Papers

Hypertension is a highly prevalent condition and a major risk factor for cardiovascular disease. The landmark Systolic Blood Pressure Intervention Trial (SPRINT) showed that lowering systolic blood pressure (BP) goals from 140 mmHg to 120 mmHg leads to significantly reduced BP, cardiovascular mortality, and morbidity. However, the underlying mechanisms are not yet fully elucidated. In patients with impaired renal function, early reduction of albuminuria has been proposed as a potential mediation pathway. Evidence from the standard causal mediation analysis (CMA), however, yields inconsistent results, possibly due to heterogeneous mediation effects across individuals. To disseminate the heterogeneity, a new framework that incorporates covariate-treatment and mediator-treatment interactions within a linear structural equation modeling system is introduced. Causal assumptions are discussed and heterogeneous natural direct and indirect effects are parameterized as functions of patient characteristics. A modified covariate approach is proposed to relax the hierarchical constraints and the generalized lasso regularization is employed to ensure parsimony in high-dimensional settings. Asymptotic properties are studied. Simulation studies demonstrate good estimation and inference performance. Analysis of the SPRINT data reveals substantial heterogeneity in mediation effects, identifying a subset of patients who stand to gain from therapies targeting albuminuria.

In genomics, differential abundance and expression analyses are complicated by the compositional nature of sequence count data, which reflect only relative-not absolute-abundances or expression levels. Many existing methods attempt to address this limitation through data normalizations, but we have shown that such approaches imply strong, often biologically implausible assumptions about total microbial load or total gene expression. Even modest violations of these assumptions can inflate Type I and Type II error rates to over 70%. Sparse estimators have been proposed as an alternative, leveraging the assumption that only a small subset of taxa (or genes) change between conditions. However, we show that current sparse methods suffer from similar pathologies because they treat sparsity assumptions as fixed and ignore the uncertainty inherent in these assumptions. We introduce a sparse Bayesian Partially Identified Model (PIM) that addresses this limitation by explicitly modeling uncertainty in sparsity assumptions. Our method extends the Scale-Reliant Inference (SRI) framework to the sparse setting, providing a principled approach to differential analysis under scale uncertainty. We establish theoretical consistency of the proposed estimator and, through extensive simulations and real data analyses, demonstrate substantial reductions in both Type I and Type II errors compared to existing methods.

The proximal causal inference framework enables the identification and estimation of causal effects in the presence of unmeasured confounding by leveraging two disjoint sets of observed strong proxies: negative control treatments and negative control outcomes. In the point exposure setting, this framework has primarily been applied to estimands comparing counterfactual outcomes under a static fixed intervention or, possibly randomized, regime that depends on baseline covariates. For continuous exposures, alternative hypothetical scenarios can enrich our understanding of causal effects, such as those where each individual receives their observed treatment dose modified in a pre-specified manner - commonly referred to as modified treatment regimes. In this work, we extend the proximal causal inference framework to identify and estimate the mean outcome under a modified treatment regime, addressing this gap in the literature. We propose a flexible strategy that does not rely on the assumption that all confounders have been measured - unlike existing estimators - and leverages modern debiased machine learning techniques using non-parametric estimators of nuisance functions to avoid restrictive parametric assumptions. Our methodology was motivated by immunobridging studies of COVID-19 vaccines aimed at identifying correlates of protection, where the individual's underlying immune capacity is an important unmeasured confounder. We demonstrate its applicability using data from such a study and evaluate its finite-sample performance through simulation studies.

Debiased inference for high-dimensional regression models has received substantial recent attention to ensure regularized estimators have valid inference. Many existing methods focus on achieving Neyman orthogonality through explicitly constructing projections onto the space of nuisance parameters, which is infeasible when an explicit form of the projection is unavailable. We introduce a general debiasing framework, Debiased Profile $M$-Estimation (DPME), which applies to a broad class of models and does not require model-specific Neyman orthogonalization or projection derivations as in existing methods. Our approach begins with obtaining an initial estimator of the parameters by optimizing a penalized objective function. To correct for the bias introduced by penalization, we construct a one-step estimator using the Newton–Raphson update, applied to the gradient of a profile function defined as the optimal objective function with the parameter of interest held fixed. We use numerical differentiation without requiring explicit calculation of the gradients. The resulting DPME estimator is shown to be asymptotically linear and normally distributed. Through extensive simulations, we demonstrate that the proposed method achieves better coverage rates than existing alternatives with largely reduced computational cost. Finally, we illustrate the utility of our method by applying it to estimate a treatment rule for multiple myeloma.

