Papers

Signed networks consist of both positive and negative relations, and structural balance theory provides an important conceptural framework for understanding their global tension structure. While existing statistical methods mainly focus on assessing empirical evidence of balance in a single observed network, many real-world signed relations evolve over time. This paper develops nonparametric inference for the population degree of structural balance at specified time points in dynamic signed networks, where the target time may or may not coincide with an observed snapshot. We consider a dynamic signed graphon model in which both edge formation and sign generation are governed by smoothly time-varying graphon functions. To exploit temporal smoothness, we construct a kernel-smoothed estimator that borrows information from snapshots near the target time point. Our theoretical analysis establishes a studentized inference procedure and a higher-order distributional approximation based on Edgeworth expansion, showing that temporal smoothing improves inference in sparse networks by reducing variance of observation noise, up to smoothing bias and time-discretization errors. We demonstrate the finite-sample performance and practical usefulness of the proposed method through extensive simulation studies and an application to a dynamic international relation network in political science.

The prediction-powered inference (PPI) proposed by Angelopoulos et al. (2023) is a popular method that leverages a small number of labeled samples and machine learning predictions for semi-supervised inference. While several variants of PPI have appeared in the literature, its rigorous statistical theory has not been fully developed. In this paper, we study the statistical optimality of PPI. Our contributions span both foundational theory and new methodology. First, we frame PPI as an M-estimation problem, revealing a link between the bias-corrected PPI estimating equation and the ideal full-data estimating equation. This connection leads to the consistency and asymptotic normality of the PPI estimator under simple random sampling without replacement. Next, we identify the efficient influence function and prove that PPI can attain the semiparametric efficiency lower bound when the predictor is score-calibrated, that is, when the predictor's output aligns with the true conditional expectation of the estimating function. Finally, for learned prediction rules, we develop asymptotic theory for cross-fitting and for a single-fit variant with variance correction in the special case of semiparametric mean estimation. Simulation experiments and a real-data application support these findings.

Heterogeneous susceptibility models for epidemic dynamics preferentially assume that individual susceptibility follows a gamma distribution, which permits analytical reduction to a low-dimensional system. However, the true empirical distributional form in any given population is unknown. Here we investigate the consequences of misspecifying the susceptibility distribution by comparing gamma and lognormal specifications in a Susceptible-Exposed-Infectious-Removed (SEIR) framework. When both distributions are matched on mean and coefficient of variation ($\nu$), we find that their epidemic trajectories diverge once heterogeneity is moderate or high ($\nu \gtrsim 1$), with the lognormal producing a later, larger peak and a greater final size. We then assess the impact of distributional misspecification on statistical inference. Using synthetic datasets, we fit correctly specified and misspecified models by maximum likelihood. In a default scenario, where inference is based on simulated data for a single epidemic, both models can reproduce the data by compensating through correlated shifts in heterogeneity and intervention parameters. When inference is based on two simulated epidemics, however, this compensation may be reduced by known constraints of how parameters are related across epidemics. In these cases, the correctly specified model recovers all parameters accurately, while the misspecified model tends to give biased estimates. These inference biases propagate into forecasts, but predictions remain relatively accurate when compared to homogeneous models which more than double peak incidences in scenarios where $\nu \approx 1$, for instance. We conclude that deviations resulting from the susceptibility distribution misspecifications assessed here are minor and encourage the adoption of heterogeneous models in future epidemic forecasting.

