randomized experiments, regression adjustment can improve the precision of average treatment effect (ATE) estimation using covariates without requiring a correctly specified outcome model. Although well studied in low-dimensional settings, its behavior in high-dimensional regimes, where the number of covariates $p$ may exceed the number of observations $n$, remains underexplored. Moreover, existing analyses are largely asymptotic, providing limited guidance for finite-sample inference. We develop a design-based, non-asymptotic framework for analyzing the regression-adjusted ATE estimator under complete randomization. This yields finite-sample-valid confidence intervals with explicit, instance-adaptive widths, even when $p > n$. While these intervals rely on oracle (population-level) quantities, we also outline data-driven envelopes computable from observed data. Our approach hinges on a refined swap sensitivity analysis of an estimator: stochastic fluctuation is controlled via a variance-adaptive Doob martingale and Freedman's inequality, and design bias is bounded by Stein's method of exchangeable pairs. The analysis elucidates how covariate geometry governs concentration and bias of the adjusted estimator, suggesting when and how regression adjustment can be effective.

State-space models (SSMs) provide a flexible framework for modelling time series data, but their reliance on Gaussian error assumptions makes them highly sensitive to outliers. We propose a robust estimation method, ROAMS, that mitigates the influence of additive outliers by introducing shift parameters at each timepoint in the observation equation of the SSM. These parameters allow the model to attribute non-zero shifts to outliers while leaving clean observations unaffected. ROAMS then enables automatic outlier detection, through the addition of a penalty term on the number of flagged outlying timepoints in the objective function, and simultaneous estimation of model parameters. We apply the method to robustly estimate SSMs on both simulated data and real-world animal location-tracking data, demonstrating its ability to produce more reliable parameter estimates than classical methods and other benchmark methods. In addition to improved robustness, ROAMS offers practical diagnostic tools, including BIC curves for selecting tuning parameters and visualising outlier structure. These features make our approach broadly useful for researchers and practitioners working with contaminated time series data.

Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. Yet ranking scores is straightforward only when they are scalar-valued, limiting CP to real-valued scores or ad-hoc one-dimensional reductions. Vector-valued scores arise naturally in multi-output regression and model aggregation, where each predictor in an ensemble provides its own score. Optimal transport (OT) defines vector ranks and center-outward multivariate quantile regions, though generally with asymptotic coverage guarantees. Applying a fixed transport map learned from calibration data to a new point introduces an uncontrolled approximation error. We restore finite-sample, distribution-free coverage by conformalizing vector-valued OT quantile regions. Each candidate's rank is defined by transporting the calibration scores augmented with that candidate's score, preserving the symmetry needed for validity. This appears to require a continuum of OT problems. However, we prove that the optimal assignment is piecewise constant across a fixed polyhedral partition of score space. This lets us characterize the entire prediction set in $O(n^3)$ time, matching the cost of a single assignment solve. It also addresses a limitation of prediction sets: they indicate which outcomes are plausible, but not their relative likelihood. In one dimension, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct, to our knowledge, the first multivariate CPDs with finite-sample calibration: a center-outward predictive distribution whose derived uncertainty regions have conformal coverage. We present both conservative and exact randomized versions; the latter generalizes the classical Dempster-Hill procedure.

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model $f(\boldsymbol{x})=g(\boldsymbol{U}\boldsymbol{x})$ with hidden subspace $\boldsymbol{U}\in \mathbb{R}^{r\times d}$, which is the canonical setup to study representation learning. We prove that under generic non-degenerate assumptions on the link function, a standard two-layer neural network trained via layer-wise gradient descent can agnostically learn the target with $o_d(1)$ test error using $\widetilde{\mathcal{O}}(d)$ samples and $\widetilde{\mathcal{O}}(d^2)$ time. The sample and time complexity both align with the information-theoretic limit up to leading order and are therefore optimal. During the first stage of gradient descent learning, the proof proceeds via showing that the inner weights can perform a power-iteration process. This process implicitly mimics a spectral start for the whole span of the hidden subspace and eventually eliminates finite-sample noise and recovers this span. It surprisingly indicates that optimal results can only be achieved if the first layer is trained for more than $\mathcal{O}(1)$ steps. This work demonstrates the ability of neural networks to effectively learn hierarchical functions with respect to both sample and time efficiency.