Explainable machine learning techniques have gained increasing attention in engineering applications, especially in aerospace design and analysis, where understanding how input variables influence data-driven models is essential. Partial Dependence Plots (PDPs) are widely used for interpreting black-box models by showing the average effect of an input variable on the prediction. However, their global sensitivity metric can be misleading when strong interactions are present, as averaging tends to obscure interaction effects. To address this limitation, we propose a global sensitivity metric based on Individual Conditional Expectation (ICE) curves. The method computes the expected feature importance across ICE curves, along with their standard deviation, to more effectively capture the influence of interactions. We provide a mathematical proof demonstrating that the PDP-based sensitivity is a lower bound of the proposed ICE-based metric under truncated orthogonal polynomial expansion. In addition, we introduce an ICE-based correlation value to quantify how interactions modify the relationship between inputs and the output. Comparative evaluations were performed on three cases: a 5-variable analytical function, a 5-variable wind-turbine fatigue problem, and a 9-variable airfoil aerodynamics case, where ICE-based sensitivity was benchmarked against PDP, SHapley Additive exPlanations (SHAP), and Sobol' indices. The results show that ICE-based feature importance provides richer insights than the traditional PDP-based approach, while visual interpretations from PDP, ICE, and SHAP complement one another by offering multiple perspectives.

In Data Science, entities are typically represented by single valued measurements. Symbolic Data Analysis extends this framework to more complex structures, such as intervals and histograms, that express internal variability. We propose an extension of multiclass Fisher's Discriminant Analysis to interval-valued data, using Moore's interval arithmetic and the Mallows' distance. Fisher's objective function is generalised to consider simultaneously the contributions of the centres and the ranges of intervals and is numerically maximised. The resulting discriminant directions are then used to classify interval-valued observations.To support visual assessment, we adapt the class map, originally introduced for conventional data, to classifiers that assign labels through minimum distance rules. We also extend the silhouette plot to this setting and use stacked mosaic plots to complement the visual display of class assignments. Together, these graphical tools provide insight into classifier performance and the strength of class membership. Applications to real datasets illustrate the proposed methodology and demonstrate its value in interpreting classification results for interval-valued data.

Transforming bi-dimensional sets of image pixels into mono-dimensional sequences with a Peano scan (PS) is an established technique enabling the use of hidden Markov chains (HMCs) for unsupervised image segmentation. Related Bayesian segmentation methods can compete with hidden Markov fields (HMFs)-based ones and are much faster. PS has recently been extended to the contextual PS, and some initial experiments have shown the value of the associated HMC model, denoted as HMC-CPS, in image segmentation. Moreover, HMCs have been extended to hidden evidential Markov chains (HEMCs), which are capable of improving HMC-based Bayesian segmentation. In this study, we introduce a new HEMC-CPS model by simultaneously considering contextual PS and evidential HMC. We show its effectiveness for Bayesian maximum posterior mode (MPM) segmentation using synthetic and real images. Segmentation is performed in an unsupervised manner, with parameters being estimated using the stochastic expectation–maximization (SEM) method. The new HEMC-CPS model presents potential for the modeling and segmentation of more complex images, such as three-dimensional or multi-sensor multi-resolution images. Finally, the HMC-CPS and HEMC-CPS models are not limited to image segmentation and could be used for any kind of spatially correlated data.

