Papers

Event history data from sports competitions have recently drawn increasing attention in sports analytics to generate data-driven strategies. Such data often exhibit self-excitation in the event occurrence and dependence within event clusters. The conventional event models based on gap times may struggle to capture those features. In particular, while consecutive events may occur within a short timeframe, the self-excitation effect caused by previous events is often transient and continues for a period of uncertain time. This paper introduces an extended Hawkes process model with random self-excitation duration to formulate the dynamics of event occurrence. We present examples of the proposed model and procedures for estimating the associated model parameters. We employ the collection of the corner kicks in the games of the 2019 regular season of the Chinese Super League to motivate and illustrate the modeling and its usefulness. We also design algorithms for simulating the event process under proposed models. The proposed approach can be adapted with little modification in many other research fields such as Criminology and Infectious Disease.

Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high dimensionality due to the number of free covariance parameters. This study introduces a spatial covariance constraint for Gaussian mixture models that requires only four free parameters for each component, independent of dimensionality. Using a coordinate system, the spatially constrained Gaussian mixture model enables clustering of multi-way spatial data and inference of spatial patterns. The parameter estimation is conducted by combining the expectation-maximization (EM) algorithm with the generalized least squares (GLS) estimator. Simulation studies and applications to Raman spectroscopy data are provided to demonstrate the proposed model.

In the post-pandemic era of COVID-19, hospitalization remains a primary public health concern and wastewater surveillance has become an important tool for monitoring its dynamics at the level of community. However, there is usually no sufficient information to know the infection process that results in both wastewater viral signals and hospital admissions. That key challenge has motived a statistical framework proposed in this paper. We formulate the connection of overtime wastewater viral signals and hospitalization counts through a latent process of infection at the level of individual subject. We provide a strategy for accommodating aggregated data, a typical form of surveillance data. Moreover, we ease the conventional procedure of the statistical learning with the joint modeling using available information on the infection process, which can be under-reporting. A simulation study demonstrates that the proposed approach yields stable inference under different degrees of under-ascertainment. The COVID-19 surveillance data from Ottawa, Canada shows that the framework recovers coherent temporal patterns in infection prevalence and variant-specific hospitalization risk under several reporting assumptions.

Predicting treatment non-response for anxiety and depression is challenging, in part because of sparse symptom assessments in real-world care. We examined whether passively captured, fine-grained emotions serve as linguistic markers of treatment outcomes by analyzing 12 weeks of de-identified teletherapy transcripts from 12,043 U.S. patients with moderate-to-severe anxiety and depression symptoms. A transformer-based small language model extracted patients' emotions at the talk-turn level; a state-space model (VISTA-SSM) clustered subgroups based on emotion dynamics over time and produced temporal networks. Two groups emerged: an improving group (n=8,230) and a non-response group (n=3,813) showing increased odds of symptom deterioration, and lower likelihood of clinically significant improvement. Temporal networks indicated that sadness and fear exerted most influence on emotion dynamics in non-responders, whereas improving patients showed balanced joy, sadness, and neutral expressions. Findings suggest that linguistic markers of emotional inflexibility can serve as scalable, interpretable, and theoretically grounded indicators for treatment risk stratification.

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems. The recent success of deep neural networks and foundation models has now given rise to a new paradigm in statistical modeling, in which Bayesian inference can be amortized through large-scale learned predictors. In amortized inference, substantial computation is required at the beginning to train a neural network, but it can subsequently produce approximate posteriors or predictions at much lower computational cost across a wide range of tasks. While the typical Bayesian inference procedures are computationally expensive due to repeated likelihood calculations and Monte Carlo steps for each new dataset, amortized inference provides a much lower computational cost at deployment. Despite the growing popularity of amortized inference, its statistical interpretation and position within Bayesian inference remain poorly explored. In this paper, we present a statistical perspective on several major neural architectures, including feedforward networks, Deep Sets, and Transformers, and examine how they naturally support amortized Bayesian inference. We explore how these models perform structured approximation and also probabilistic reasoning in ways that yield controlled generalization error throughout a wide range of deployment scenarios, and how these properties can be harnessed for Bayesian computation. Via simulation studies, we evaluate the accuracy, robustness, and uncertainty quantification of amortized inference across varying sample sizes, varying noise distributional families, varying sparsity levels, and multimodality, highlighting its strengths and limitations.

