Papers

As demand-side flexibility becomes increasingly necessary to integrate variable renewable energy, understanding electricity demand composition across different grid levels is essential. However, at regional and national scales, visibility into the relative contributions of different consumer categories remains limited due to the complexity and cost of collecting end-use consumption data. To address this challenge, we propose a blind source separation framework to disaggregate open-access high-voltage grid load measurements into sectoral contributions. The approach relies on a constrained variant of non-negative matrix factorization, termed linearly-constrained non-negative matrix factorization (LCNMF), which allows prior information to be incorporated as linear constraints on the factor matrices, thereby providing weak supervision of the separation process. The framework is evaluated using Italian national load data from 2021 to 2023. Results demonstrate the identifiability of residential, services, and industrial load components and provide monthly sectoral consumption estimates consistent with reported statistics. The proposed method is generalizable and applicable to load disaggregation problems across multiple grid scales where disaggregated measurements are unavailable.

We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the flat-spike case, offering little guidance when spike energy is unevenly distributed across the support. Motivated by this, we propose Spectral Energy Pursuit (SEP), an effective iterative scheme that repeatedly screens and reselects coordinates, with a sample complexity that adapts to the energy profile. We develop our framework around a structure function \(s(p)\) that quantifies how spike energy accumulates over its top \(p\) entries. To our knowledge, SEP is the first polynomial-time SPCA method with a sample-complexity guarantee governed by the full energy profile: it succeeds with \(m\gtrsim \max_{1\le p\le k} p\,s^2(p)\,\log n\) samples, recovering the classical \(k^2\log n\) rate for flat spikes and improving to \(k\log n\) for sufficiently concentrated profiles. As a lightweight post-processing, a single truncated power iteration is proven to enable the final estimator to attain a uniform statistical error bound. Empirical simulations using a flat profile and offset-regularized decaying profiles validate that SEP adapts to profile structure without profile-specific tuning and outperforms existing algorithms.

The Poisson-gamma state space (PGSS) models have been utilized in the analysis of non-negative integer-valued time series to sequentially obtain closed form filtering and predictive densities. In this study, we show the underlying mechanics and non-stationary properties of multi-step ahead predictive distributions for the PGSS family of models. By exploiting the non-stationary structure of the PGSS model, we establish that the predictive mean remains constant while the predictive variance diverges with the forecast horizon, a property also found in Gaussian random walk models. We show that, in the long run, the predictive distribution converges to a zero-degenerated distribution, such that both point and interval forecasts eventually converge towards zero. In doing so, we comment on the effect of hyper-parameters and the discount factor on the long-run behavior of the forecasts.

The Stratified Bootstrap Test (SBT) provides a nonparametric, resampling-based framework for assessing the stability of group-specific ranking patterns in multivariate survey or rating data. By repeatedly resampling observations and examining whether a group's top-ranked items remain among the highest-scoring categories across bootstrap samples, SBT quantifies ranking robustness through a non-containment index. In parallel, the stratified bootstrap test extends this framework to formal statistical inference by testing ordering hypotheses among population means. Through resampling within groups, the method approximates the null distribution of ranking-based test statistics without relying on distributional assumptions. Together, these techniques enable both descriptive and inferential evaluation of ranking consistency, detection of aberrant or adversarial response patterns, and rigorous comparison of groups in applications such as survey analysis, item response assessment, and fairness auditing in AI systems.

