Papers

Standard Adjacency Spectral Embedding (ASE) relies on a global low-rank assumption often incompatible with the sparse, transitive structure of real-world networks, causing local geometric features to be 'smeared'. To address this, we introduce Local Adjacency Spectral Embedding (LASE), which uncovers locally low-dimensional structure via weighted spectral decomposition. Under a latent position model with a kernel feature map, we treat the image of latent positions as a locally low-dimensional set in infinite-dimensional feature space. We establish finite-sample bounds quantifying the trade-off between the statistical cost of localisation and the reduced truncation error achieved by targeting a locally low-dimensional region of the embedding. Furthermore, we prove that sufficient localisation induces rapid spectral decay and the emergence of a distinct spectral gap, theoretically justifying low-dimensional local embeddings. Experiments on synthetic and real networks show that LASE improves local reconstruction and visualisation over global and subgraph baselines, and we introduce UMAP-LASE for assembling overlapping local embeddings into high-fidelity global visualisations.

In this work, a novel approach to Bayesian model calibration routines is developed which reinterprets the traditional definition of model discrepancy as defined by Kennedy and O'Hagan (KOH). The novelty lies in the integration of $\delta_\theta(x_i)$ GPs within the simulator, which is approximated as a GP surrogate model to ensure computational tractability. This approach assumes that the utilized simulator sufficiently predicts observed trends when calibrated with respect to the application domain, and that all model-form errors can be attributed to uncertainty in the input parameters. In contrast, the KOH method assumes discrepancy to be inherently decoupled from the simulator, acting as a 'catch-all' for various sources of model error. The new method is applied to Molecular Dynamics observations of the critical stress to drive dislocation dipoles, and equivalent predictions using a Discrete Dislocation Dynamics simulator whose coarse-grained physical interpretation of the underlying physical mechanisms requires calibration against MD observations. We present an overview of similar state-aware calibration routines; differentiate the provided approach through redefining the commonly used discrepancy Gaussian process and benchmark against KOH. A philosophical argument as to when application of the proposed method is appropriate is provided, and future directions for expanding upon this methodology are proposed.

We propose Distributionally Balanced Designs (DBD), a new class of probability sampling designs that target representativeness at the level of the full auxiliary distribution rather than selected moments. In disciplines such as ecology, forestry, and environmental sciences, where field data collection is expensive, maximizing the information extracted from a limited sample is critical. More precisely, DBD can be viewed as minimum discrepancy designs that minimize the expected discrepancy between the sample and population auxiliary distributions. The key idea is to construct samples whose empirical auxiliary distribution closely matches that of the population. We present a first implementation of DBD based on an optimized circular ordering of the population, combined with random selection of a contiguous block of units. The ordering is chosen to minimize the design-expected energy distance, a discrepancy measure that captures differences between distributions beyond low-order moments. This criterion promotes strong spatial spread, and yields low variance for Horvitz-Thompson estimators of totals of functions that vary smoothly with respect to auxiliaries. Simulation results show that approximate DBD achieves better distributional fit than state-of-the-art methods such as the local pivotal and local cube designs. Hence, DBD can improve the reliability of estimates from costly field data, making distributional balancing effective for constructing representative surveys in resource-constrained applications.

Reliable uncertainty quantification is paramount for forecasting multivariate time series and spatiotemporal data. While Transformer architectures excel at sequence modeling, current probabilistic approaches typically rely on restrictive parametric likelihoods or quantile-based objectives, thereby limiting their ability to capture complex joint distributions in correlated time series. To overcome these limitations, we propose Enformer and its spatiotemporal extension, GEnformer. These models synthesize the expressive power of Transformers with engression, a stochastic learning paradigm for modeling conditional distributions. By injecting stochastic noise and optimizing a strictly proper scoring objective, our frameworks directly learn conditional predictive distributions without imposing parametric assumptions. This design ensures the generation of coherent multivariate trajectories while maintaining the Transformer's efficacy in modeling long-range dependencies and cross-series interactions. The probabilistic capability of Enformer is achieved with an asymptotic overhead of only a constant factor over a deterministic Transformer with an identical configuration. We extensively evaluate our frameworks on prominent multivariate benchmarks for temporal dynamics and real-world epidemic datasets for spatiotemporal dynamics. Empirical results demonstrate that both frameworks yield calibrated probabilistic forecasts and consistently outperform state-of-the-art baselines.