Bühlmann–Straub (B-S) credibility assigns each account a weight $Z_i = E_i/(E_i+K)$, where $K$ is a single portfolio-wide ratio. The formula assumes $K$ is the same for every account regardless of size, history length, or volatility, and that recent and older years carry equal weight. On a held-out US commercial auto dataset these assumptions fail: standard B-S applied to 96 companies produces a calibration slope of 29 for small accounts, a signature of severe under-crediting. We propose a joint framework that retains B-S interpretability while addressing these limitations. The credibility weight $Z_i$ is modelled as a logistic function of account characteristics; historical experience is discounted by an EWMA decay parameter $\lambda$ estimated from the data; and $Z$, $\lambda$, and the complement are optimised in a single likelihood pass. The framework formally nests Bühlmann–Straub as a special case, admitting a likelihood-ratio test for any proposed extension. On a two-year held-out test set the proposed model restores calibration (slope = 1.00) and reduces exposure-weighted prediction error by 38% (90% bootstrap interval: 26%–50%). A size gradient in the decay rate emerges ($\hat\lambda \approx 0.6$, $0.84$, $0.13$ for Small, Mid, Large) and replicates qualitatively on Other Liability. A simulation study confirms the mechanisms. The model requires only account-year summaries and delivers three transparent outputs: credibility weight, complement, and recommended renewal rate.

Modern data-driven applications increasingly involve learning from multiple heterogeneous sources, where a target dataset is limited but related information is available across domains. Naively combining these sources can degrade performance when relevance varies or spurious signals are present, posing a fundamental challenge for trustworthy cross-domain learning. We propose Projection Transfer Learning (ProjectionTL), a unified framework that integrates hierarchical Bayesian modeling with adaptive projection for selective knowledge transfer. The key idea is to decouple transfer at two levels: first, we construct a source-guided hierarchical prior that aggregates information across sources using data-driven weights, capturing global alignment between each source and the target; second, we refine this borrowing through a posterior-projection step that operates at the feature level, selectively retaining coordinates that exhibit local agreement with the target signal. This two-stage design enables the method to simultaneously perform source selection and feature selection, thereby mitigating negative transfer while preserving interpretability. ProjectionTL provides a principled approach to integrating heterogeneous data across domains, bridging statistical modeling and modern machine learning paradigms for robust and interpretable transfer. Through simulations and real-world biomedical applications, we demonstrate improved accuracy, stability, and interpretability compared to existing methods. Our framework offers a scalable and generalizable strategy for trustworthy cross-domain learning in high-dimensional settings.

Pretrained models are often evaluated on multi-task leaderboards to measure their applicability in diverse contexts. However, current methods for aggregating performance across tasks into leaderboard-level rankings do not address the uncertainty and variability at the task level. While recent works have proposed interval-based model rankings, the principled aggregation of uncertainty from individual tasks to leaderboard-level rankings remains unaddressed, and variation in models' performance across tasks is frequently obscured. In this work, we introduce a hierarchical framework that constructs model rank intervals with statistical guarantees at both levels: task-level rank confidence intervals from pairwise comparisons, and leaderboard-level rank prediction intervals using a conformal approach. This enables reliable quantification of model rank for each observed task and for new potential tasks. Experiments on simulated data and the TabArena and PromptEval (MMLU) benchmarks show that our method yields statistically valid and informative intervals, enabling reliable, uncertainty-aware model ranking on leaderboards.

Optimal subsampling efficiently selects the most informative data points, enabling accurate statistical inference while significantly reducing computational burden for massive datasets. However, the existing relevant methods can not directly be applied to pairwise loss problems, particularly for convoluted rank regression (CRR), due to the double summation structure in objective function. To this end, we first propose a new BIweighted Poisson Subsampling (BIPS) framework for such problems through designing a proper weight for a pair of observations instead of for a single observation for objective function. Two concrete inverse probability weighting strategies are considered. Secondly, we focus on the CRR models, under which the BIPS estimator (BIPS-CRR) is formulated. We establish consistency and asymptotic normality for BIPS-CRR, derive its optimal Poisson subsampling probabilities under the L-optimality criterion, and provide a practical algorithm to facilitate implementation. Thirdly, we develop a distributed estimator for CRR that incorporates BIPS as a pilot subsampling strategy. This estimation is globally efficient and is robust to both randomly and non-randomly distributed datasets in distributed computing environments. Extensive simulations and a real-world application demonstrate the excellent finite-sample performance of proposed methodology. Additionally, our BIPS can be readily extended to other U-statistics optimization problems and pairwise learning tasks.

