Papers

Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley–Terry (BT) model, but its convergence can be slow in practice. To accelerate computation, Newman introduced a family of Zermelo-type fixed-point iterations parameterized by $\alpha$, with Zermelo's algorithm recovered at $\alpha=1$. Empirical evidence suggests that the choice $\alpha=0$ often converges substantially faster, making it a promising alternative, yet the mechanism underlying this acceleration remains elusive. This paper provides theoretical insight into this phenomenon through a systematic local convergence analysis. We derive closed-form expressions for local convergence factors under synchronous and asynchronous updates and analyze their dependence on $\alpha$ via spectral analysis of the associated Jacobian matrices. For synchronous updates, we show that the algorithm may fail to converge when $\alpha<1$, and its local convergence factor is quasi-convex in $\alpha$ under the population BT model. In contrast, asynchronous updates are always locally convergent, and their local convergence factor is provably monotonically increasing in $\alpha$ under the population BT model of consistently ordered bipartite comparison graphs, establishing the optimality of $\alpha=0$ in this setting. We further establish asymptotic approximation results for the population convergence factors under the BT model, justifying their practical relevance. Numerical experiments on synthetic and real-world datasets confirm the theory. Our analysis complements existing convergence results and shows that the acceleration of $\alpha=0$ arises not only from the parameter choice but, more importantly, from the use of asynchronous updates.

Score-based diffusion models have achieved remarkable empirical success in generative modeling, yet their approximation-theoretic foundations remain incomplete. In particular, although classical universal approximation theorems guarantee that neural networks can approximate score functions, it remains unclear whether such approximation guarantees translate into approximation of the probability distributions generated by reverse diffusion processes. In this paper, we establish a rigorous quantitative connection between these two notions. Specifically, we prove that if a neural network approximates the true score function sufficiently accurately, then the probability distribution generated by the corresponding reverse diffusion model is close to the target data distribution in Kullback-Leibler (KL) divergence, up to an irreducible mismatch between the terminal distribution of the forward diffusion process and the prior used to initialize the reverse process. More precisely, we derive an explicit upper bound on the distribution approximation error in terms of the score approximation error, the diffusion noise schedule, and the terminal prior mismatch. Our analysis combines Hornik's universal approximation theorem, Girsanov's theorem on path space, and the data processing inequality for relative entropy. Complementary to recent work that studies score approximation under finite-sample statistical settings and structural assumptions on the data distribution, our work develops an approximation-theoretic analysis based on classical neural network approximation theory. The resulting theorem provides a simple and explicit guarantee linking neural network approximation of score functions to approximation of the probability distributions generated by reverse diffusion models.

Regime-conditioned transition probabilities and moments are basic inputs for prediction and decision making in hybrid systems, but their short-time infinitesimal structure is not directly observable. We study nonparametric estimation of regime-indexed semigroup blocks for switching diffusions observed together with their regimes. A Dynkin–Taylor expansion identifies the first two block-generator coefficients, and localized probes recover switching intensities, drift, and diffusion. Under shrinking meshes, a common-design difference cancels the localized level and yields a martingale array; nonoverlapping second differences preserve within-block covariance and produce the variance factor two. The resulting first- and second-order estimators are asymptotically normal, admit feasible studentization, and support short-horizon approximation and specification checks for interactions among primitive coefficients. Fixed-mesh local-polynomial theory and a numerical study complement the recovery results.

We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and multiple-change scans and joint convergence over a finite set of regularization parameters. These results provide asymptotically exact calibration of a Cauchy-aggregated adaptive test through the joint Gaussian limit, together with guarantees for local power and single-change localization. We further embed the ERHT score in wild binary segmentation and prove consistency for estimating the number and locations of multiple changes. Simulations show that ERHT is generally well calibrated and delivers competitive power under heavy-tailed distributions, particularly when cross-sectional dependence is substantial. An analysis of the Fama–French 49 industry portfolios reveals persistent evidence of location instability and identifies four structural breaks.