Multiple myeloma (MM) is preceded by a long preclinical phase spanning decades, yet scalable, non-specialist tools to identify individuals at elevated risk before end-organ damage are lacking. In a prospective analysis of 299,035 cancer-free UK Biobank participants followed for a median of 12.4 years, during which 768 developed incident MM, we conducted a biomarker-wide association scan across 61 routinely measured blood analytes spanning hematological, protein metabolism, renal, and immune categories. Markers of protein dysregulation-elevated total protein, depressed albumin, and a low albumin-to-globulin (A/G) ratio-showed the strongest preclinical associations (hazard ratios 0.61-1.54 per SD), consistent with progressive monoclonal immunoglobulin accumulation and suppression of normal polyclonal synthesis years before diagnosis. These signals were accompanied by indicators of erythropoietic suppression, morphological red cell dysregulation, and a shift toward lower neutrophil and higher lymphocyte fractions, reflecting coordinated perturbations across hematopoietic and immune compartments. Longitudinal trajectory analyses showed that these multi-system deviations emerge more than a decade before diagnosis and intensify as clinical onset approaches. Dose-response modelling revealed pronounced nonlinear associations for protein and erythrocytic markers, with risk concentrated among individuals with extreme values. Incorporating significant biomarkers into a clinical risk model improved 10-year MM discrimination from a C-index of 0.684 to 0.744, with the high-risk decile accumulating 0.79% cumulative incidence versus 0.47% under the clinical model alone. These findings provide a practical framework for biomarker-guided MM risk stratification and targeted surveillance using routinely available clinical tests.

This study applies a Geospatial Explainable AI (GeoXAI) framework to analyze the spatially heterogeneous and nonlinear determinants of traffic crash density in Florida. By combining a high-performing machine learning model with GeoShapley, the framework provides interpretable, tract-level insights into how roadway characteristics and socioeconomic factors contribute to crash risk. Specifically, results show that variables such as road density, intersection density, neighborhood compactness, and educational attainment exhibit complex nonlinear relationships with crashes. Extremely dense urban areas, such as Miami, show sharply elevated crash risk due to intensified pedestrian activities and roadway complexity. The GeoShapley approach also captures strong spatial heterogeneity in the influence of these factors. Major metropolitan areas including Miami, Orlando, Tampa, and Jacksonville display significantly higher intrinsic crash contributions, while rural tracts generally have lower baseline risk. Each factor exhibits pronounced spatial variation across the state. Based on these findings, the study proposes targeted, geography-sensitive policy recommendations, including traffic calming in compact neighborhoods, adaptive intersection design, speed management on high-volume corridors such as I-95 in Miami, and equity-focused safety interventions in disadvantaged rural areas of central and northern Florida. Moreover, this paper compares the results obtained from GeoShapley framework against other established methods (e.g., SHAP and MGWR), demonstrating its powerful ability to explain nonlinearity and spatial heterogeneity simultaneously.

In this paper, we derive a general representation for the expectation of the Gini coefficient estimator in terms of the Laplace transform of the underlying distribution, together with the mean and the Gini coefficient of its exponentially tilted version. This representation leads to a new characterization of the gamma family within the class of nonnegative scale families, based on a stability property under exponential tilting. As direct applications, we show that the Gini estimator is biased for both Poisson and geometric populations and provide an alternative, unified proof of its unbiasedness for gamma populations. By using the derived bias expressions, we propose plug-in bias-corrected estimators and assess their finite-sample performance through a Monte Carlo study, which demonstrates substantial improvements over the original estimator. Compared with existing approaches, our framework highlights the fundamental role of scale invariance and exponential tilting, rather than distribution-specific algebraic calculations, and complements recent results in Baydil et al. (2025) [Unbiased estimation of the gini coefficient. SPL, 222:110376] and Vila and Saulo (2025a,b) [Bias in Gini coefficient estimation for gamma mixture populations. STPA, 66:1-18; and The mth gini index estimator: Unbiasedness for gamma populations. J. Econ. Inequal].

Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper draws the reader's attention to the fact that, while for infinite sequences of observations the two assumptions are almost indistinguishable, the difference between them becomes very significant for finite sequences of a given length.

A plethora of dimension reduction methods have been developed to visualize high-dimensional data in low dimensions. However, different dimension reduction methods often output different and possibly conflicting visualizations of the same data. This problem is further exacerbated by the choice of hyperparameters, which may substantially impact the resulting visualization. To obtain a more robust and trustworthy dimension reduction output, we advocate for a consensus approach, which summarizes multiple visualizations into a single consensus dimension reduction visualization. Here, we leverage ideas from multi-view learning in order to identify the patterns that are most stable or shared across the many different dimension reduction visualizations, or views, and subsequently visualize this shared structure in a single low-dimensional plot. We demonstrate that this consensus visualization effectively identifies and preserves the shared low-dimensional data structure through both simulated and real-world case studies. We further highlight our method's robustness to the choice of dimension reduction method and hyperparameters – a highly-desirable property when working towards trustworthy and reproducible data science.