We introduce a Process Oriented Guided Inquiry Learning (POGIL)-style activity for teaching Bayesian reasoning in introductory statistics through conditional probability, Bayes' theorem, and belief updating. The activity is self-contained, uses hand-computable probabilities organized in two-way tables, and engages students in structured team roles. We evaluated the activity in four sections of an undergraduate introductory statistics course using a quasi-experimental comparison of POGIL-style and lecture-based instruction for a Bayes' theorem unit. Outcomes included student performance on Bayes' theorem final exam questions and satisfaction with instruction. We used a Bayesian bivariate generalized linear model to compare the two approaches while accounting for major type, gender, and race. The results indicated similar exam performance and similar probabilities of high satisfaction across instructional styles and demographic groups, with considerable uncertainty and no clear evidence of meaningful differences. These findings suggest that the POGIL-style activity performed comparably to lecture-based instruction for this unit while offering an active and classroom-ready way to introduce Bayesian reasoning without requiring difficult computation or simulation. We provide adaptable instructional materials and a reproducible Bayesian analytic framework for evaluating active learning innovations in introductory statistics. Our study supports the feasible inclusion of Bayesian reasoning in introductory courses and may help instructors considering active learning.

In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier–Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and constructs the local uncertainty scale by comparing the predictions of two operators trained on nearly identical datasets: one on the original labels and one on labels perturbed by small Gaussian noise. We consider this procedure in the data-scarce regime, where the total label budget is fixed and methods that require a separate uncertainty network must divide training data between multiple models. On the 2D Navier–Stokes benchmark, the perturbation-based method produces substantially narrower conformal bands than existing methods under matched total data budgets while maintaining the target simultaneous coverage. These results suggest that perturbation sensitivity is a practical and sample-efficient uncertainty proxy for conformalized neural operators.

Externally controlled trials (ECTs), including single-arm studies augmented with historical data and hybrid randomized designs with partial external augmentation, are increasingly used when concurrent randomized controls are infeasible or unethical. Regulatory guidance from the FDA, EMA, and NMPA calls for sensitivity analysis of borrowing assumptions, yet provides no structured template for which analyses to run or how to interpret them together. We propose a three-pillar framework organized around three questions: was the borrowing appropriate, did it contribute meaningful value, and are the conclusions robust to perturbation? The framework comprises eight modular analyses covering heterogeneity diagnostics, source influence, no-borrowing references, effective sample size, prior sensitivity, tipping points, alternative borrowing methods, and structural model sensitivity. It is method-agnostic and applies to both Bayesian and frequentist borrowing in patient-level or hybrid settings. We illustrate the framework using simulated data that mimic a hybrid evidence synthesis from a historical approval of ethnic-bridging submission under a real-world-evidence regulatory pathway. That original analysis combined individual patient data from a global pivotal study and a regional real-world study with aggregate data from two published cohorts, fitted via a Bayesian longitudinal model with ethnic-difference parameters. The worked example provides a reproducible template for sensitivity analysis in ECT submissions.

Statistical post-processing has proven to be an effective tool in improving ensemble forecast of different weather variables. Case studies show that post-processing can remedy the typically underdispersive and potentially biased behaviour of the ensemble while optimizing a proper scoring rule expressing the forecast skill. The price of these positive effects is generally a deterioration in sharpness; the width of the central prediction intervals and the uncertainty of the predictions are increasing, especially for shorter lead times. This work aims to reduce the extent of the latter phenomenon for neural network-based parametric post-processing methods by extending the network's loss function with a penalty term. We demonstrate the effect of the proposed technique for 2m temperature ensemble forecasts of the European Centre for Medium-Range Weather Forecasts downloaded from the EUPPBench benchmark dataset and verified against synoptic observations. Here, the predictive distribution is Gaussian, and we use the continuous ranked probability score (CRPS) as loss function. The case studies confirm a substantial relative decrease ($8.2\%-12.5\%$) in the width of the nominal central prediction interval compared to the width of the predictive distribution computed without the penalty term, while there is no deterioration in the mean CRPS of probabilistic forecasts and in the RMSE of the predictive mean.