Cities are beginning to enforce carbon limits on existing buildings. Science-based decarbonisation pathways set those limits one asset type and one jurisdiction at a time. Owners, however, report for the whole firm. We measure what that mismatch costs on two sets of public corporate reports: a census of 502 reports from the 119 listed built-environment firms with a collected report inside a 2,246-firm panel (2003-2023), and 519 real-estate reports from 101 firms (2007-2024). BeDA, a multimodal language-model tool whose reliability we test first, read them. Running the pathway frameworks' own entry tests over published disclosure: 16.5% of census reports (43.7% of real-estate reports) print an operational carbon intensity per square metre; 6.6% (25.0%) can be matched to a pathway for their property type in a covered jurisdiction; and only 5.0% (16.4%) disclose the floor area they divided by. Of the failures at the pathway test, 82-84% follow from reports lumping the portfolio together and 16-18% from a missing curve in the pathway library. The obstacle is the reporting unit, not missing data. The rate is roughly twice as high for European as for US listings (65-71% versus 35% in listed real estate). We also show that a US portfolio's carbon verdict cannot be worked out from disclosure at all. Within one climate zone, the pathway's carbon limit varies by up to 2.79-fold with the electricity subregion, which no report names; its energy limit does not move. Extraction is checked against the source PDFs (97.3% of extracted intensities appear verbatim) and repeats on a second extractor (kappa = 0.97). Recall of the non-disclosing class was 95.1% in a blinded hand audit of 122 reports. The fix follows from the measurement: split intensity by asset type and jurisdiction, and report floor area.

Model-based analyses of rainfall enhancement trial data typically involve modelling log-transformed rainfall using linear mixed models to assess the effectiveness of enhancement methods under real-world conditions. This approach improves on traditional average-based analyses by allowing explicit control for the effects of meteorological and topographical covariates that may affect precipitation amounts. However, a key issue with such analyses is the bias that arises when back-transforming the log-rainfall to the original scale for estimating attribution, defined as the additional raw-scale rainfall attributable to the enhancement method. To address this issue, we propose a new attribution estimator that incorporates theoretically justified, observation-specific bias-adjustment terms. The proposed estimator improves upon existing estimators that rely on arbitrary adjustments, and satisfies a coherence property that ensures zero estimated attribution for observations without enhancement intervention. A proportional random effect block bootstrap is further used to conduct inference on the attribution quantities. Applying both the proposed estimator and an existing estimator to the Oman rainfall enhancement trial from 2013 to 2018, we find statistically significant positive effect of the ground-based ionization technology on downwind rainfall at the 5% significance level, with our proposed estimator indicating a smaller effect than the existing method. A simulation study further support the findings based on the proposed estimator, demonstrating its superior estimation accuracy and improved inferential performance of the associated bootstrap confidence intervals.

The rapid advancement of large language models has introduced AI-generated fake news alongside traditional human-written misinformation, raising questions about whether detectability depends on the source of deceptive content. This study examines that issue through two controlled binary classification tasks: distinguishing real news from human-written fake news and from AI-generated fake news. Each article is represented using features related to lexical diversity, readability, and emotional characteristics, and evaluated with several machine learning models, including logistic regression, random forests, support vector machines, gradient boosting, neural networks, and ensemble methods. Performance is measured using the area under the receiver operating characteristic curve (AUC). Across all models, AI-generated fake news is detected with near-perfect accuracy, while human-written fake news is substantially more difficult to distinguish from real news. Because both tasks use the same modeling pipeline, this performance gap reflects intrinsic statistical differences in the text rather than methodological variation. Feature-level analysis shows that AI-generated fake news exhibits more uniform readability and emotional patterns, producing less overlap with real news. These findings reveal a key asymmetry in misinformation detection: current methods may be highly effective at identifying AI-generated content but remain less reliable against sophisticated human-authored misinformation. Detection systems should therefore account for the source of misinformation and continue adapting as generative models evolve.