Decentralized online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time-and agent-varying feedback delays. While recent work has addressed this problem (Nguyen et al., 2024), existing algorithms assume prior knowledge of the total delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of O N $\sqrt$ d tot + N $\sqrt$ T (1-$\sigma$2) 1/4 , where T is the total horizon, d tot denotes the average total delay across agents, N is the number of agents, and 1 -$\sigma$ 2 is the spectral gap of the network. Our approach builds upon recent advances in D-OCO (Wan et al., 2024a), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive a sharper regret bound of O N $\delta$max ln T $\alpha$ , where $\alpha$ is the strong convexity parameter and $\delta$ max is the maximum number of missing observations averaged over agents. We also show that our upper bounds for both settings are tight up to logarithmic factors. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field.

Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using THRML (Thermodynamic HypergRaphical Model Library), a JAX-based library for building and sampling probabilistic graphical models that reformulates index tracking as probabilistic inference on an Ising Hamiltonian. Unlike traditional methods that seek a single optimal solution, THRML samples from the Boltzmann distribution of high-quality portfolios using GPU-accelerated block Gibbs sampling, providing natural regularization against overfitting. We implement three key innovations: (1) dynamic coupling strength that scales inversely with market volatility (VIX), adapting diversification pressure to market regimes; (2) rebalanced bias weights prioritizing tracking quality over momentum for index replication; and (3) sector-aware post-processing ensuring institutional-grade diversification. Backtesting on a 100-stock S and P 500 universe from 2023 to 2025 demonstrates that THRML achieves 4.31 percent annualized tracking error versus 5.66 to 6.30 percent for baselines, while simultaneously generating 128.63 percent total return against the index total return of 79.61 percent. The Diebold-Mariano test confirms statistical significance with p less than 0.0001 across all comparisons. These results position energy-based models as a promising paradigm for portfolio construction, bridging statistical mechanics and quantitative finance.

Many large-scale testing procedures learn signal structure from the data to boost power. Direct data reuse can inflate Type-I error ("double dipping"), so a common remedy is masking: withholding some information during learning and using it for testing. Sample splitting masks by withholding observations for testing, while null augmentation (e.g., knockoffs or full-conformal outlier detection) masks by appending null samples or variables and withholding their identities until testing. In many settings, little is known about how the power of masking methods compares across mechanisms, across tuning choices, or against more data-efficient non-masking alternatives. We study these questions in a stylized two-groups multivariate normal means model with an unknown signal direction learned from the data. Within this testbed, we develop a transparent, unified set of asymptotic power expressions for three parallel methods differing in masking choices: a sample splitting method, a full-conformal-style null augmentation method, and an oracle in-sample benchmark. Our main findings are: (1) the augmentation method is more powerful than the splitting method with matched tuning; (2) the power-optimal number of null samples for the augmentation method is a vanishing fraction of the number of tests, in which case its power approaches that of the in-sample benchmark; and (3) for a tractable approximation to the augmentation method, the optimal number of null samples scales as the square root of the number of tests, with empirical evidence suggesting a similar scaling for the method itself. These results characterize masking-induced power trade-offs in a tractable model and suggest qualitative lessons for other settings.

Estimating the Riesz representer is central to debiased machine learning, yet the generator and representer model determine which regression directions their first-order conditions protect. We introduce generalized Riesz regression, which minimizes a Bregman divergence made observable by the Riesz identity. Squared and Kullback–Leibler-type choices recover Riesz regression, tailored loss minimization, and density-ratio objectives. For any twice-differentiable generator and differentiable representer model, the first-order conditions impose empirical Riesz equations in model-dependent tangent directions. Compatibility aligns those directions with regressors chosen in advance. These equations give sharp control of the systematic Neyman error and an orthogonal-score identity under exact balance. We derive convergence rates for sparse models linear in dual coordinates, reproducing kernel Hilbert space models, and neural networks, with generator curvature entering the sparse rate. We establish asymptotic normality under Donsker conditions or nuisance estimation via cross-fitting. Applications include treatment effects, average marginal effects, and covariate shift.