We study the conditional expert Kaplan-Meier estimator, an extension of the classical Kaplan–Meier estimator designed for time-to-event data subject to both right-censoring and contamination. Such contamination, where observed events may not reflect true outcomes, is common in applied settings, including insurance and credit risk, where expert opinion is often used to adjudicate uncertain events. Building on previous work, we develop a comprehensive asymptotic theory for the conditional version incorporating covariates through kernel smoothing. We establish functional consistency and weak convergence under suitable regularity conditions and quantify the bias induced by imperfect expert information. The results show that unbiased expert judgments ensure consistency, while systematic deviations lead to a deterministic asymptotic bias that can be explicitly characterized. We examine finite-sample properties through simulation studies and illustrate the practical use of the estimator with an application to loan default data.

High-content screening microscopy generates large amounts of live-cell imaging data, yet its potential remains constrained by the inability to determine when and where to image most effectively. Optimally balancing acquisition time, computational capacity, and photobleaching budgets across thousands of dynamically evolving regions of interest remains an open challenge, further complicated by limited field-of-view adjustments and sensor sensitivity. Existing approaches either rely on static sampling or heuristics that neglect the dynamic evolution of biological processes, leading to inefficiencies and missed events. Here, we introduce the restless multi-process multi-armed bandit (RMPMAB), a new decision-theoretic framework in which each experimental region is modeled not as a single process but as an ensemble of Markov chains, thereby capturing the inherent heterogeneity of biological systems such as asynchronous cell cycles and heterogeneous drug responses. Building upon this foundation, we derive closed-form expressions for transient and asymptotic behaviors of aggregated processes, and design scalable Whittle index policies with sub-linear complexity in the number of imaging regions. Through both simulations and a real biological live-cell imaging dataset, we show that our approach achieves substantial improvements in throughput under resource constraints. Notably, our algorithm outperforms Thomson Sampling, Bayesian UCB, epsilon-Greedy, and Round Robin by reducing cumulative regret by more than 37% in simulations and capturing 93% more biologically relevant events in live imaging experiments, underscoring its potential for transformative smart microscopy. Beyond improving experimental efficiency, the RMPMAB framework unifies stochastic decision theory with optimal autonomous microscopy control, offering a principled approach to accelerate discovery across multidisciplinary sciences.

Sleep difficulties in children are heterogeneous in presentation, yet conventional assessment tools like the Children's Sleep Habits Questionnaire (CSHQ) reduce this complexity to a single cumulative score, obscuring distinct patterns of sleep disturbance that require different interventions. Latent Class Regression (LCR) models offer a principled approach to identify subgroups with shared sleep behaviour profiles whilst incorporating predictors of group membership, but Bayesian inference for these models has been hindered by computational challenges and the absence of variable selection methods. We propose a fully Bayesian framework for LCR that uses Pólya-Gamma data augmentation, enabling efficient sampling of regression coefficients. We extend this framework to include variable selection for both predictors and item responses: predictor variable selection via latent inclusion indicators and item selection through a partially collapsed approach. Through simulation studies, we show that the proposed methods yield accurate parameter estimates, resolve identifiability issues arising in full models and successfully identify informative predictors and items while excluding noise variables. Applying this methodology to CSHQ data from 148 children reveals distinct latent subgroups with different sleep behaviour profiles, anxious nighttime sleepers, short/light sleepers and those with more pervasive sleep problems, with each carrying distinct implications for intervention. Results also highlight the predictive role of Autism Spectrum Disorder diagnosis in subgroup membership. These findings demonstrate the limitations of conventional CSHQ scoring and illustrate the benefits of a probabilistic subgroup-based approach as an alternative for understanding paediatric sleep difficulties.