As large language models (LLMs) are increasingly deployed, reliable and efficient mechanisms for distinguishing AI-generated text from human-written content have become essential. Statistical watermarking has emerged as a promising solution, yet most existing methods are typically fixed-horizon procedures, precluding valid early stopping in streaming generation. In this paper, we develop an efficient online watermark detection framework with anytime-valid inference based on Rao-Blackwellized e-processes, enabling recursive token-level evidence updates without storing the full history. In particular, we instantiate the framework for the Gumbel-max watermark and reduce the original token-level dependence testing problem to a pivot-induced sequential testing problem with an explicit null distribution. Theoretically, we prove anytime-valid Type I error control under arbitrary optional stopping and establish positive asymptotic log-growth under watermarking, implying consistency of the proposed stopping rules. Simulations and experiments on real LLM-generated text demonstrate efficient online detection with rigorous anytime-valid guarantees.

Systematic literature review of clinical trials drives regulatory decision-making, but conventional screening and extraction are time-consuming, labor-intensive, and vulnerable to study selection bias. We propose two fit-to-purpose multi-agentic systems (MAS) for systematic literature review, with human-in-the-loop. The screening MAS uses multiple LLM agents with heterogeneous personas and multiround cross-review, and uniformly improves accuracy over a single-LLM baseline. The extraction MAS combines standardization, an iterative correction loop, and retrieval-based context control to ensure accuracy and scalability. Both MAS are specifically designed to support Human-In-The-Loop which is essential for clinical decisions. The novelty of the proposed approach lies in the system architecture rather than in any single foundation tools: the system can naturally benefit from future improvements in the underlying tools, for instance, stronger LLM agents, retrieval engines, image recognition methods, etc. As a real-world application, a published network meta-analysis is reproduced by the MAS. The result recovers all trials from the original study and identifies additional eligible trials missed by manual review, leading to updated clinical conclusions.

Scientists increasingly express their ideas as dynamic models of complex processes. It is often much easier to simulate these models than to calculate the probability of their generating a particular outcome, making likelihood-based estimation infeasible. Existing likelihood-free approaches rely either on manually chosen summary statistics or on representations learned by neural networks. The former is error-prone and laborious, while the latter is computationally intensive, leaving many scientists in a difficult position. We show that, for a large class of dynamic models, parameters can be estimated by matching a small number of random features of the observed and simulated data. In particular, we show that models with a $p$-dimensional parameter can be identified from just $2p+1$ generic random Fourier features. We introduce two estimators for stationary and nonstationary processes, respectively, and we establish their consistency under mild regularity conditions. More broadly, our results serve as the foundation for a new class of methods for simulation-based inference.

Let $p(x)$ be the joint density of variables $X$, and let $\psi(x)=\nabla_x\log p(x)$ be its score field. Geometry constructed from $p$ and $\psi$ alone cannot identify causal direction: structural models with the same observational distribution have the same score geometry. I develop an interventional analogue. A hard intervention $\operatorname{do}(X_k=\xi)$ does not merely reweight the joint law; it restricts the distribution to the submanifold ${x_k=\xi}$. Its score should therefore be defined on the remaining $d-1$ free coordinates. I define causal influence $X_k\rightsquigarrow X_j$ as variation of the interventional marginal distribution of $X_j$ with $\xi$, and show that the corresponding derivative of the marginal interventional score gives a local sufficient condition for influence. Projecting the observational score onto admissible intervention directions does not generally recover causal response: two models may share the same observational score and admissible set yet respond differently. I therefore introduce an interventional response field supplied by structural information. A causal metric is defined as the Fisher information metric on a family of interventions with a common target, avoiding ill-posed comparisons across targets. The framework yields a geometric dictionary for randomized trials, instrumental variables, and conditional-independence designs, clarifying what each does and does not identify. A bivariate Gaussian example gives two models with the same observational score but different interventional score derivatives. The framework organizes relations among designs, interventions, and score fields, but adds no identification beyond the underlying assumptions. In Pearl's Ladder of Causation, observational score geometry belongs to association, intervention-indexed score fields to intervention, and unit-level counterfactual geometry is left for future work.