Estimating Individual Treatment Effects (ITE) in multi-treatment scenarios faces two critical challenges: the Hyperparameter Selection Dilemma for balancing weights and the Curse of Dimensionality in computational scalability. This paper derives a novel multi-treatment generalization bound and proposes a theoretical estimator for the optimal balancing weight $\alpha$, eliminating expensive heuristic tuning. We investigate three balancing strategies: Pairwise, One-vs-All (OVA), and Treatment Aggregation. While OVA achieves superior precision in low-dimensional settings, our proposed Treatment Aggregation ensures both accuracy and O(1) scalability as the treatment space expands. Furthermore, we extend our framework to a generative architecture, Multi-Treatment CausalEGM, which preserves the Wasserstein geodesic structure of the treatment manifold. Experiments on semi-synthetic and image datasets demonstrate that our approach significantly outperforms traditional models in estimation accuracy and efficiency, particularly in large-scale intervention scenarios.

The estimation of marginal loan write-off probabilities is a non-trivial task when modelling the loss given default (LGD) risk parameter in credit risk. We explore two types of survival models in estimating the overall write-off probability over default spell time, where these probabilities form the term-structure of write-off risk in aggregate. These survival models include a discrete-time hazard (DtH) model and a conditional inference survival tree. Both models are compared to a cross-sectional logistic regression model for write-off risk. All of these (first-stage) models are then ensconced in a broader two-stage LGD-modelling approach, wherein a loss severity model is estimated in the second stage. In expanding the model suite, a novel dichotomisation step is introduced for collapsing the write-off probability into a 0/1-value, prior to LGD-calculation. A benchmark study is subsequently conducted amongst the resulting LGD-models. We find that the DtH-model outperforms other two-stage LGD-models admirably across most diagnostics. However, a single-stage LGD-model still had the best results, likely due to the peculiar `L-shaped' LGD-distribution in our data. Ultimately, we believe that our tutorial-style work can enhance LGD-modelling practices when estimating the expected credit loss under IFRS 9.

Randomized controlled trials (RCTs) are the gold standard for causal inference, yet practical constraints often limit the size of the concurrent control arm. Borrowing control data from previous trials offers a potential efficiency gain, but naive borrowing can induce bias when historical and current populations differ. Existing test-then-pool (TTP) procedures address this concern by testing for equality of control outcomes between historical and concurrent trials before borrowing; however, standard implementations may suffer from reduced power or inadequate control of the Type-I error rate. We develop a new TTP framework that fuses control arms while rigorously controlling the Type-I error rate of the final treatment effect test. Our method employs kernel two-sample testing via maximum mean discrepancy (MMD) to capture distributional differences, and equivalence testing to avoid introducing uncontrolled bias, providing a more flexible and informative criterion for pooling. To ensure valid inference, we introduce partial bootstrap and partial permutation procedures for approximating null distributions in the presence of heterogeneous controls. We further establish the overall validity and consistency. We provide empirical studies demonstrating that the proposed approach achieves higher power than standard TTP methods while maintaining nominal error control, highlighting its value as a principled tool for leveraging historical controls in modern clinical trials.

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the success of quaternions. The most useful feature of quaternions lies in their ability to model three-dimensional rotations which, in turn, have found various industrial applications such as in aeronautics and computergraphics. Recently, we have witnessed a renaissance of quaternions due to the rise of machine learning. To equip the reader to contribute to this emerging research area, this chapter lays down the foundation for: - augmented statistics for modelling quaternion-valued random processes, - widely linear models to exploit such advanced statistics, - quaternion calculus and algebra for algorithmic derivations, - mean square estimation for practical considerations. For ease of exposure, several examples are offered to facilitate the learning, understanding, and(hopefully) the adoption of this multidimensional domain.

Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness of the involved test statistics. Drawing upon the well-established theory of incremental information gain for well-posed sequential analyses, we develop an approach that does not rely on modeling assumptions that infringe upon the robustness of the resulting estimators while simultaneously testing a much wider range of hypotheses. Our methodology provides general submatrix-level asymptotic theory for the evaluation of joint covariance matrices of sequential test statistics. Moreover, this framework allows us to construct a novel approach to computing efficacy boundaries, the likes of which can be estimated with greater precision at later interim times. These constructions also accommodate accessible multiple imputation procedures, thereby allowing for our approach to be applied to incomplete datasets. Type I error and power are assessed through a series of comprehensive simulations mirroring the simulations of recent work to facilitate a proper comparison. We conclude by applying our methods to a dataset from a longitudinal study concerning the impact of race on the efficacy a treatment for hepatitis C.

As scaling laws push the training of frontier large language models (LLMs) toward ever-growing data requirements, training pipelines are approaching a regime where much of the publicly available online text may be consumed. At the same time, widespread LLM usage increases the volume of machine-generated content on the web; together, these trends raise the likelihood of generated text re-entering future training corpora, increasing the associated risk of performance degradation often called model collapse. In practice, model developers address this concern through data cleaning, watermarking, synthetic-data policies, or, in some cases, blissful ignorance. However, the problem of model collapse in generative models has not been examined from a learning-theoretic perspective: we study it through the theoretical lens of the language generation in the limit framework, introducing a replay adversary that augments the example stream with the generator's own past outputs. Our main contribution is a fine-grained learning-theoretic characterization of when replay fundamentally limits generation: while replay is benign for the strongest notion of uniform generation, it provably creates separations for the weaker notions of non-uniform generation and generation in the limit. Interestingly, our positive results mirror heuristics widely used in practice, such as data cleaning, watermarking, and output filtering, while our separations show when these ideas can fail.

This paper studies the optimality and complexity of Follow-the-Perturbed-Leader (FTPL) policy in $m$-set semi-bandit problems. FTPL has been studied extensively as a promising candidate of an efficient algorithm with favorable regret for adversarial combinatorial semi-bandits. Nevertheless, the optimality of FTPL has still been unknown unlike Follow-the-Regularized-Leader (FTRL) whose optimality has been proved for various tasks of online learning. In this paper, we extend the analysis of FTPL with geometric resampling (GR) to $m$-set semi-bandits, which is a special case of combinatorial semi-bandits, showing that FTPL with Fréchet and Pareto distributions with certain parameters achieves the best possible regret of $O(\sqrt{mdT})$ in adversarial setting. We also show that FTPL with Fréchet and Pareto distributions with a certain parameter achieves a logarithmic regret for stochastic setting, meaning the Best-of-Both-Worlds optimality of FTPL for $m$-set semi-bandit problems. Furthermore, we extend the conditional geometric resampling to $m$-set semi-bandits for efficient loss estimation in FTPL, reducing the computational complexity from $O(d^2)$ of the original geometric resampling to $O(md(\log(d/m)+1))$ without sacrificing the regret performance.

Classical influence maximization optimizes expected reach, which can be misaligned with welfare when exposures have heterogeneous, saturating, or adverse effects. We study seed selection for steady-state causal welfare under network interference. Under our exposure-separable outcome model and weak independent live-edge propagation, a deterministic surrogate built from expected activations and exposure counts approximates welfare with uniform $O(\varepsilon^2)$ error for a fixed graph and seed budget, where $\varepsilon$ bounds edge activation probabilities. Building on this reduction, our two-stage method, CIM, learns shape-constrained exposure-response functions from logged diffusion-outcome data and estimates expected activations and exposures by Monte Carlo simulation. For unregularized fits on a design that covers the evaluated exposures, and under noise and simulation conditions, we bound the welfare-estimation error uniformly over seed sets, separating structural, statistical, and simulation errors; with an approximation guarantee for the optimizer, the bound transfers to the selected seeds. Experiments on real network topologies with simulated outcomes and a synthetic benchmark show that CIM attains the highest mean welfare among the compared methods.