Standard weather forecast evaluations focus on the forecaster's perspective and on a statistical assessment comparing forecasts and observations. In practice, however, forecasts are used to make decisions, so it seems natural to take the decision-maker's perspective and quantify the value of a forecast by its ability to improve decision-making. Decision calibration provides a novel framework for evaluating probabilistic forecast performance at the decision level rather than the forecast level. We evaluate decision calibration to compare a Machine Learning and a classical numerical weather prediction model on various weather-dependent decision tasks, though the framework is applicable to any set of forecast models. We find that model performance at the forecast level does not reliably translate to performance in downstream decision-making: some performance differences only become apparent at the decision level, and even among seemingly similar decision tasks, model rankings can change. Our results confirm that typical forecast evaluations are insufficient for selecting the optimal forecast model for a specific decision task.

Modern operational systems ranging from logistics and cloud infrastructure to industrial IoT, are governed by complex, interdependent processes. Understanding how interventions propagate through such systems requires causal inference methods that go beyond direct effects to quantify mediated pathways. Traditional mediation analysis, while effective in simple settings, fails to scale to the high-dimensional directed acyclic graphs (DAGs) encountered in practice, particularly when multiple treatments and mediators interact. In this paper, we propose a scalable mediation analysis framework tailored for large causal DAGs involving multiple treatments and mediators. Our approach systematically decomposes total effects into interpretable direct and indirect components. We demonstrate its practical utility through applied case studies in fulfillment center logistics, where complex dependencies and non-controllable factors often obscure root causes.

Stochastic optimization is fundamental to modern machine learning. Recent research has extended the study of stochastic first-order methods (SFOMs) from light-tailed to heavy-tailed noise, which frequently arises in practice, with clipping emerging as a key technique for controlling heavy-tailed gradients. Extensive theoretical advances have further shown that the oracle complexity of SFOMs depends on the tail index $\alpha$ of the noise. Nonetheless, existing complexity results often cover only the case $\alpha \in (1,2]$, that is, the regime where the noise has a finite mean, while the complexity bounds tend to infinity as $\alpha$ approaches $1$. This paper tackles the general case of noise with tail index $\alpha\in(0,2]$, covering regimes ranging from noise with bounded variance to noise with an infinite mean, where the latter case has been scarcely studied. Through a novel analysis of the bias-variance trade-off in gradient clipping, we show that when a symmetry measure of the noise tail is controlled, clipped SFOMs achieve improved complexity guarantees in the presence of heavy-tailed noise for any tail index $\alpha \in (0,2]$. Our analysis of the bias-variance trade-off not only yields new unified complexity guarantees for clipped SFOMs across this full range of tail indices, but is also straightforward to apply and can be combined with classical analyses under light-tailed noise to establish oracle complexity guarantees under heavy-tailed noise. Finally, numerical experiments validate our theoretical findings.

Score estimation has recently emerged as a key modern statistical challenge, due to its pivotal role in generative modelling via diffusion models. Moreover, it is an essential ingredient in a new approach to linear regression via convex $M$-estimation, where the corresponding error densities are projected onto the log-concave class. Motivated by these applications, we study the minimax risk of score estimation with respect to squared $L^2(P_0)$-loss, where $P_0$ denotes an underlying log-concave distribution on $\mathbb{R}$. Such distributions have decreasing score functions, but on its own, this shape constraint is insufficient to guarantee a finite minimax risk. We therefore define subclasses of log-concave densities that capture two fundamental aspects of the estimation problem. First, we establish the crucial impact of tail behaviour on score estimation by determining the minimax rate over a class of log-concave densities whose score function exhibits controlled growth relative to the quantile levels. Second, we explore the interplay between smoothness and log-concavity by considering the class of log-concave densities with a scale restriction and a $(\beta,L)$-Hölder assumption on the log-density for some $\beta \in [1,2]$. We show that the minimax risk over this latter class is of order $L^{2/(2\beta+1)}n^{-\beta/(2\beta+1)}$ up to poly-logarithmic factors, where $n$ denotes the sample size. When $\beta < 2$, this rate is faster than could be obtained under either the shape constraint or the smoothness assumption alone. Our upper bounds are attained by a locally adaptive, multiscale estimator constructed from a uniform confidence band for the score function. This study highlights intriguing differences between the score estimation and density estimation problems over this shape-constrained class.