Independent component analysis (ICA) is widely used to recover latent structure from signal and imaging data, but standard ICA assumes that the observed measurement scale preserves a linear mixing structure. This assumption may fail for features produced through nonlinear preprocessing, such as band-specific power in motor-imagery EEG. We propose AdaptICA, an adaptive transformation-based framework that jointly learns grouped componentwise transformations and the demixing structure using a profiled mutual-information criterion. Because the transformation and demixing parameters may compensate for one another, their joint estimation introduces new identifiability and asymptotic challenges. We establish identifiability, consistency, and asymptotic normality of the transformation estimator, together with joint strong consistency of the transformation and demixing estimators. AdaptICA selects the transformation structure data-adaptively and includes the identity transformation as a candidate, thereby reducing to standard ICA when no scale adjustment is needed. Extensive simulations support the theoretical results. Applications demonstrate that AdaptICA can recover more independent and interpretable sources when transformation is beneficial while retaining standard ICA when the original measurement scale is adequate.

This work establishes a theoretical foundation for joint feature selection with multivariate outcomes, positioning the permutation-based variable importance measure (PVIM) of multivariate random forests (MRF) as a principled tool for high-dimensional feature selection. We establish the first consistency guaranty for MRF, showing that it retains all truly influential features with probability tending to one as the sample size grows to infinity under mild regularity conditions. Incomplete U-statistics is employed to incorporate three layers of randomness: subsampling of subjects for training each tree, subsampling of features at each split, and permutation of each feature for the out-of-bag (OOB) samples. Unlike independence-based screening that evaluates each feature in isolation, PVIM is a joint screening approach that accounts for multicollinearity, nonlinear, high-order interactions, and subject heterogeneity via ensemble aggregation. Moreover, we demonstrate the practical utility of MRF through a genome-wide association study (GWAS) of human facial morphology (with 2,342 subjects and 453,273 SNPs), where MRF identifies several novel loci and interaction hubs that extend prior findings. Extensive simulations show that MRF accurately identifies truly influential signals while producing parsimonious feature sets with well controlled false selection rates, outperforming canonical correlation analysis (CCA) and several other independence multivariate screening approaches. In addition, we also propose a novel simulation framework, including image outcomes, that more closely mimic the intricate nature of real-world data and provide rigorous testbeds for machine learning research.

Entry-only automatic fare collection systems record boardings but not alightings, preventing direct construction of origin-destination (OD) matrices. This study develops a Hierarchical Bayesian Latent-Destination (HBLD) model that combines station-hour boarding and inferred alighting demand with passenger card histories. Trip-chain destinations are treated as noisy evidence with a reliability parameter, allowing destination uncertainty to propagate into OD flows. The model was applied to 838,305 bus tap-ins collected in Changzhou in May 2025 and linked to stop-network and hourly weather data. It estimates destination distributions over feasible downstream and reverse-direction through-terminal stops using network, time-of-day, weather, and smoothed historical demand effects. A Bayesian personalization layer uses prior card trips and reverts to the shared trip-level distribution when history is unavailable. Fitted by stochastic variational inference and evaluated on the final week, HBLD outperformed the strongest baseline. Observed boarding patterns consistently improved prediction, especially without card history, while inferred alighting patterns helped only when trip-chain evidence was strongly trusted. The model captured travel consistent with through-terminal riding and bus-assisted road crossing and estimated destinations for trips unresolved by deterministic chaining. Because true alightings were unavailable, scores measure agreement with trip-chain outputs rather than actual destination accuracy. HBLD provides uncertainty-aware destination predictions and OD matrices for service management, planning, scheduling, and resource allocation.