Understanding how vaccine effectiveness (VE) changes over time can provide evidence-based guidance for public health decision making. While commonly reported by practitioners, time-varying VE estimates obtained using Cox regression are vul- nerable to hidden biases. To address these limitations, we describe how to leverage vaccine-irrelevant infections to identify hazard-based, time-varying VE in the pres- ence of unmeasured confounding and selection bias. We articulate assumptions under which our approach identifies a causal effect of an intervention deferring vaccination and interaction with the community in which infections circulate. We develop sieve and efficient influence curve-based estimators and discuss imposing monotone shape constraints and estimating VE against multiple variants. As a case study, we examine the observational booster phase of the Coronavirus Vaccine Efficacy (COVE) trial of the Moderna mRNA-1273 COVID-19 vaccine which used symptom-triggered multi- plex PCR testing to identify acute respiratory illnesses (ARIs) caused by SARS-CoV-2 and 20 off-target pathogens previously identified as compelling negative controls for COVID-19. Accounting for vaccine-irrelevant ARIs supported that the mRNA-1273 booster was more effective and durable against Omicron COVID-19 than suggested by Cox regression. Our work offers an approach to mitigate bias in hazard-based, time- varying treatment effects in randomized and non-randomized studies using negative controls.

Urban decarbonization is central to meeting global climate goals, yet progress toward integrated low-carbon energy systems remains slow. The SolarEV City Concept, linking rooftop photovoltaics with electric vehicles as mobile storage offers a technically robust pathway for deep CO2 reduction, potentially meeting 60-95 percent of municipal electricity demand when deployed synergistically. Despite rapid global growth of PVs and EVs, integration through bidirectional Vehicle-to-Home and Vehicle-to-Grid systems has lagged, revealing a persistent SolarEV paradox. This review examines that paradox through a socio-technical framework across four dimensions, technology, economics, policy, and society. Cross-national comparison shows that while technical feasibility is well established, large-scale implementation is limited by fragmented charging-protocol standards, immature and often non-profitable V2G business models, regulatory misalignments between energy and transport sectors, and social-equity barriers that restrict participation mainly to high-income homeowners. Emerging national archetypes from Japans resilience-driven model to Europes regulation-first trajectory highlight strong path dependence in current integration strategies. The analysis concludes that advancing SolarEV Cities requires a shift from parallel PV-EV promotion toward coordinated policy frameworks, interoperable digital infrastructure, and inclusive market designs that distribute economic and resilience benefits more equitably. Achieving this integrated energy transition will require strategic collaboration among researchers, governments, industries, and communities to build adaptive, resilient, and socially just urban energy systems.

Individualized treatments are crucial for optimal decision making and treatment allocation, specifically in personalized medicine based on the estimation of an individual's dose-response curve across a continuum of treatment levels, e.g., drug dosage. Current works focus on conditional mean and median estimates, which are useful but do not provide the full picture. We propose viewing causal inference with a continuous treatment as a covariate shift. This allows us to leverage existing weighted conformal prediction methods with both quantile and point estimates to compute individualized uncertainty quantification for dose-response curves. Our method, individualized prediction bands (IPB), is demonstrated via simulations and a real data analysis, which demonstrates the additional medical expenditure caused by continued smoking for selected individuals. The results demonstrate that IPB provides an effective solution to a gap in individual dose-response uncertainty quantification literature.

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely unaddressed. This paper focuses on classification trees and makes two key contributions. First, we introduce a novel tree-fitting method that replaces the greedy splitting of the predictor space in standard tree algorithms with a probabilistic approach. Each split in our approach is selected according to sampling probabilities defined by an exponential mechanism, with a temperature parameter controlling its deviation from the deterministic choice given data. Second, while our approach can fit a tree that with high probability coincides with the fit produced by standard tree algorithms at low temperatures, it is not merely predictive; unlike standard algorithms, it enables inference by taking into account the highly adaptive tree structure. Our method produces pivots directly from the sampling probabilities in the exponential mechanism. In theory, our pivots allow asymptotically valid inference on the parameters in the predictive fit, and in practice, our method delivers powerful inference without sacrificing predictive accuracy, in contrast to data splitting methods.

Survival is a key metric for evaluating standards of care for people living with HIV. In resource-limited settings, high rates of loss to follow-up (LTFU) often result in underestimation of mortality when only observed deaths are considered. Resampling, which tracks a subset of LTFU patients to ascertain their outcomes, mitigates bias and improves survival estimates. However, common estimators for survival in resampling designs, such as weighted Kaplan-Meier (KM), fail to leverage covariate information collected during repeated clinic visits, even though this information is highly predictive of survival. We propose a Targeted Maximum Likelihood Estimator (TMLE) for survival in resampling designs, which addresses these limitations by leveraging baseline and longitudinal covariates to achieve greater efficiency. Our TMLE is a plug-in estimator and is robust to misspecification of the initial model for the conditional hazard of death, guaranteeing consistency of our estimator due to known resampling probabilities. We present: (1) a fully efficient TMLE for data from resampling studies with fixed follow-up time for all participants and (2) an inverse probability of censoring weighted (IPCW) TMLE that accounts for varied follow-up times by stratifying on patients with sufficient follow-up to evaluate survival. This IPCW-TMLE can be made highly efficient through nonparametric or targeted estimation of the follow-up censoring mechanism. In simulations, our TMLE reduced variance by up to 55% compared with the commonly used weighted KM estimator while preserving nominal confidence interval coverage. These findings demonstrate the potential of our TMLE to improve survival estimation in resampling designs, offering a robust and resource-efficient framework for HIV research. Keywords: Resampling designs, Survival analysis, Targeted Maximum Likelihood Estimation, Inverse probability weighting