Personalized AI-based services involve a population of individual reinforcement learning agents. However, most reinforcement learning algorithms focus on harnessing individual learning and fail to leverage the social learning capabilities commonly exhibited by humans and animals. Social learning integrates individual experience with observing others' behavior, presenting opportunities for improved learning outcomes. In this study, we focus on a social bandit learning scenario where a social agent observes other agents' actions without knowledge of their rewards. The agents independently pursue their own policy without explicit motivation to teach each other. We propose a free energy-based social bandit learning algorithm over the policy space, where the social agent evaluates others' expertise levels without resorting to any oracle or social norms. Accordingly, the social agent integrates its direct experiences in the environment and others' estimated policies. The theoretical convergence of our algorithm to the optimal policy is proven. Empirical evaluations validate the superiority of our social learning method over alternative approaches in various scenarios. Our algorithm strategically identifies the relevant agents, even in the presence of random or suboptimal agents, and skillfully exploits their behavioral information. In addition to societies including expert agents, in the presence of relevant but non-expert agents, our algorithm significantly enhances individual learning performance, where most related methods fail. Importantly, it also maintains logarithmic regret.

In pre- and non-clinical toxicology, the reduction of animal use is highly desireable. Although approaches for possible sample size reduction in the concurrent control group were suggested previously under the virtual control groups framework for continuous endpoints, methodology that is applicable to binary outcomes that occur in long-term carcinogenicity studies is currently missing. In order to augment animals in the current control group with historical control data, we propose approaches that rely on dynamic Bayesian borrowing and simultaneous credible intervals for risk ratios. Several operation characteristics such as familywise error rate (FWER) and power are assessed via Monte-Carlo simulations and compared to the ones of approaches that rely on pooling of historical and current observations. It turned out that under optimal conditions, Bayesian approaches based on robustified prior distributions enable a substantial reduction of the control groups sample size, while still controlling the FWER up to a satisfactory level. Furthermore, at least to some extend, these approaches were able to protect against possible drift. This hightlights the potential of Bayesian study designs to reduce animal use in toxicology through re-use of the large pool of existing control data.

We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed model representation of penalized splines, the level of smoothness can be estimated jointly with other variance components. The integration over random effects needed to obtain the marginal likelihood is carried out using the Laplace approximation. Exact derivatives for evaluation and maximization of the resulting likelihood are obtained via automatic differentiation implemented through Template Model Builder. In simulation studies, the method produces improved inferential performance and reduced computational burden when compared to the existing procedures. The approach is further illustrated through a case study on infant height growth in the first two years of life.

Bipartite networks, which encode interactions between two distinct types of entities, arise widely in applications and exhibit inherent asymmetry across node sets. Despite a growing literature on bipartite community detection, estimating community numbers $(K_1, K_2)$, a critical issue for bipartite network analysis, remains theoretically underdeveloped without any model selection consistency established, to our knowledge. Indeed, the inherent asymmetry and the two-dimensional parameter space with possibly drastically different $K_1$ and $K_2$ pose unique challenges that differ from unipartite cases. In particular, the candidate models may simultaneously overfit one node set while underfitting the other. To address these challenges, we propose Bipartite Cross-Validation (BCV), a penalized cross-validation framework that jointly selects $(K_1,K_2)$ in a fully data-driven manner. We establish the first model selection consistency for bipartite networks, notably accommodating the regime where the numbers of communities scale with the network size, revealing the intricate interplay between sparsity and model complexity. Simulations and real-data applications demonstrate strong finite-sample performance of BCV.