Whole-slide survival models commonly provide risk rankings without calibrated statements about individual event times. We evaluate fixed-cutoff drcosarc, a post-hoc conformal wrapper for discrete-time multiple-instance learning survival heads using frozen UNI2-h representations, in an internal 18-configuration sweep across five TCGA cohorts and an external five-configuration evaluation across three CPTAC cohorts. We distinguish configuration–fold–split summaries of the inverse-probability-of-censoring-weighted (IPCW) estimate and median lower predictive bound (LPB) from a hierarchy-aware patient-ensemble estimand of the mean drcosarc–naive LPB difference. At $\alpha=0.1$, the drcosarc IPCW estimate was nearest 0.90 in KIRC, LUAD, and STAD. Patient-ensemble drcosarc–naive intervals excluded zero in KIRC, KIRP, STAD, UCEC, and CPTAC-CCRCC, but included zero in internal LUAD, CPTAC-LUAD, CPTAC-UCEC, and the internal LUSC extension. In a 20-replicate low-censoring semi-synthetic setting with known event times, drcosarc empirical coverage was 0.9129 [0.9053, 0.9207]. An exploratory analysis supported a head-error-by-censoring interaction within that data-generating process. In a two-cohort ABMIL sensitivity analysis, increasing the hazard grid to $K=16$ raised localized marginal IPCW estimates above the prespecified 0.87 threshold and yielded positive paired LPB differences, although worst-group estimates remained below 0.87. Overall, performance was cohort dependent, and its interpretation changed with the patient-level unit, estimand, and censoring assumptions.

Leaf veins exhibit remarkable diversity in architecture and patterning, yet existing gene–environment association studies have primarily quantified leaf venation using a small collection of low-dimensional summary traits, thereby discarding most of the structural information contained in the original images. We propose an integrated deep learning and statistical framework. The proposed framework achieves four methodological advances. First, it represents the complete leaf vascular architecture as a whole-network image phenotype. Second, it fine-tunes the deep learning-based Edge Detection with Transformers (EDTER) model to accurately extract whole-network leaf vascular architecture from RGB images by jointly learning local and global contextual features. Third, it constructs a new annotated leaf image database by integrating edge maps generated by DiffusionEdge with the Berkeley Segmentation Database (BSDS500). Fourth, it applies Semiparametric Sparse Canonical Correlation Analysis (SSCCA) to perform variable selection and model associations between repeatedly measured high-dimensional Bivariate image responses and high-dimensional predictors while simultaneously accommodating sparse, zero-inflated data represented by edge maps through a truncated latent Gaussian copula model. Two simulation studies demonstrate the performance of the proposed framework under increasing levels of complexity. Application to a real Populus dataset identifies three significant gene–geography interactions associated with leaf vascular architecture, providing new biological insights and establishing a broadly applicable methodological framework for high-dimensional complex image phenotypes.

Causal inference has become a central issue across various fields, including computer science, statistics, economics, education, healthcare, and medicine. The broad applicability of this discipline has garnered increased research funding and attention. In recent years, the estimation of causal effects from observational data has gained traction due to the vast amounts of collected data and the lower costs compared to randomized controlled trials. Advances in causal effect estimation methods have enhanced service personalization tools. For instance, these tools can help identify the most effective type of treatment (considering both cost and success rate) for each patient among different medical service options. This paper proposes an innovative method for estimating the heterogeneity of treatment effects. The structure of the proposed model is based on a deep neural network and a pseudo-single learner. The proposed method has been compared with other state-of-the-art methods on the IHDP benchmark. Acceptable results have been obtained by using one estimator to estimate the potential outcomes of two treatment groups. Accordingly, this paves the way for further development and improvement of the proposed method.

We present the R package exdqlm for Bayesian quantile regression, with primary emphasis on dynamic state-space quantile models for time series. The package is built around extended dynamic quantile linear models (exDQLMs), which use the extended asymmetric Laplace (exAL) family, a parametric extension of the asymmetric Laplace (AL) distribution commonly used in quantile regression. The software provides posterior simulation via Markov chain Monte Carlo (MCMC) and fast approximate posterior inference via Laplace-delta variational Bayes (LDVB), supporting posterior uncertainty quantification while also providing a computationally efficient option for longer time series. The same package interface supports static exAL quantile regression with regularized priors, dynamic transfer-function models for nonlinear input effects at a given quantile, post hoc posterior-predictive synthesis across separately fitted quantiles, forecasting, and quantitative and visual diagnostics for model evaluation.