We consider the distribution of the top eigenvector $\widehat{v}$ of a spiked matrix model of the form $H = \theta vv^* + W$, in the supercritical regime where $H$ has an outlier eigenvalue of comparable magnitude to $\|W\|$. We show that, if $v$ is sufficiently delocalized, then the distribution of the individual entries of the projector $\widehat{v}\widehat{v}^*$ (not, we emphasize, merely the inner product $|\langle \widehat{v}, v\rangle|^2$) is universal over a large class of generalized Wigner matrices $W$ having independent entries, depending only on the first two moments of the distributions of the entries of $W$. This complements the observation of Capitaine and Donati-Martin (2021) that these distributions are not universal when $v$ is instead sufficiently localized. Further, for $W$ having entrywise variances close to constant and thus resembling a Wigner matrix, we show by comparing to $W$ drawn from the Gaussian orthogonal or unitary ensembles that averages of entrywise functions of $\widehat{v}\widehat{v}^*$ behave as they would if $\widehat{v}$ had Gaussian fluctuations around a suitable multiple of $v$. We also establish such results for several possibly dependent spiked matrices, showing that, if such matrices are entrywise uncorrelated, then their leading eigenvectors behave as they would with independent Gaussian fluctuations. We apply these results to spectral algorithms with rounding procedures for synchronization problems over the cyclic and circle groups, obtaining the first precise asymptotic error rates for such algorithms. Using our analysis of multiple spiked matrices, we also show that multi-frequency spectral algorithms using estimates from several matrices often have asymptotic error rate superior to that of naive spectral algorithms using just one matrix.

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets with correct conditional coverage, leaving practitioners without a clear way to interpret local deviations. To overcome sample-inefficiency and overfitting issues of existing metrics, we cast conditional coverage estimation as a classification problem. Conditional coverage is violated if and only if some classifier can achieve lower risk than the target coverage. Through the choice of a (proper) loss function, the resulting risk difference gives a conservative estimate of natural miscoverage measures such as L1 and L2 distance, and can even separate the effects of over- and under-coverage, and non-constant target coverages. We call the resulting family of metrics excess risk of the target coverage (ERT). We show experimentally that the use of modern classifiers provides much higher statistical power than simple classifiers underlying established metrics like CovGap. Additionally, we use our metric to benchmark different conformal prediction methods. Finally, we release an open-source package for ERT as well as previous conditional coverage metrics. Together, these contributions provide a new lens for understanding, diagnosing, and improving the conditional reliability of predictive systems.

Spectral clustering is a popular tool in network data analysis, with applications in a variety of scientific application areas. However, many studies have shown that classical spectral clustering does not perform well on certain network structures, particularly core-periphery networks. To improve clustering performance in core-periphery structures, Adjacency Spectral Embedding (ASE) has been introduced, which performs clustering via a network's adjacency matrix instead of the graph Laplacian. Despite its advantages in this setting, the optimal performance of ASE is limited to dense networks, whilst network data observed in practice is often sparse in nature. To address this limitation, we propose a new approach which we term Doubled Adjacency Spectral Embedding (DASE), motivated by the observation that the squared adjacency matrix will leverage the fewer connections in sparse structures more efficiently in clustering applications. Theoretical results establish that the resulting clustering algorithm enjoys good consistency properties when determining sparse community structure. The performance and general applicability of the proposed method is evaluated using extensive simulations on both directed and undirected networks. Our results highlight the improved clustering performance on both sparse and dense networks in the presence of core-periphery structures. We illustrate our proposed technique on real-world employment and transportation datasets.

Data integration often requires aligning datasets without unique identifiers; for network data this is commonly addressed through graph matching. Despite the widespread availability of node and edge covariates in many applications, most existing methods rely solely on the structural similarity between the two graphs, limiting their flexibility and robustness to non-identifiable matches and structural noise. In this article, we study the seeded graph matching problem, where a partial alignment for a set of nodes (seeds) is known, in the presence of informative node and edge covariates. We propose two covariate-assisted methods: a global approach based on a quadratic assignment problem (QAP), and a scalable local approach that leverages the neighborhood of the seeds. Both methods are based on a flexible conditional modeling framework that enables covariate integration using predictive models ranging from generalized linear models to machine learning methods. We provide estimation error rates for the generalized linear model, and sufficient conditions for exact recovery of the true correspondences via the QAP. We further specialize these results to Erdős-Rényi model with covariates. The effectiveness in achieving improved performance by leveraging additional covariates is demonstrated through simulations and in an application to matching the statistics academic genealogy and the collaboration networks.