We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are linearly independent, allowing the factors to be correlated and the factor loading vectors to be not nearly orthogonal. The procedure adapts to the sparsity of the factor loading vectors, accommodates weak factors, and demonstrates strong performance across a wide range of scenarios. To further reduce estimation errors, we also introduce an iterative algorithm based on a novel double projection approach. We theoretically justify the improved convergence rate of the iterative estimator, and derive the associated limiting distribution. A consistent estimator of the asymptotic variance is also provided, which plays a key role in the related inference problems. All results are validated through extensive simulations and two real data applications.

There is growing interest in constructing conformal prediction sets that provide approximate or asymptotic conditional coverage guarantees, capturing local data heterogeneity. However, methods like localized conformal prediction (LCP) may face challenges in ensuring reliable prediction sets in regions with sparse calibration data. This paper introduces Enhanced Localized Conformal Prediction (ELCP), a novel approach that incorporates auxiliary data to refine localized prediction sets while preserving finite-sample marginal coverage guarantees. By utilizing a density-ratio-weighted kernel estimator, ELCP seamlessly integrates auxiliary and calibration data, accommodating potential distributional shifts and improving the local reliability of prediction sets. Theoretical analysis confirms that ELCP maintains marginal coverage and enhances asymptotic test-conditional coverage. Simulation results demonstrate its superior local coverage and smaller prediction sets compared to standard LCP, highlighting its effectiveness in settings with limited calibration data but available auxiliary information from related tasks.

Control-variate and polynomial-maximization (PMM) estimators are optimized at a single fixed distribution, yet they are increasingly proposed to strengthen hypothesis tests, which decide between two regions of a parameter family. We give a closed-form criterion for when this transfer succeeds. For an H0-centered augmentation of a target moment statistic with null-optimized weight vector K0, the alternative-side expectation equals the target plus K0^T mu_a,H1, where mu_a,H1 is the alternative-side mean of the augmenting basis. Null-variance reduction therefore transfers without bias only under the orthogonality condition K0^T mu_a,H1 = 0; requiring each augmenting function to remain mean-zero is sufficient but not necessary. We instantiate the criterion on the recently proposed Wiedermann-Shi third-order cumulant test for measurement-error independence. A second-order PMM correction is unbiased and lower-variance under the null (relative efficiency >= 1 in all 36 conditions; aggregated mean ARE values 1.23-5.16; Type-I 0.04-0.09), yet provably inconsistent under the alternative: the antisymmetric polynomial auxiliaries acquire nonzero means, attenuating the target by a closed-form factor and costing 7-52 percentage points of power, worst where the test is strongest and worsening under heavy tails. A fourth-order variant reduces variance (ratio 1.127) but fails a nuisance guard (rejection 0.295 versus 0.10). We derive a reusable alternative-consistency acceptance gate for variance-reduced test statistics.

This manuscript studies the problem of independence testing between two high-dimensional time series without assuming weak stationarity, that is, allowing their autocovariances to vary over time. To this end, we propose a bimodal weighted-average test statistic that removes the bias induced by temporal dependence under the null hypothesis, thereby avoiding the need to whiten the time series prior to hypothesis testing – a procedure that is challenging in high-dimensional and nonstationary settings. To facilitate statistical inference, we develop a dependent wild bootstrap procedure. On the theoretical side, we derive a concentration inequality for quadratic forms of time series data stemming from a class of high-dimensional, nonlinear, and nonstationary processes. This result enables us to derive the asymptotic null distribution of the proposed test statistic and to establish the validity of the bootstrap algorithm. Numerical results show that the proposed test attains desired size and good power performance even when the dimension exceeds the sample size or when the data-generating process exhibits time-varying autocovariances. In contrast, tests based on whitening time series fail to maintain correct size in the presence of unstable autocovariance structures. Since nonstationary autocovariances commonly arise in real-life time series data, our work offers a robust procedure for independence testing.