Balanced repeated replication (BRR) and the jackknife are two widely used methods for estimating variances in stratified samples with two primary sampling units per stratum. While both methods produce variance estimators that can be expressed as sums of squared stratum-level contrasts, they differ fundamentally in their construction and in the dependence structure of their replicate estimates. This article examines the independence properties of the components contributing to these variance estimators. For BRR, we show that although the replicate estimates themselves are correlated, the balancing property of Hadamard matrices collapses the variance estimator into a sum of independent stratum-specific components. For the jackknife, the independence of components follows directly from the construction. Using these independence results, we derive the variance of each variance estimator and establish a direct connection to the Welch-Satterthwaite degrees of freedom approximation. This yields a practical formula for estimating degrees of freedom when constructing confidence intervals for population totals. The derivation highlights the unified treatment of both replication methods and provides insights into their relative efficiency and applicability.

Many machine learning tasks admit multiple models that perform almost equally well, a phenomenon known as predictive multiplicity. A fundamental source of this multiplicity is observational multiplicity, which arises from the stochastic nature of label collection: observed training labels represent only a single realization of the underlying ground-truth probabilities. While theoretical frameworks for observational multiplicity have been established for logistic regression, their implications for non-smooth, partition-based models like decision trees remain underexplored. In this paper, we introduce two complementary notions of observational multiplicity for decision tree classifiers: leaf regret and structural regret. Leaf regret quantifies the intrinsic variability of predictions within a fixed leaf due to finite-sample noise, while structural regret captures variability induced by the instability of the learned tree structure itself. We provide a formal decomposition of observational multiplicity into these two components and establish statistical guarantees. Our experimental evaluation across diverse credit risk scoring datasets confirms the near-perfect alignment between our theoretical decomposition and the empirically observed variance. Notably, we find that structural regret is the primary driver of observational multiplicity, accounting for over 15 times the variability of leaf regret in some datasets. Furthermore, we demonstrate that utilizing these regret measures as an abstention mechanism in selective prediction can effectively identify arbitrary regions and improve model safety, elevating recall from 92% to 100% on the most stable sub-populations. These results establish a rigorous framework for quantifying observational multiplicity, aligning with recent advances in algorithmic safety and interpretability.

The Teissier distribution, originally proposed by Teissier [31], was designed to model mortality due to aging in domestic animals. More recently, Krishna et al. [19] introduced the Unit Teissier (UT) distribution on the interval (0, 1) through the transformation $X=e^{-Y}$, where $Y$ follows the Teissier distribution. In their work, the authors derived several fundamental properties of the UT distribution and investigated parameter estimation using maximum likelihood, least squares, weighted least squares and Bayesian methods. Building upon this work, the present paper develops additional theoretical and inferential results for the UT distribution. In particular, closed-form expressions for single moments of order statistics and L-moments are obtained, and characterization results based on truncated moments are established. Furthermore, several alternative parameter estimation methods are considered, including maximum product of spacings, Cramér-von Mises, Anderson-Darling, right-tail Anderson-Darling, percentile and L-moment estimation, while the estimation methods previously studied by Krishna et al. [19] are also included for comparison. Extensive simulation studies under various parameter settings and sample sizes are conducted to assess and compare the performance of the estimators. Finally, the flexibility and practical utility of the UT distribution are demonstrated using a real dataset.

Individual claims reserving has not yet become established in actuarial practice. We attribute this to the absence of a satisfactory methodology: existing approaches tend to be either overly complex or insufficiently flexible and robust for practical use. Building on the classical chain-ladder (CL) method, we introduced a new perspective on individual claims reserving in Richman and Wüthrich [arXiv:2602.15385]. This manuscript has sparked considerable discussion within the actuarial community. The aim of the present paper is to continue and deepen that discussion, with the ultimate goal of advancing toward a new standard for micro-level reserving.

We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic order constraints and formulate the estimation task as a mixed-integer convex quadratic optimization problem. Experiments on both synthetic and real datasets show that the proposed method reduces the Jensen-Shannon divergence by 2.2% on average (up to 6.3%) when the sample size is small, while performing comparably to existing methods when sufficient data are available.