While balancing covariates between groups is central for observational causal inference, selecting which features to balance remains a challenging problem. Kernel balancing is a promising approach that first estimates a kernel that captures similarity across units and then balances a (possibly low-dimensional) summary of that kernel, indirectly learning important features to balance. In this paper, we propose forest kernel balancing, which leverages the underappreciated fact that tree-based machine learning models, namely random forests and Bayesian additive regression trees (BART), implicitly estimate a kernel based on the co-occurrence of observations in the same terminal leaf node. Thus, even though the resulting kernel is solely a function of baseline features, the selected nonlinearities and other interactions are important for predicting the outcome – and therefore are important for addressing confounding. Through simulations and applied illustrations, we show that forest kernel balancing leads to meaningful computational and statistical improvement relative to standard kernel methods, which do not incorporate outcome information when learning features.

Spatial transcriptomics technologies enable the measurement of gene expression with spatial context, providing opportunities to understand how gene regulatory networks vary across tissue regions. However, existing graphical models focus primarily on undirected graphs or directed acyclic graphs, limiting their ability to capture feedback loops that are prevalent in gene regulation. Moreover, ensuring the so-called stability condition of cyclic graphs, while allowing graph structures to vary continuously with spatial covariates, presents significant statistical and computational challenges. We propose BNP-DCGx, a Bayesian nonparametric approach for learning spatially varying gene regulatory networks via covariate-dependent directed cyclic graphical models. Our method introduces a covariate-dependent random partition as an intermediary layer in a hierarchical model, which discretizes the covariate space into clusters with cluster-specific stable directed cyclic graphs. Through partition averaging, we obtain smoothly varying graph structures over space while maintaining theoretical guarantees of stability. We develop an efficient parallel tempered Markov chain Monte Carlo algorithm for posterior inference and demonstrate through simulations that our method accurately recovers both piecewise constant and continuously varying graph structures. Application to spatial transcriptomics data from human dorsolateral prefrontal cortex reveals spatially varying regulatory networks with feedback loops, identifies potential cell subtypes within established cell types based on distinct regulatory mechanisms, and provides new insights into spatial organization of gene regulation in brain tissue.

The Automatic Identification System (AIS) provides time stamped vessel positions and kinematic reports that enable maritime authorities to monitor traffic. We consider the problem of relabeling AIS trajectories when vessel identifiers are missing, focusing on a challenging nationwide setting in which tracks are heavily downsampled and span diverse operating environments across continental U.S. waters. We propose a hybrid pipeline that first applies a physics-based screening step to project active track endpoints forward in time and select a small set of plausible ancestors for each new observation. A supervised neural classifier then chooses among these candidates, or initiates a new track, using engineered space time and kinematic consistency features. On held out data, this approach improves posit accuracy relative to unsupervised baselines, demonstrating that combining simple motion models with learned disambiguation can scale vessel relabeling to heterogeneous, high volume AIS streams.

We introduce a method for approximating posterior probabilities of phylogenetic trees and reconstructing ancestral sequences under models of sequence evolution with site-dependence, where standard phylogenetic likelihood computations (pruning) fail. Our approach uses a combined data-augmentation and importance sampling scheme. A key advantage of our approach is the ability to leverage existing highly optimized phylogenetic software. We apply our approach to the reconstruction of B cell receptor affinity maturation lineages from high-throughput repertoire sequencing data and evaluate the impact of incorporating site-dependence on the reconstruction accuracy of both trees and ancestral sequences. We show that accounting for context-dependence during inference always improves the estimates of both ancestral sequences and lineage trees on simulated datasets. We also examine the impact of incorporating priors based on VDJ recombination models, and find that they significantly improve ancestral sequence reconstruction in germline-encoded regions, but increase errors in non-templated nucleotides. We propose a modified, piecewise prior to address this demonstrate that it improves empirical reconstruction accuracy. We apply our approach to the analysis of the HIV broadly neutralizing antibodies DH270 and CH235 which are important targets of current vaccine design efforts.