Tissue graph counterfactuals ask how a cell's expression would change under altered spatial neighbor contexts. Such queries are central to predicting cell behavior in tissues, but lack a unified definition, with existing methods targeting specific intervention types or treating cells as i.i.d. In this work, we first formalize tissue graph counterfactuals as a class of spatial interventions that either rewire connections between cells (edge perturbation) or modify the expression of their neighbors (node perturbation). We then introduce Cellina (https://cellina.readthedocs.io) - a framework that uses supervised disentanglement to decompose a cell's intrinsic state from its spatial context, using the latter as a conditioning input for counterfactual predictions. Across benchmarks spanning over 2.5 million spatially-resolved cells in colorectal cancer and mouse brain, Cellina outperforms spatially-informed and non-spatial competitors in in-silico graph perturbations, disentanglement, and scalability. Additionally, we show that Cellina reveals biologically distinct cancer subdomains in an unsupervised manner and enables targeted neighbor perturbation simulations.

Ordinary differential equation models are widely used to describe how complex systems change over time, but reliable conclusions depend on how well their parameters can be estimated from limited, noisy data. Common measures of uncertainty, such as confidence intervals and coefficients of variation, do not provide a single, easy-to-interpret scale for comparing uncertainty across parameters, models, error structures, and data-collection designs. We introduce the Practical Identifiability Index (PII), a unit-free, scale-invariant measure of uncertainty for individual positive-valued parameters, defined as the base-10 logarithm of the ratio between the upper and lower bounds of a confidence interval; a value of 1 corresponds to a tenfold ratio between the interval bounds. We study PII using parametric bootstrap experiments in growth and compartmental epidemic models. PII decreases as longer data windows are used for model fitting and tends to increase with observation noise (although not uniformly across settings) and when several parameters must be estimated together. PII remains larger for parameters associated with latent or indirectly observed processes, while adding more measured quantities substantially improves estimation of progression and recovery parameters. We then apply PII to daily influenza incidence from the 1918 San Francisco epidemic. As a benchmark, PII and normalized confidence-interval width (NCIW) with equivalent thresholds give the same classification in 134 of 135 model, scenario, parameter, and error-structure combinations (99.3% agreement), while PII expresses uncertainty directly as a multiplicative range, without normalization by the parameter estimate. PII is meant to complement, rather than replace, other identifiability and uncertainty analyses, and should be considered together with empirical coverage and other diagnostic measures.

Undirected graphical models provide a fundamental framework for representing conditional independence structures among high-dimensional random variables. While undirected graphical model selection has become a central problem in high-dimensional statistics, most existing methods are restricted to parametric settings. In this paper, we develop a nonparametric approach to undirected graphical model selection based on diffusion models. Recent work has shown that diffusion models can adapt to the unknown graph structure of the underlying distribution, yet utilizing these models for explicit graph estimation remains unexplored. To bridge this gap, we introduce a novel diffusion-based method for nonparametric undirected graphical model selection. We establish the model selection consistency of the proposed method and demonstrate its empirical performance through extensive simulations and two real data analyses.

Data-adaptive two-sample testing assesses if two samples come from the same distribution, using a discrepancy learned from the data (e.g., via kernel-based feature representations). Such methods typically rely on data splitting to decouple learning from testing and control type I error. However, this paradigm is ill-suited to few-shot settings with severe sample-size imbalance: abundant reference samples are available, while only a handful of query samples arrive. In this paper, we show how this imbalance can be leveraged constructively. Using abundant reference data, we learn reference-dependent representations that summarize salient structure of the reference distribution and provide informative signals for detecting departures. We incorporate a collection of representation families that capture both global and local structure, and adaptively weight them using only reference samples via an uncertainty-guided principle. Theoretically, we establish permutation-based type I error control and show consistency of the aggregated test: as the sample sizes grow, the test power converges to one whenever the representation set contains at least one consistent representation. Empirically, our aggregation achieves strong performance across a range of benchmarks while retaining type I error control.

Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\mathbf{x}^{\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\mathbf{x}^{\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.

Many model evaluation tasks reduce to estimating an average loss, error rate, or subgroup metric on a stratified pool when each label, human rating, or simulator call is costly. The precision-optimal Neyman allocation depends on within-stratum variances, which must be learned from the same observations used for estimation. We formulate this as a sequential allocation problem and use the exact one-step marginal variance reduction as the priority index. Replacing the unknown variances by independent inverse-chi-squared posterior draws yields TS-Neyman, a Thompson-sampling rule that preserves the oracle marginal-gain structure while randomizing over variance uncertainty. For any fixed finite number of strata, we prove almost-sure convergence of the TS-Neyman allocation proportions to the Neyman target, asymptotic optimality of the variance proxy, and a central limit theorem for the resulting adaptive stratified estimator. In two five-stratum budget-scaling benchmarks, one bounded-loss benchmark and one binary model-error benchmark in the spirit of Dai et al. 2023, TS-Neyman's relative efficiency stays within 5 percent of the oracle on the bounded-loss population and within about 15 percent on the binary benchmark. In an additional CivilComments real-data replay with confidence-based strata, it stays within about 8 percent of the oracle and improves on equal allocation by roughly 7 to 14 percent in MSE across budgets, while plug-in greedy and two-stage plug-in can degrade by over an order of magnitude under sparse pilots. Common-pilot warm-start and prior-sensitivity studies show that this behavior is stable under working-model and working-prior misspecification.

Phylogenetic networks are graphs inferred from molecular sequence data that represent ancestral histories shaped by reticulate processes such as recombination, hybridization, and horizontal gene transfer. We introduce a family of distance metrics for rooted, ranked, unlabeled phylogenetic networks, extending a previously developed distance for ranked trees. Our approach relies on a bijective triangular matrix representation of phylogenetic networks that captures the temporal order of internal events, speciations, and hybridizations. Our metrics, defined as standard matrix norms, allow efficient quantitative comparisons of network topologies, timed networks and networks with differing numbers of hybridizations. Our distance can be used for both isochronous networks where all tips are sampled at one time point, and heterochronous networks where tips are allowed to be sampled at different time points. We show that our metrics capture biologically meaningful differences among evolutionary histories in both simulations and empirical posterior distributions of viral phylogenetic networks. These tools fill a methodological gap, enabling principled comparisons of ranked, unlabeled phylogenetic networks, including ancestral recombination graphs.

Characterizing directed information flow in brain networks is difficult because neural circuits are full of recurrent feedback loops. Many existing tools for directed dependence assume a directed acyclic graph (DAG) structure to resolve directional ambiguity, and therefore cannot represent these loops. We present a nonparametric, information-theoretic framework that addresses this by coupling the discrete Hodge decomposition with lead-lag mutual information, splitting the resulting edge flow into three orthogonal components: a gradient term capturing hierarchical, feed-forward relationships; a curl term isolating triangle-level feedback loops; and a harmonic term capturing cyclic flow around topological holes. This separation makes it possible to disentangle feed-forward drive from recurrent circulation, which conventional measures conflate. We further develop a permutation-based hypothesis-testing layer that identifies nodes and triangular motifs whose information-flow signatures change significantly between conditions. We validate the framework on simulations with known ground-truth structure and apply it to local field potential recordings from a rodent model of focal ischemic stroke. In three of four animals, we find a post-stroke shift toward hierarchical, source-driven propagation at the expense of recurrent feedback, while the fourth shows no significant change.