Prior classical-ML learning-curve work fits power laws to tree, linear, and kernel models on tabular data, but at small scale: typically one curve, one team, a handful of cells. We present a distributed classroom-scale replication: 127 graduate students each ran a fixed protocol on 3 assigned datasets, drawn from 18 tabular classification and regression datasets and 6 model families (Boosting, Random Forest, SVM, Linear/Logistic, Ridge, Lasso), yielding 11,536 training runs and 1,648 fitted power-law curves of the form error(N) = a N^(-b) + c. Three findings. (1) Power laws fit: R^2 > 0.8 on 77.7% of cells, with tree ensembles dominating at full data (Boosting 50% of datasets, RandomForest 33%; linear models underperform on classification). (2) Approximate shared exponents within a model family: for 5 of 6 families, a single family-level exponent predicts each family's cross-dataset curves nearly as well as per-dataset exponents (R^2 gap < 0.011), though AIC favors the unconstrained fit and curve collapse is partial (32-58% of points within +/-0.5 dex). We frame this as approximate predictive compressibility, not dataset-independent universality; Lasso fails outright (negative control) and Ridge is fragile under leave-one-dataset-out. (3) Replicator-implementation variance: with random_state=42 fixed, independent re-implementations of the same protocol still differ by mean CV(b) = 0.144 on the fitted exponent – not seed variance, but the spread induced by unconstrained parts of the protocol (preprocessing, encoding, missing-value handling). We release the aggregated curves, per-cell fits, and a practical data-requirement table for N* to reach target error 0.15.

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.

Empirical Bayes (EB) performs simultaneous inference across many related latent variables. Classical EB assumes that the likelihood p(x | z) is tractable. In many scientific applications, however, the likelihood is available only through a simulator. This paper develops EB for such implicit likelihoods. We introduce simulation-based empirical Bayes (SBEB), which connects nonparametric EB to simulation-based inference (SBI). SBEB computes EB estimates without an explicit density by using the observed data, simulator samples, and an amortized inference network. SBEB iteratively refines the fitted EB prior toward the population prior. With several scientific simulators and real-world data, we demonstrate that SBEB improves accuracy over SBI with a fixed prior.

Learning high-fidelity point-cloud features in the 3D space poses significant challenges, including permutation invariance, lack of local context, difficulty in fine-grained surface reconstruction, and high computational cost. In this article, we propose Trans-Unet, a novel framework that addresses these issues by first tansforming 3D point-cloud data into a 2D grid domain and then employing a U-shaped hybrid model that integrates Convolutional Neural Networks, and self-attention mechanisms. The proposed Trans-Unet effectively learns and reconstructs precise features from high-resolution 3D point-cloud data (with 40,401 points in surface and 2,382 points in fiber) derived from a predefined finite element brain patch growth model, enabling accurate prediction of brain folding patterns. By combining multiple techniques, Trans-Unet leverages the complementary strengths: the 3D-to-2D transformation preserves fine-grained structural information while significantly reducing computational cost and the curse of dimensionality; convolutional blocks capture hierarchical, low-level local representations; and the self-attention mechanism models global, high-level semantics and long-range dependencies. The dataset consists of 3D point-clouds containing both brain surface patches and fiber information generated by a large-scale finite element model. Trans-Unet is applied to predict brain surface folding from the initial state (state 0 or states 0-2) to the final state (state 3). Experimental results demonstrate that Trans-Unet achieves high-resolution predictions of brain patch growth, surpassing existing methods in both fidelity and accuracy.