Why are some neighborhoods strongly connected while others remain isolated? Although standard explanations focus on demographics, economics, and geography, movement across the city may also depend on cultural styles and amenity mix. This study proposes a relational, cross-national model in which local culture and amenity mix alignment creates a "soft infrastructure" of urban mobility, i.e., symbolic cues and functional features that shape expectations about the character of places. Using ~650 million Google Places reviews to measure co-visitation between U.S. ZIP codes and ~30 million Canadian change-of-address to track residential mobility, results show that neighborhoods with similar cultural styles and amenities are significantly more connected. These effects persist even after controlling for race, income, education, politics, housing costs, and distance. Urban cohesion and segregation depend not only on who lives where or how far apart neighborhoods are, but on the shared cultural and material ecologies that structure movement across the city.

This article proposes a unified framework for portfolio optimization (PO), recognizing an object called the `gain probability density function (PDF)' as the fundamental object of the problem from which any objective function could be derived. The gain PDF has the advantage of being 1-dimensional for any given portfolio and thus is easy to visualize and interpret. The framework allows us to naturally incorporate all existing approaches (Markowitz, CVaR-deviation, higher moments...) and represents an interesting basis to develop new approaches. It leads us to propose a method to directly match a target PDF defined by the portfolio manager, giving them maximal control on the PO problem and moving beyond approaches that focus only on expected return and risk. As an example, we develop an application involving a new objective function to control high profits, to be applied after a conventional PO (including expected return and risk criteria) and thus leading to sub-optimality w.r.t. the conventional objective function. We then propose a methodology to quantify a cost associated with this optimality deviation in a common budget unit, providing a meaningful information to portfolio managers. Numerical experiments considering portfolios with energy-producing assets illustrate our approach. The framework is flexible and can be applied to other sectors (financial assets, etc).

We introduce the Dynamic Conditional SKEPTIC (DCS), a semiparametric approach for efficiently and robustly estimating time-varying correlations in multivariate models. We exploit nonparametric rank-based statistics, namely Spearman's rho and Kendall's tau, to estimate the unknown correlation matrix and discuss the stationarity, beta- and rho- mixing conditions of the model. We illustrate the methodology by estimating the time-varying conditional correlation matrix of the stocks included in the S&P100 and S&P500 during the period from 02/01/2013 to 23/01/2025. The results show that DCS improves diagnostic checks compared to the classical Dynamic Conditional Correlation (DCC) models, providing uncorrelated and normally distributed residuals. A risk management application shows that global minimum variance portfolios estimated using the DCS model exhibit lower turnover than those based on the DCC and DCC-NL models, while also achieving higher Sharpe ratios for portfolios constructed from S&P 100 constituents.

Conventional ideal point models rely on Gaussian or quadratic utility functions that violate the triangle inequality, producing non-metric distances that complicate geometric interpretation and undermine clustering and dispersion-based analyses. We introduce a distance-based alternative that adapts the Latent Space Item Response Model (LSIRM) to roll-call data, treating legislators and bills as nodes in a bipartite network jointly embedded in a Euclidean metric space. Through controlled simulations, Euclidean LSIRM consistently recovers latent coalition structure with superior cluster separation relative to existing methods. Applied to the 118th U.S. House, the model provides competitive predictive performance while yielding bill embeddings that clarify cross-cutting issue alignments. The results show that restoring metric structure to ideal point estimation provides a clearer and more coherent inference about party cohesion, factional divisions, and multidimensional legislative behavior.