When a neural time-series model reports that one variable modulates another's effect on a target, is the discovered interaction a property of the data or an artifact of model flexibility? We argue that this is fundamentally a question of identifiability, governed by the geometry of the observed input support rather than by the specific neural architecture. We study the problem in a multiplicative-gating extension of neural additive vector autoregression (GNAVAR), in which source contributions are modulated by other lagged variables. We show that representational capacity is not identifiability: dependent inputs induce leakage between edge-specific interaction terms, and low-dimensional support permits distinct interaction decompositions that agree on the observed data while differing elsewhere. We then prove a population identifiability theorem for normalized minimal GNAVAR decompositions under explicit support conditions, including settings with shared modulators. The theory yields a simple practitioner-facing diagnostic: the effective rank of the joint lag-block covariance predicts, before fitting, whether interaction recovery is feasible for a given candidate set. When the candidate set is unknown, a two-seed stability check provides a practical operational test. The same support condition organizes empirical outcomes into the three states predicted by the theory. Our results show that interaction recoverability depends on support geometry, that effective rank provides a practical pre-fit diagnostic, and that instability across independent fits is a characteristic signature of non-identifiable interaction discovery. The identifiability phenomenon, the support condition, and the instability signature are model-agnostic; GNAVAR is the vehicle that makes them provable.

Muon replaces a matrix gradient $G=U\Sigma V^\top$ by its polar factor $UV^\top$. This keeps the singular directions selected by the gradient, but makes the update spectrum flat. We study the optimization bias created by this operation. Under explicit alignment assumptions, we prove that the polar update is the one-step entropy-maximizing choice among bounded updates that use the gradient singular directions and do not adapt to the current weight spectrum. In an underdetermined regression model, we derive exact singular-value dynamics for continuous-time Muon and identify a measurement-dependent condition under which the normalized spectrum moves toward equal nonzero singular values. This geometry also rules out a common low-rank interpretation: at fixed Frobenius norm, Muon's distinguished state has a flat spectrum, whereas nuclear-norm minimization favors spectral concentration. Controlled matrix-sensing experiments separate the effect from simple gradient rescaling, show that norm-matched gradient descent does not reproduce Muon, and recover the predicted flattening trend across broad ablations. In small NanoGPT pretraining, Muon preserves stable rank, has a broad learning-rate plateau, and improves validation loss relative to AdamW; in a matched small-ViT control, the ranking reverses. The resulting picture is regime-dependent: Muon is not universally superior, but its flat-spectrum bias can help when many spectral directions need to remain active.

Adaptive beamforming is a cornerstone of array signal processing, yet its performance often collapses in the face of complex, rapidly changing interference. When interferers appear or move unpredictably, conventional estimators encounter a fundamental memory trade-off: short windows enable rapid tracking but suffer from high estimation variance, while long windows provide stable rejection but fail to adapt to shifts. This challenge is resolved by introducing the Universal Switching Beamformer (USB), which integrates competitive sequential prediction into the beamforming architecture. By employing a linear transition diagram, the USB implicitly maintains an exponentially large family of candidate covariance histories and dynamically re-weights them based on their cumulative output power. This mechanism allows the beamformer to automatically vary its effective memory length without explicit change detection or heuristic parameter tuning. A theoretical upper bound is proven on the regret relative to an omniscient oracle that selects the best piecewise-stationary covariance model in hindsight. Extensive simulations and experiments on the SwellEx-96 dataset demonstrate that the USB achieves the agility of short-window estimators and the precision of long-term integration, providing a principled solution for tracking highly non-stationary scenes.