This paper considers the estimation of binary choice models when survey responses are possibly misclassified but one of the response category can be validated. Partial validation may occur when survey questions about participation include follow-up questions on that particular response category. In this case, we show that the initial two-sided misclassification problem can be transformed into a one-sided one, based on the partially validated responses. Using the updated responses naively for estimation does not solve or mitigate the misclassification bias, and we derive the ensuing asymptotic bias under general conditions. We then show how the partially validated responses can be used to construct a model for participation and propose consistent and asymptotically normal estimators that overcome misclassification error. Monte Carlo simulations are provided to demonstrate the finite sample performance of the proposed and selected existing methods. We provide an empirical illustration on the determinants of health insurance coverage in Ghana. We discuss implications for the design of survey questionnaires that allow researchers to overcome misclassification biases without recourse to relatively costly and often imperfect validation data.

Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for classical rank correlations, including Kendall's tau, Spearman's rho, Goodman-Kruskal's gamma, Kendall's tau-b, and grade correlation. We derive asymptotic distributions for both iid and time series data, resorting to asymptotic results for U-statistics, and introduce consistent variance estimators. This enables the construction of confidence intervals and tests, generalizes classical results for continuous random variables and leads to corrected versions of widely used tests of independence. We analyze the finite-sample performance of our variance estimators, confidence intervals, and tests in simulations and illustrate their use in case studies.

Sparse longitudinal (SL) textual data arises when individuals generate text repeatedly over time (e.g., customer reviews, occasional social media posts, electronic medical records across visits), but the frequency and timing of observations vary across individuals. These complex textual data sets have immense potential to inform future policy and targeted recommendations. However, because SL text data lack dedicated methods and are noisy, heterogeneous, and prone to anomalies, detecting and inferring key patterns is challenging. We introduce LLmFPCA-detect, a flexible framework that pairs LLM-based text embeddings with functional data analysis to detect clusters and infer anomalies in large SL text datasets. First, LLmFPCA-detect embeds each piece of text into an application-specific numeric space using LLM prompts. Sparse multivariate functional principal component analysis (mFPCA) conducted in the numeric space forms the workhorse to recover primary population characteristics, and produces subject-level scores which, together with baseline static covariates, facilitate data segmentation, unsupervised anomaly detection and inference, and enable other downstream tasks. In particular, we leverage LLMs to perform dynamic keyword profiling guided by the data segments and anomalies discovered by LLmFPCA-detect, and we show that cluster-specific functional PC scores from LLmFPCA-detect, used as features in existing pipelines, help boost prediction performance. We support the stability of LLmFPCA-detect with experiments and evaluate it on two different applications using public datasets, Amazon customer-review trajectories, and Wikipedia talk-page comment streams, demonstrating utility across domains and outperforming state-of-the-art baselines.

To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an independent edge set, hidden in an Erdős-Rényi random graph, which is formulated as a hypothesis testing problem. We identify the critical regime for this testing problem and prove that the log-likelihood ratio is asymptotically normal. Via analyses of computationally efficient edge or wedge count test statistics that attain the optimal limits of detection, our results also reveal the absence of a statistical-to-computational gap. Our main technical tool is the cluster expansion from statistical physics, which allows us to prove a precise, non-asymptotic characterization of the log-likelihood ratio. Our analyses rely on a careful reorganization and cancellation of terms that occur in the difference between monomer-dimer log partition functions on the complete and Erdős-Rényi graphs. This combinatorial and statistical physics approach represents a significant departure from the more established methods such as orthogonal decompositions, and positions the cluster expansion as a viable technique in the study of log-likelihood ratios for planted models in general.

Gaussian Dynamic Bayesian Networks (GDBNs) are a widely used tool for learning network structures from continuous time-series data. To capture both time-lagged and contemporaneous dependencies, advanced GDBNs allow for dynamic inter-slice edges as well as static intra-slice edges. In the literature, two Bayesian modeling approaches have been developed for GDBNs. Both build on and extend the well-known Gaussian BGe score. We refer to them as the mean-adjusted BGe (mBGe) and the extended BGe (eBGe) models. In this paper, we contrast the two models and compare their performance empirically. The main finding of our study is that the two models induce different equivalence classes of network structures. In particular, the equivalence classes implied by the eBGe model are non-standard, and we propose a new variant of the DAG-to-CPDAG algorithm to identify them. To the best of our knowledge, these non-standard equivalence classes have not been previously reported.