In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate analyses. But outliers pose a new challenge to the existing likelihood-based modeling approaches. In this paper, we propose a new robust joint modeling framework for data with both continuous and binary responses. It is based on the density power divergence (DPD) loss function with the $\ell_1$ regularization. The proposed framework leads to a sparse estimator that simultaneously predicts continuous and binary responses in high-dimensional input settings while down-weighting influential outliers and mislabeled samples. We also develop an efficient proximal gradient algorithm with Barzilai-Borwein spectral step size and a robust information criterion (RIC) for data-driven selection of the penalty parameters. Extensive simulation studies under a variety of contamination schemes demonstrate that the proposed method achieves lower prediction error and more accurate parameter estimation than several competing approaches. A real case study on wafer lapping in semiconductor manufacturing further illustrates the practical gains in predictive accuracy, robustness, and interpretability of the proposed framework.

This paper develops a framework for variance estimation under dependence and heterogeneous means. This paper shows that consistent estimation of the variance target is impossible in general, and characterizes necessary and sufficient conditions for conservative variance estimation using dual cones. To choose among the valid estimators, this paper formulates three criteria – minimal correction, pointwise level estimand, and pointwise MSE – and shows how an eigenvalue truncation solution is optimal under all three criteria. This characterization and solution allow us to assess if existing variance estimators are valid and optimal in their respective settings, and construct the first optimal variance estimator that is simultaneously robust to heterogeneous means and cross-cluster serial correlation.

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient interval condition that characterizes the admissible number of connections at each step, thereby guaranteeing global feasibility. Based on this result, we develop bipartite graph enumeration and sampling algorithms suitable for different problem sizes. We then extend these bipartite graph algorithms to the directed and undirected cases by incorporating additional connection constraints, as well as feasibility verification and symmetric connection steps, while preserving the same algorithmic principles. Finally, numerical experiments demonstrate the performance of the proposed algorithms, particularly their scalability to large instances where existing methods become computationally prohibitive.

This paper proposes dynamic Bayesian regression quantile synthesis (DRQS), a novel method for quantile forecasting within the Bayesian predictive synthesis (BPS) framework designed to combine quantile-specific information from multiple agent models. While existing BPS approaches primarily focus on mean forecasting, our method directly targets the conditional quantiles of the response variable by utilizing the asymmetric Laplace distribution for the synthesis function. The resulting framework can be interpreted as a dynamic quantile linear model with latent predictors. We extend the univariate DRQS to a multivariate setting-factor DRQS (FDRQS)-by introducing a time-varying latent factor structure for the synthesis weights. This allows the model to leverage cross-sectional dependencies and shared information across multiple time series simultaneously. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior inference, utilizing data augmentation and forward-filtering backward-sampling. Empirical applications to US inflation and global GDP growth demonstrate the improved performance of the proposed methods for quantile forecasting. In particular, FDRQS exhibits superior resilience during periods of extreme economic stress, such as the COVID-19 pandemic, by adaptively rebalancing agent contributions and capturing emergent global dependencies.

Transfer learning is beneficial for survival analysis, especially when the target study has a limited number of events. However, existing transfer learning methods rely on the restrictive assumption that the target and source studies share similar parameters under Cox models, and most require access to individual-level source data. In this article, we propose a novel transfer learning framework that enhances model-based survival prediction by transferring predictive rather than distributional knowledge from source studies. Our approach employs flexible semiparametric transformation models for the target data while eliminating the need to model or share the source data. The ingeniously designed penalty enables simple and stable computation via an EM algorithm. We rigorously establish the asymptotic properties of the proposed estimator and show that it achieves a faster convergence rate than the target-only estimator when source knowledge is sufficiently accurate. We demonstrate the advantages of our methods through extensive simulation studies and an application to two major breast cancer studies, with the objective of improving survival prediction in a target cohort using predictive information from an external study.