Biodiversity measures are often used descriptively: one computes a diversity index from an observed or estimated community composition and maps the resulting values across space. Conservation planning, however, also requires a site-specific benchmark against which the observed community can be compared. This chapter develops an information-geometric framework for such potential diversity and the associated diversity gap. The central object is a pair of probability vectors on the species simplex: an observed or realized composition \(p^{\mathrm{obs}}\), and a potential composition \(p^{\mathrm{pot}}\) obtained by a constrained variational principle. The gap is then defined by comparing a diversity functional at these two compositions. The framework is developed for both Hill-type diversity, which measures abundance and evenness, and Rao's quadratic entropy, which incorporates trait, phylogenetic, or ecological dissimilarities among species. A spatial point-process interpretation clarifies how local ecological capacities can be defined before passing to the simplex. Escort constraints, capacity constraints, and divergence projections then provide a unified way to define nontrivial benchmarks beyond the uniform distribution. The resulting formulation separates two distinct questions: how diverse a community is, and how far it is from a locally admissible potential benchmark. It also connects the ecological idea of dark diversity with a continuous, abundance-weighted comparison on the probability simplex. We also outline a dynamic extension in which capacities, species migration, and climate-driven shifts vary over time. Empirical implementation with large-scale citizen-science biodiversity data and trait databases is left for future work.

This methodological study analyzes the effects of collinearity, effective dimensionality, and cluster stability in a 2023 study of US airline profit cycles from 1995 to 2020 by Renold et al., which uses k-means clustering, principal component analysis, and system dynamic modelling.We replicate their clustering experiment in three spaces – the original 7-dim. raw-variable space, a 3-dim. PC score space, and a 4-dim. PC score space using their dataset. We show that the six-cluster taxonomy is geometrically robust: k-means in 3-PC space produces bit-for-bit identical cluster assignments relative to 7D raw space. As a nonlinearity check we apply kernel PCA under six kernels spanning three families plus a linear baseline. The kernels confirm an intrinsically linear manifold with no detectable curvature. The silhouette criterion reveals that the dataset structurally supports only three clusters, not six. Collinearity in the raw 7D space suppresses the silhouette signal. A kernel ridge regression check confirms no nonlinear accuracy gain over linear ridge once the COVID19 year is excluded. Together, these results argue for clustering on PC scores rather than raw variables in collinearity-prone panel data.

Externally controlled survival trials are increasingly used when concurrent randomized controls are infeasible, particularly in oncology and rare-disease settings with time-to-event endpoints. We target an average-treatment-effect-on-the-treated (ATT)-type marginal hazard-ratio estimand, comparing treatment with counterfactual control in the treated trial population, and estimate it using inverse-probability-weighted (IPW) Cox regression. Valid inference is challenging because IPW Cox regression depends on the weights through both event contributions and risk-set averages, making flexible machine-learning nuisance estimation difficult to incorporate directly. Building on machine-learning-assisted generalized entropy calibration (MEC) by Lee and Kim (2026), we propose MEC-Cox for ATT-weighted IPW Cox regression. The method begins with normalized source-propensity-score odds weights for external controls and then applies Bregman calibration to balance cross-fitted prognostic summaries between external controls and treated trial patients. The calibration basis may include control-survival predictions, Cox linear predictors, penalized-survival-model predictions, or other prognostic-score summaries. MEC-updated weights therefore play a dual role as source-transport and prognostic-score balancing weights. We establish consistency, characterize a calibration-induced efficiency gain, and develop a stacked sandwich variance estimator. Simulations show that MEC-Cox can reduce bias, increase efficiency, and improve coverage through flexible machine-learning-assisted adjustment.

National statistical offices (NSOs) produce their estimates under a single weighting system (uni-weight approach): one set of weights, independent of the variable of interest, is used to estimate multiple parameters and multiple subpopulations (domains). In this paper we study, within the family of model-assisted estimators and from a design-based perspective of direct estimation, the use of regression trees as the assisting model for estimating totals in unplanned domains. We distinguish two strategies: (i) fitting a single tree at the population level and deriving from it uni-weight weights applicable to any domain, and fitting a domain-specific tree. We show that both estimators can be written as weighted sums with weights that do not depend on $y$, preserving the uni-weight property and additivity benchmarking with respect to the population total. Extending to trees the classical result, we argue why the estimator built from a population-level model tends to behave like the Horvitz-Thompson estimator within domains, whereas the domain-specific model can achieve substantial variance reductions. A simulation study based on microdata from the Uruguayan Continuous Household Survey (ECH) illustrates the behavior of the estimators at the population level and by department