Understanding the relationships between data points in the latent decision space derived by the deep learning system is critical to evaluating and interpreting the performance of the system on real world data. Detecting out-of-distribution (OOD) data for deep learning systems continues to be an active research topic. We investigate the connection between latent space OOD detection and classification accuracy of the model. Using open source simulated and measured Synthetic Aperture RADAR (SAR) datasets, we empirically demonstrate that the OOD detection cannot be used as a proxy measure for model performance. We hope to inspire additional research into the geometric properties of the latent space that may yield future insights into deep learning robustness and generalizability.

Accurate prediction of project duration and cost remains one of the most challenging aspects of project management, particularly in resource-constrained and interdependent task networks. Traditional analytical techniques such as the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) rely on simplified and often static assumptions regarding task interdependencies and resource performance. This study proposes a novel resource-based predictive framework that integrates network representations of project activities with graph neural networks (GNNs) to capture structural and contextual relationships among tasks, resources, and time-cost dynamics. The model represents the project as a heterogeneous activity-resource graph in which nodes denote activities and resources, and edges encode temporal and resource dependencies. We evaluate multiple learning paradigms, including GraphSAGE and Temporal Graph Networks, on both synthetic and benchmark project datasets. Experimental results show that the proposed GNN framework achieves an average 23 to 31 percent reduction in mean absolute error compared to traditional regression and tree-based methods, while improving the coefficient of determination R2 from approximately 0.78 to 0.91 for large and complex project networks. Furthermore, the learned embeddings provide interpretable insights into resource bottlenecks and critical dependencies, enabling more explainable and adaptive scheduling decisions.

Scientific progress is inherently sequential: collective knowledge is updated as new studies enter the literature. We propose the sequential meta-analysis research trace (SMART), which quantifies the influence of each study at the time it enters the literature. In contrast to classical meta-analysis, our method can capture how new studies may cast doubt on previously held beliefs, increasing collective uncertainty. For example, a new study may present a methodological critique of prior work and propose a superior method. Even small studies, which may not materially affect a retrospective meta-analysis, can be influential at the time they appeared. To contrast SMART with classical meta-analysis, we re-analyze two meta-analysis datasets, from psychology and labor economics. One assembles studies using a single methodology; the other contains studies that predate or follow an important methodological innovation. Our formalization of sequential learning highlights the importance of methodological innovation that might otherwise be overlooked by classical meta-analysis.

The area under the ROC curve (AUC) is the standard measure of a biomarker's discriminatory accuracy; however, AUC is rarely treated as a population-specific estimand. When validation cohorts differ from the intended target population in case mix, Naïve AUC estimates can mislead both generalization and cross-study comparison. We develop an estimand-focused framework that anchors biomarker AUC inference to a prespecified target population, aligning with the ICH E9(R1) estimand perspective adapted to discrimination rather than treatment effect. The framework supports two scientific goals: generalizing a study-specific AUC to a clinically relevant target population, and benchmarking AUCs across studies on a common population footing. Methodologically, we extend calibration weighting to the U-statistic formulation of AUC, allowing valid estimation even when the target population is characterized only by summary-level covariate information. This setting is common in biomarker validation, where individual-level target data are often unavailable and existing transportability methods may not be applicable. When patient-level real-world data are accessible, the proposed augmented variants provide double robustness and improved efficiency. We establish asymptotic properties and study their performances through comprehensive simulations. Furthermore, we demonstrate the proposed framework on the POWER trials, evaluating baseline stair-climb power (SCP) as a prognostic marker for 6-month survival in advanced non-small-cell lung cancer (NSCLC). Unlike prior work on transporting model-based predictive accuracy, our framework targets the biomarker-level estimand directly and addresses cross-study comparability - an issue not resolved by current methods.