Learning a dynamical system and reconstructing the underlying regulatory network from $p$ discretely observed state trajectories remain challenging problems. Existing approaches often produced a large number of spurious edges and suffered from several methodological limitations. We propose a new approach, Reconstruction of Enhanced Causal Omnidirectional Network (RECON), that leverages an integral-based additive nonparametric ODE model to reconstruct regulatory networks from $p$ time-course data. RECON incorporates five methodological advances. First, it incorporates a new data-driven edge selection procedure that substantially reduces spurious edges while preserving true regulatory edges. Second, it reconstructs an omnidirectional network that captures causal regulatory relationships rather than merely statistical associations or noise artifacts. Third, it substantially broadens the applicability of standard ODE-based approaches by accommodating both dense regular and sparse irregular longitudinal sampling scenarios. Fourth, it models both node trajectories and edge regulatory effects as time-varying functions, emphasizing a dynamic regulatory network. Fifth, it reconstructs a signed and weighted regulatory network and provides comprehensive network interpretation through two-way direction, activatory/inhibitory indicator, and strength, together with keystone node identification and topological structure. Across five simulation studies, RECON consistently outperforms GRADE by removing nearly all spurious edges while retaining nearly all true regulatory edges, resulting in highly accurate network reconstruction. In the most challenging scenario, the number of spurious edges is reduced from 239 to 0.

Longitudinal studies often collect data at sparse, irregular, and unequally spaced time points. Such heterogeneity is often driven by subject-specific covariates, yet existing methods have been restricted to a scalar endpoint value, completely neglecting the underlying response trajectories. We propose a novel Longitudinal Random Forest (LRF) framework that leverages tree-based ensemble machine learning with adaptive node-wise longitudinal trajectory estimation. The LRF framework makes five methodological contributions. it captures each subject's individual response trajectory while simultaneously accommodating within-node correlation, between-node heterogeneity, and nonlinear and interactive covariate effects. It introduces a novel trajectory-based splitting criterion that maximizes trajectory separation while incorporating a size-weighted penalty; it provides two variants, Principal Analysis by Conditional Expectation (LRF-PACE) and adaptive linear mixed-effects models (LRF-adaptiveLMM), which employ nonparametric and semiparametric node-wise smoothers, respectively, while learning covariate effects in a data-driven manner. It provides a comprehensive interpretation of covariates using both the classical trajectory-based permutation variable importance measure (PVIM) and a newly proposed finite-way interaction frequency count, and it not only predicts entire trajectories for new subjects but also forecasts future trajectories for existing subjects. Extensive simulation studies demonstrate that LRF achieves superior performance over several competing methods, even under severe sparsity. The practical significance of the LRF framework lies in its ability to address five important clinical questions.

Classifying patients into different clusters based on genomic data can offer valuable insights into their projected disease-specific survival trajectories over time. Here we apply two supervised learning methods—Nearest Shrunken Centroids and LASSO— to the METABRIC Breast Cancer data {metabric} of 1980 patients and 754 genes to perform this task. The {pamr} R package implements the Nearest Shrunken Centroids classifier and the { glmnet} R package is used to fit an ungrouped multinomial model, a grouped multinomial model, and a One-Versus-Rest model. Splitting our data into discovery and validation sets, we evaluate all four models' classification performance and the survival implications of their class predictions using cross validation and Kaplan-Meier curves. We find that the One-Versus-Rest model produces the lowest misclassification error of 0.0572 and the lowest median log-rank test of 0.380 statistic measuring the similarity between its Kaplan-Meier curves and the discovery set's true Kaplan-Meier curves. We show that a multinomial classification task split into several LASSO binomial classifiers offers promising results for patient clustering.

In a discrete choice model, choice probabilities observed for a finite collection of choice sets may not identify a counterfactual choice probability under an unobserved choice set. We represent this counterfactual probability as a linear functional of a mixing distribution. Because the target is a functional of a distribution whose support is not restricted to a finite set, the parameter space is infinite-dimensional, while the data impose only finitely many moment restrictions. Therefore, observed choice probabilities need not point identify such a target. The identified set is defined as the set of target values compatible with observed choice probabilities. Rather than imposing conditions to ensure point identification, we characterize the identified set, and conduct inference on its lower and upper endpoints. We represent each endpoint as the value of a linear program over probability measures, and give conditions to obtain pathwise differentiability of the identification bounds. As a consequence, we are able to prove asymptotic normality of plug-in endpoint estimators. Finally, we provide an Expectation-Maximization-like algorithm for certifying membership of candidate values in the identified set and establish local convergence guarantees.