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based method originally developed for time series, we introduce two test statistics, one based on Gini's mean difference and a novel variance-based variant. Under mild moment conditions, we derive asymptotic normality of the variance-based statistic and prove its consistency against almost all non-constant mean functions (in a sense of positive Lebesgue measure). To accommodate spatial dependence, we modify our procedures for M-dependent data and we further develop a de-correlation algorithm based on estimated autocovariances. Monte Carlo simulations demonstrate that the tests maintain appropriate size and power for both independent and dependent data. In an application to satellite images, especially our variance-based test reliably detects regions undergoing deforestation.

Evaluating the health effects of complex environmental mixtures remains a central challenge in environmental health research. Existing approaches vary in their flexibility, interpretability, scalability, and support for diverse outcome types, often limiting their utility in real-world applications. To address these limitations, we propose a neural network-based partial-linear single-index (NeuralPLSI) modeling framework that bridges semiparametric regression modeling interpretability with the expressive power of deep learning. The NeuralPLSI model constructs an interpretable exposure index via a learnable projection and models its relationship with the outcome through a flexible neural network. The framework accommodates continuous, binary, and time-to-event outcomes, and supports inference through a bootstrap-based procedure that yields confidence intervals for key model parameters. We evaluated NeuralPLSI through simulation studies under a range of scenarios and applied it to data from the National Health and Nutrition Examination Survey (NHANES) to demonstrate its practical utility. Together, our contributions establish NeuralPLSI as a scalable, interpretable, and versatile modeling tool for mixture analysis. To promote adoption and reproducibility, we release a user-friendly open-source software package that implements the proposed methodology and supports downstream visualization and inference (https://github.com/hyungrok-do/NeuralPLSI).

Several frameworks have been proposed for studying causal mediation analysis. What these frameworks have in common is that they all make assumptions for point identifications that can be violated even when treatment is randomized. When a causal effect is not point-identified, one can sometimes derive bounds, i.e. a range of possible values that are consistent with the observed data. In this work, we study causal bounds for mediation effects under both the natural effects framework and the separable effects framework. In particular, we show that when there are unmeasured confounders for the intermediate variables(s) the sharp symbolic bounds on separable (in)direct effect coincide with existing bounds for natural (in)direct effects in the analogous setting. We compare these bounds to valid bounds for the natural direct effects when only the cross-world independence assumption does not hold. Furthermore, we demonstrate the use and compare the results of the bounds on data from a trial investigating the effect of peanut consumption on the development of peanut allergy in infants through specific pathways of measured immunological biomarkers.

Time series forecasting predicts future values from past data. In real-world settings, some anomalous events have lasting effects and influence the forecast, while others are short-lived and should be ignored. Standard forecasting models fail to make this distinction, often either overreacting to noise or missing persistent shifts. We propose Co-TSFA (Contrastive Time Series Forecasting with Anomalies), a regularization framework that learns when to ignore anomalies and when to respond. Co-TSFA generates input-only and input-output augmentations to model forecast-irrelevant and forecast-relevant anomalies, and introduces a latent-output alignment loss that ties representation changes to forecast changes. This encourages invariance to irrelevant perturbations while preserving sensitivity to meaningful distributional shifts. Experiments on the Traffic and Electricity benchmarks, as well as on a real-world cash-demand dataset, demonstrate that Co-TSFA improves performance under anomalous conditions while maintaining accuracy on normal data. An anonymized GitHub repository with the implementation of Co-TSFA is provided and will be made public upon acceptance.

In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating posterior density values as probability masses at pre-specified support points. The resulting discrete distribution can be a good approximation to the target posterior distribution. All posterior quantities, including means, standard deviations, and quantiles, can be approximated by those of this completely known discrete distribution. We establish the convergence rate of discretization approximation as the number of support points goes to infinity. If the support points are generated from quasi-Monte Carlo sequences, then the rate is actually the same as that in integration approximation, generally faster than the optimal statistical rate. In this sense, discretization approximation is superior to the popular Markov chain Monte Carlo method. We also provide random sampling and representation point construction methods from discretization approximation. Numerical examples including some benchmarks demonstrate that the proposed method performs quite well for both low-dimensional and high-dimensional cases.