Copula models of multivariate data are popular because they allow separate specification of marginal distributions and the copula function. These components can be treated as inter-related modules in a modified Bayesian inference approach called ”cutting feedback” that is robust to their misspecification. Recent work uses a two module approach, where all $d$ marginals form a single module, to robustify inference for the marginals against copula function misspecification, or vice versa. However, marginals can exhibit differing levels of misspecification, making it attractive to assign each its own module with an individual influence parameter controlling its contribution to a joint semi-modular inference (SMI) posterior. This generalizes existing two module SMI methods, which interpolate between cut and conventional posteriors using a single influence parameter. We develop a novel copula SMI method and select the influence parameters using Bayesian optimization. It provides an efficient continuous relaxation of the discrete optimization problem over $2^d$ cut/uncut configurations. We establish theoretical properties of the resulting semi-modular posterior and demonstrate the approach on simulated and real data. The real data application uses a skew-normal copula model of asymmetric dependence between equity volatility and bond yields, where robustifying copula estimation against marginal misspecification is strongly motivated.

Student experiences and empirical studies report that "black box" AI text detectors produce high false positive rates with disproportionate errors against certain student populations, yet typically theoretical analyses model detection as a test between two known distributions for human and AI prose. This framing omits the structural feature of university assessment whereby an assessor generally does not know the individual student's writing distribution, making the null hypothesis composite. Standard application of the variational characterisation of total variation distance to this composite null shows trade-off bounds that any text-only, one-shot detector with useful power must produce false accusations at a rate governed by the distributional overlap between student writing and AI output. This is a constraint arising from population diversity that is logically independent of AI model quality and cannot be overcome by better detector engineering or technology. A subgroup mixture bound connects these quantities to observable demographic groups, providing a theoretical basis for the disparate impact patterns documented empirically. We propose suggestions to improve policy and practice, and argue that detection scores should not serve as sole evidence in misconduct proceedings.

Modern mobile health (mHealth) assessment combines self-reported measures of participants' health experiences with passively collected health behavior data throughout the day. These data are collected across multiple measurement scales, including continuous (physical activity), truncated (pain), ordinal (mood), and binary (daily life events). When indexed by time of day and stacked across assessment domains, these data structures can be treated as multivariate functional data comprising continuous, truncated, ordinal, and binary variables. Motivated by these applications, we propose a multivariate functional principal component analysis for mixed-type data ($M^2$FPCA). The approach is based on a semiparametric Gaussian copula model and assumes that the observed data arise from an underlying multivariate generalized latent nonparanormal functional process. Latent temporal and inter-variable dependence are estimated semiparametrically through Kendall's tau bridging method. Two covariance estimation procedures are developed: a fully multivariate block-wise estimator and a computationally efficient alternative based on partial separability that assumes shared principal components across domains. The proposed method yields interpretable latent functional principal component scores that can serve as participant-specific digital biomarkers. Simulation studies demonstrate the method's competitive performance under various complex dependence structures. The method is applied to mHealth data from 307 participants in the National Institute of Mental Health Family Study of Mood and Affective Spectrum Disorders. Our approach identifies time-of-day patterns shared across mood, anxiety, energy, and physical activity that meaningfully stratify mood disorder subtypes.

When outcome data are expensive or onerous to collect, scientists increasingly substitute predictions from machine learning and AI models for unlabeled cases, a process which has consequences for downstream statistical inference. While recent methods provide valid uncertainty quantification under independent sampling, real-world applications involve missing at random (MAR) labeling and spatial dependence. For inference in this setting, we propose a doubly robust estimator with cross-fit nuisances. We show that cross-fitting induces fold-level correlation that distorts spatial variance estimators, producing unstable or overly conservative confidence intervals. To address this, we propose a jackknife spatial heteroscedasticity and autocorrelation consistent (HAC) variance correction that separates spatial dependence from fold-induced noise. Under standard identification and dependence conditions, the resulting intervals are asymptotically valid. Simulations and benchmark datasets show substantial improvement in finite-sample calibration, particularly under MAR labeling and clustered sampling.