Existing approaches to modelling antibody concentration data are mostly based on finite mixture models that rely on the assumption that individuals can be divided into two distinct groups: seronegative and seropositive. Here, we challenge this dichotomous modelling assumption and propose a latent variable modelling framework in which the immune status of each individual is represented along a continuum of latent seroreactivity, ranging from minimal to strong immune activation. This formulation provides greater flexibility in capturing age-related changes in antibody distributions while preserving the full information content of quantitative measurements. We show that the proposed class of models can accommodate a large variety of model formulations, both mechanistic and regression-based, and also includes finite mixture models as a special case. We also propose a computationally efficient $L_2$-based estimator as an alternative to maximum likelihood estimation, which substantially reduces computational cost, and we establish its consistency. Through a case study on malaria serology, we demonstrate how the flexibility of the novel framework enables joint analyses across all ages while accounting for changes in transmission patterns. We conclude by outlining extensions of the proposed modelling framework and its relevance to other omics applications.

The increased prevalence of observational data and the need to integrate information from multiple sources are critical challenges in contemporary data analysis. Record linkage is a widely used tool for combining datasets in the absence of unique identifiers. The presence of linkage errors such as mismatched records, however, often hampers the analysis of data sets obtained in this way. This issue is more difficult to address in secondary analysis settings, where linkage and subsequent analysis are performed separately, and analysts have limited information about linkage quality. In this paper, we investigate the estimation of average treatment effects in the conventional potential outcome-based causal inference framework under linkage uncertainty. To mitigate the bias that would be incurred with naive analyses, we propose an approach based on estimating equations that treats the unknown match status indicators as missing data. Leveraging a variant of the Expectation-Maximization algorithm, these indicators are imputed based on a corresponding two-component mixture model. The approach is amenable to asymptotic inference. Simulation studies and a case study highlight the importance of accounting for linkage uncertainty and demonstrate the effectiveness of the proposed approach.

In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods in linear regression under the squared loss, for every covariance and every signal. This result enables us, for a given linear regression problem, to define a pre-order on the set of spectral methods according to their convergence rates, thereby characterizing which spectral algorithm is superior for that specific problem. Furthermore, this allows us to generalize the saturation effect proposed in inverse problems and to provide necessary and sufficient conditions for its occurrence. Our method also shows that, under broad conditions, any spectral algorithm cannot overcome the barrier of the information exponent in problems such as single-index learning.

We propose a procedure for sparse regression with pairwise interactions, by generalizing the Univariate Guided Sparse Regression (UniLasso) methodology. A central contribution is our introduction of TripletScan, which screens a pair $(j,k)$ using the coefficient of $X_jX_k$ in the local regression of the response on $1$, $X_j$, $X_k$, and $X_jX_k$. The retained products are incorporated either jointly with the main effects through UniLasso, yielding uniPairs, or after a first-stage main-effects fit, yielding uniPairs-2stage. For the UniLasso components of the procedures, we prove false-positive exclusion and uniform coefficient-error bounds. In simulations and an HIV drug-resistance application, the proposed procedures produce substantially smaller fitted models than competing interaction methods while retaining competitive predictive performance.

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on SINDy-type algorithms. STLS is an algorithm to solve the $\ell_0$ sparse least-squares problem, which relies on splitting to efficiently solve the least-squares portion while handling the sparse term via proximal methods. It produces coefficient vectors whose components depend on both the projected reconstruction errors, here referred to as the scores, and the mutual coherence of dictionary terms. The first contribution of this work is a theoretical analysis of the score and dictionary-selection strategy. This could be understood in both the original and weak SINDy regime. Second, numerical experiments on ordinary and partial differential equations highlight the effectiveness of score-based screening, improving both accuracy and interpretability in dynamical system identification. These results suggest that integrating score-guided methods to refine the dictionary more accurately may help SINDy users in some cases to enhance their robustness for data-driven discovery of governing equations.

Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However, their flexibility comes with the drawback of a high-dimensional parameter space. To tackle this problem, truncated vine copulas were introduced by Kurowicka (2010) (Gaussian case) and Brechmann and Czado (2013) (general case). Truncated vine copulas contain conditionally independent pair copulas after the truncation level. So far, in the general case, truncated vine constructing algorithms started from the lowest tree in order to encode the largest dependences in the lower trees. The novelty of this paper starts from the observation that a truncated vine is determined by the first tree after the truncation level (see Kovács and Szántai (2017)). This paper introduces a new score for fitting truncated vines to given data, called the Weight of the truncated vine. Then we propose a completely new methodology for constructing truncated vines. We prove theorems which motivate this new approach. While earlier algorithms did not use conditional independences, we give algorithms for constructing and encoding truncated vines which do exploit them. Finally, we illustrate the algorithms on real datasets and compare the results with well-known methods included in R packages. Our method generally compare favorably to previously known methods.

Wu [10] proposed a method for constructing two-level supersaturated designs by using a Hadamard design with n runs and n-1 columns as a staring design and by supplementing it with two-column interactions, as long as they are partially aliased. Bulutoglu and Cheng [2] proved that this method results in E(s^2)-optimal supersaturated designs when certain interaction columns are selected. In this paper, we extend these results and prove E(s^2)-optimality for supersaturated designs that are constructed using Wu's method when the starting design is any orthogonal array with n runs and n-1, n-2 or n-3 columns, as long as its main effects and two-column interactions are partially aliased with two-column interactions.

In population genetics, there is often interest in inferring selection coefficients. This task becomes more challenging if multiple linked selected loci are considered simultaneously. For such a situation, we propose a novel generalized Bayesian framework where we compute a scoring rule posterior for the selection coefficients in multi-locus temporal population genetics models. As we consider trajectories of allele frequencies over time as our data, we choose to use a signature kernel scoring rule - a kernel scoring rule defined for high-dimensional time-series data using iterated path integrals of a path (called signatures). We can compute an unbiased estimate of the signature kernel score using model simulations. This enables us to sample asymptotically from the signature kernel scoring rule posterior of the selection coefficients using pseudo-marginal MCMC-type algorithms. Through a simulation study, we were able to show the inferential efficacy of our method compared to existing benchmark methods for two and three selected locus scenarios under the standard Wright-Fisher model with recombination and selection. We also consider a negative frequency-dependent selection model for one and two locus scenarios, and also joint inference of selection coefficients and initial haplotype frequencies under the standard Wright-Fisher model. Finally, we illustrate the application of our inferential method for two real-life dataset. More specifically, we consider a data set on Yeast, as well as data from an Evolve and Resequence (E&R) experiment on Drosophila simulans.

Privacy-preserving data analysis has become a central challenge in modern statistics. At the same time, a long-standing goal in statistics is the development of adaptive procedures – methods that achieve near-optimal performance across diverse function classes without prior knowledge of underlying smoothness or complexity. While adaptation is often achievable at no extra cost in the classical non-private setting, this naturally raises a fundamental question: to what extent is adaptation still possible under privacy constraints? We address this question in the context of density estimation under federated differential privacy (FDP), a framework that encompasses both central and local DP models. We establish sharp results that characterize the cost of adaptation under FDP for both global and pointwise estimation, revealing fundamental differences from the non-private case. We then propose an adaptive FDP estimator that achieves explicit performance guarantees by introducing a new noise mechanism, enabling one-shot adaptation via post-processing. This approach strictly improves upon existing adaptive DP methods. Finally, we develop new lower bound techniques that capture the limits of adaptive inference under privacy and may be of independent interest beyond this problem. Our findings reveal a sharp contrast between private and non-private settings. For global estimation, where adaptation can be achieved for free in the classical non-private setting, we prove that under FDP an intrinsic adaptation cost is unavoidable. For pointwise estimation, where a logarithmic penalty is already known to arise in the non-private setting, we show that FDP introduces an additional logarithmic factor, thereby compounding the cost of adaptation. Taken together, these results provide the first rigorous characterization of the adaptive privacy-accuracy trade-off.