Post-marketing pharmacovigilance is essential for identifying adverse drug reactions (ADRs) that elude detection during pre-marketing clinical trials. This study explores a novel approach that integrates an adverse event (AE) ontology into a zero-inflated negative binomial model to improve ADR detection. By accounting for the biological similarities among correlated AEs and addressing the excess of zero counts, this method more effectively disentangles AE associations. Statistical significance is evaluated using a permutation-based maximum statistic that preserves AE correlations within individual reports. Simulations and an application to real data from the Veneto drug safety database demonstrate that the ontology-based model consistently outperforms classical models such as the Gamma-Poisson Shrinker (GPS). For post-selection inference, we furthermore explore a data thinning technique for convolution-closed families, enabling the creation of independent training and validation datasets while retaining all drug-AE pairs. This approach is compared with conventional random train/test splitting, which may leave some drugs or AEs absent from one subset, and stratified splitting, which requires expanding aggregated counts into individual instances. The data-thinning technique and stratified splitting yield very similar results, with stratified splitting showing a slight benefit, and both clearly outperform random splitting in ensuring reliable and consistent model evaluation.

Clustering is a fundamental unsupervised learning task for uncovering patterns in data. While Gaussian Blurring Mean Shift (GBMS) has proven effective for identifying arbitrarily shaped clusters in Euclidean space, it struggles with datasets exhibiting hierarchical or tree-like structures. In this work, we introduce HypeGBMS, a novel extension of GBMS to hyperbolic space. Our method replaces Euclidean computations with hyperbolic distances and employs Möbius-weighted means to ensure that all updates remain consistent with the geometry of the space. HypeGBMS effectively captures latent hierarchies while retaining the density-seeking behavior of GBMS. We provide theoretical insights into convergence and computational complexity, along with empirical results that demonstrate improved clustering quality in hierarchical datasets. This work bridges classical mean-shift clustering and hyperbolic representation learning, offering a principled approach to density-based clustering in curved spaces. Extensive experimental evaluations on $11$ real-world datasets demonstrate that HypeGBMS significantly outperforms conventional mean-shift clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.

The study of dependence between random variables under external influences is a challenging problem in multivariate analysis. We address this by proposing a novel semi-parametric approach for conditional copula models using Bayesian additive regression trees (BART) models. BART is becoming a popular approach in statistical modelling due to its simple ensemble type formulation complemented by its ability to provide inferential insights. Although BART allows us to model complex functional relationships, it tends to suffer from overfitting. In this article, we exploit a loss-based prior for the tree topology that is designed to reduce the tree complexity. In addition, we propose a novel adaptive Reversible Jump Markov Chain Monte Carlo algorithm that is ergodic in nature and requires very few assumptions allowing us to model complex and non-smooth likelihood functions with ease. Moreover, we show that our method can efficiently recover the true tree structure and approximate a complex conditional copula parameter, and that our adaptive routine can explore the true likelihood region under a sub-optimal proposal variance. Lastly, we provide case studies concerning the effect of gross domestic product on the dependence between the life expectancies and literacy rates of the male and female populations of different countries.

High-dimensional multivariate time series are common in many scientific and industrial applications, where the interest lies in identifying key dependence structure within the data for subsequent analysis tasks, such as forecasting. An important avenue to achieve this is through the estimation of the conditional independence graph via graphical models, although for time series data settings the underpinning temporal dependence can make this task challenging. In this article, we propose a novel wavelet domain technique that allows the data-driven inference of the (sparse) conditional independence graph of a high-dimensional stationary multivariate time series. By adopting the locally stationary wavelet modelling framework, we repose the estimation problem as a well-principled wavelet domain graphical lasso formulation. Theoretical results establish that our associated estimation scheme enjoys good consistency properties when determining sparse dependence structure in input time series data. The performance of the proposed method is illustrated using extensive simulations and we demonstrate its applicability on a real-world dataset representing hospitalisations of COVID-19 patients.

Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting – two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. First, we introduce the resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. Following this, we introduce the resource theory that arises naturally when one has uncertainty about the functional dependence. We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, and we provide an interpretation of each.