Assessing covariate balance is a core diagnostic step in causal inference, but commonly used summary measures can miss meaningful distributional differences they are not designed to detect. Distributional goodness-of-fit tests, including the Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Cramer-von Mises (CVM) tests, offer a more complete comparison but have previously been available only for unweighted data. We extend all three to accommodate case weights of any origin, using a shared label-permutation inference procedure that requires no assumption about how the weights were generated. In a four-scenario simulation study, all three weighted tests controlled Type I error close to nominal across sample sizes from 1,000 to 4,000 under substantial weight variability. Each test's known unweighted comparative advantage was preserved under weighting for two of three discrepancy types: KS was most powerful against a centrally located discrepancy, and AD was overwhelmingly most powerful against a tail-located discrepancy, while AD and CVM performed comparably against a diffuse discrepancy, both outperforming KS. These findings support AD as a reasonable general-purpose default for routine covariate balance assessment, while KS retains an advantage when a centrally concentrated imbalance is specifically suspected. The methods are implemented in the Stata commands kstest, adtest, and cvmtest.

We develop a Bayesian optimal sample allocation approach for stratified sampling in heteroscedastic populations. Existing optimal allocation theory typically assumes knowledge of certain design parameters (e.g., strata variances) that may be unknown, leading practitioners to substitute in survey-based estimates when planning samples, often without considering the effects of this substitution on sample efficiency. Bayesian decision theory for optimal experimental design avoids such substitutions and can be applied to sample allocation. Bayesian sample optimization methods were studied heavily from the mid-1960s through early 1980s, but have been overlooked since, in spite of modern computing advances that have facilitated a proliferation of Bayesian methods in other areas of statistics. A limitation of this early Bayesian sample design work is that it did not accommodate heteroscedastic error structures, which underlie commonly used ratio estimation models. Our paper, which optimizes the design under a univariate regression model with heteroscedastic errors, addresses this limitation of earlier work, while illustrating the Bayesian approach to design. We identify the optimal Bayesian allocation under our model, then compare performance of the proposed Bayesian sampling strategy with that of key design-based and model-assisted alternatives across several settings, finding that the proposed methods do as well or better than the alternatives under the scenarios considered. We apply our methods in analyzing revenues of public charities, using publicly available IRS Form 990 data.

Given an isotropic, exchangeable, and unconditional random vector $\mathbf X$, we consider the sample covariance matrix constructed from i.i.d. copies of several tensor models of $\mathbf X$, such as the tensor power $\mathbf{X}^{\otimes d}$. Under appropriate moment conditions on $\mathbf X$, we show that almost surely, the empirical spectral distribution converges weakly to the Marchenko-Pastur law. This extends previous results which required the coordinates of $\mathbf X$ to be independent. As we demonstrate, our extension applies to many new random vectors $\mathbf X$ of interest.

Sequential Multiple Assignment Randomized Trials (SMARTs) provide evidence for treatment sequences based on patient profiles, which is relevant in chronic disease settings. Sample size formulae implemented in calculators are the primary tool available to power SMARTs, though they require strong assumptions. We propose a simulation-based procedure omitting these assumptions, instead generating realistic synthetic SMART data by fitting models to real pilot data, to power SMARTs to compare treatment strategies. The proposed framework powers designs in two ways: by fixing the data generating mechanism and estimating effect size under different designs, or by fixing effect size and varying operational decisions within the SMART. Comparing our results to a calculator (SMARTsize), estimated sample sizes at varying power levels were similar at larger fixed effect sizes, whereas a discrepancy was apparent at smaller effect sizes due to differences between fixed and observed effect sizes in the simulated trials. The simulation-based procedure's ability to capture this effect size fluctuation is advantageous for smaller expected effect sizes, as it is essential to ensure adequate sample size to avoid a type II error. In providing flexible tools to power competing SMART designs, the full potential of SMARTs to build treatment sequences can be better realized.