Supervised learning with large-scale data usually leads to complex optimization problems, especially for classification tasks with multiple classes. Stochastic subgradient methods can enable efficient learning with a large number of samples for classification techniques that minimize the average loss over the training samples. However, recent techniques, such as minimax risk classifiers (MRCs), minimize the maximum expected loss and are not amenable to stochastic subgradient methods. In this paper, we present a learning algorithm based on the combination of constraint and column generation that enables efficient learning of MRCs with large-scale data for classification tasks with multiple classes. Experiments on multiple benchmark datasets show that the proposed algorithm provides upto a 10x speedup for general large-scale data and around a 100x speedup with a sizeable number of classes.

Clinical and gene-expression models predict breast cancer outcomes, but simple linear fusion ignores dependence between their risk scores. Using METABRIC, we tested whether modeling the joint distribution of clinical and gene-expression scores improved stratification of 5-year cancer-specific mortality. We defined clinical and mRNA-expression predictor views, trained classifiers, and obtained out-of-fold probabilities through 5-fold cross-validation. The scores were transformed into pseudo-observations on (0,1)^2 and used to fit Gaussian, Clayton, Gumbel, and Frank copulas. The clinical model discriminated better than the gene-expression model (AUC 0.783 vs 0.721). Frank had the smallest goodness-of-fit statistic, with Gaussian performing similarly. Copula fusion did not improve ROC-AUC over the clinical model. However, joint score groups showed clear survival differences, with patients scoring high on both views having the poorest outcomes. Competing-risks analysis showed the same pattern for cancer-death incidence. We also conducted an external evaluation in independent TCGA data using shared predictors and a harmonized 5-year overall-mortality endpoint. Copula-fused, individual, and simple-fusion scores showed comparable discrimination with overlapping confidence intervals. All received the same METABRIC-based recalibration. No gene met the prespecified stability criterion under repeated cross-validated permutation importance, so gene-level findings were treated as exploratory. Copulas provide an explicit, interpretable description of dependence between clinical and gene-expression risk scores and support descriptive joint-group analyses. This methodological study does not establish superior prediction, validated clinical risk categories, or clinical utility.

Automated scoring of written constructed responses typically relies on separate models per task, straining computational resources, storage, and maintenance in real-world education settings. We propose UniMoE-Guided, a knowledge-distilled multi-task Mixture-of-Experts (MoE) approach that transfers expertise from multiple task-specific large models (teachers) into a single compact, deployable model (student). The student combines (i) a shared encoder for cross-task representations, (ii) a gated MoE block that balances shared and task-specific processing, and (iii) lightweight task heads. Trained with both ground-truth labels and teacher guidance, the student matches strong task-specific models while being far more efficient to train, store, and deploy. Beyond efficiency, the MoE layer improves transfer and generalization: experts develop reusable skills that boost cross-task performance and enable rapid adaptation to new tasks with minimal additions and tuning. On nine NGSS-aligned science-reasoning tasks (seven for training/evaluation and two held out for adaptation), UniMoE-Guided attains performance comparable to per-task models while using $\sim$6$\times$ less storage than maintaining separate students, and $87\times$ less than the 20B-parameter teacher. The method offers a practical path toward scalable, reliable, and resource-efficient automated scoring for classroom and large-scale assessment systems.

In this work, we study the finite-population behaviour of the Reed-Frost epidemic model. Our analysis relies on the exact expression for the final epidemic size, replaced by Monte Carlo simulations in cases where the exact formula becomes numerically unstable. When the initial reproduction number is greater than a critical threshold, the distribution of the final size becomes bimodal. We therefore define the probabilities of small and large outbreaks, providing an intuitive answer to the question posed in the title through simple arguments based on the geometric distribution. Finally, an agent-based simulation confirms that the Reed-Frost model offers a good approximation in the case of the COVID-19 outbreak.

Estimating racial disparities in loan-approval probabilities when race is unobserved is routinely required for fair lending compliance. In such cases, race probabilities-typically from Bayesian Improved Surname Geocoding (BISG)-stand in for true race. Prior work shows that common heuristic approaches, including the Threshold and Weighting estimators, are inconsistent under valid identification assumptions, compromising internal validity. A recent Bayesian approach demonstrates consistency under assumptions reasonable in many fair lending contexts. This approach hinges on the insight that identification requires the race predictors to be exogenous with respect to loan approval, essentially an instrumental-variables design. We present a frequentist counterpart to this solution via Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) under a similar exogeneity assumption. To satisfy these assumptions in practice, we introduce (i) a surname-only proxy analogous to BISG and (ii) an income-stratified prior for race probabilities. Monte Carlo simulations and an application to 2023 Los Angeles HMDA data confirm superior performance: this method reduces RMSE in the LA Black/White adverse-impact ratio by 79.7% (from 10.639pp to 2.158pp) compared to a Weighting estimator with the standard prior.