Differential ethnic-based record linkage errors can bias epidemiologic estimates. Prior evidence often conflates heterogeneity in error mechanisms with unequal exposure to error. Using snapshots of the North Carolina Voter Registry (Oct 2011-Oct 2022), we derived empirical name-discrepancy profiles to parameterise realistic corruptions. From an Oct 2022 extract (n=848,566), we generated five replicate corrupted datasets under three settings that separately varied mechanism heterogeneity and exposure inequality, and linked records back to originals using unadjusted Jaro-Winkler, Term Frequency (TF)-adjusted Jaro-Winkler, and a cluster-based forename-embedding comparator combined with TF-adjusted surname comparison. We evaluated false match rate (FMR), missed match rate (MMR) and white-centric disparities. At a fixed MMR near 0.20, overall error rates and ethnic disparities diverged substantially by model under disproportionate exposure to corruption. Term-frequency (TF)-adjusted Jaro-Winkler achieved very low overall FMR (0.55% (95% CI 0.54-0.57)) at overall MMR 20.34% (20.30-20.39), but large white-centric under-linkage disparities persisted: Hispanic voters had 36.3% (36.1-36.6) and Non-Hispanic Black voters 8.6% (8.6-8.7) higher FMRs compared to Non-Hispanic White groups. Relative to unadjusted string similarity, TF adjustment reduced these disparities (Hispanic: +60.4% (60.1-60.7) to +36.3%; Black: +13.1% (13.0-13.2) to +8.6%). The cluster-based forename-embedding model reduced missed-match disparities further (Hispanic: +10.2% (9.8-10.3); Black: +0.6% (0.4-0.7)), but at a cost of increasing overall FMR (4.28% (4.22-4.35)) at the same threshold. Unequal exposure to identifier error drove substantially larger disparities than mechanism heterogeneity alone; cluster-based embeddings markedly narrowed under-linkage disparities beyond TF adjustment.

Recent advances in nonlinear shrinkage yield asymptotically optimal cleaners for large covariance matrices and have been extended to empirical cross-covariances via singular-value shrinkage. However, these approaches rely on stationarity and bounded-spectrum assumptions that are violated by real equity returns, which exhibit dependence drift and macroscopic common modes. We propose a physics-informed neural estimator that parameterizes the cleaned cross-covariance matrix in the empirical singular-vector basis and learns a nonlinear map from empirical singular values and marginal projections to cleaned singular values, recovering the cleaning performances of the analytical solution as a limiting case. On U.S. equity data, the learned correction not only improves out-of-sample cross-covariance prediction but also translates these statistical gains into better tracking-error minimization for portfolio replication. Furthermore, it remains stable in regimes where the analytical cross-covariance estimation deteriorates with universe size, suggesting an interpolation between sample-size denoising and a learned forecast correction under non-stationary dependence.

Estimating conditional means using only the marginal means available from aggregate data is known as the ecological inference problem. We reassess this literature, arguing that it has understudied two issues: how practitioners should control for confounding, and how methodologists can leverage the linearity inherent in the structure of the problem. On the former, we formalize ignorability conditions like those in causal inference and outline consistent plug-in estimators: These are credible when covariates make the ignorability condition plausible. On the latter, we show that aggregation restricts the target function to be partially linear. Such linearity clarifies the connections between King's (1997) methodology, its predecessors, and subsequent developments. That motivates a recent doubly-robust technique that enters covariates flexibly while leveraging linearity. Finally, we test these methods in datasets where the ground truth is fortuitously observed. In these common applications, all methods tested were prone to overestimating racial polarization and underestimating split-ticket voting.

This paper develops an approach for multi-step forecasting of dynamical systems by integrating probabilistic input forecasting with physics-informed output prediction. Accurate multi-step forecasting of time series systems is important for the automatic control and optimization of physical processes, enabling more precise decision-making. While mechanistic-based and data-driven machine learning (ML) approaches have been employed for time series forecasting, they face significant limitations. Incomplete knowledge of process mathematical models limits mechanistic-based direct employment, while purely data-driven ML models struggle with dynamic environments, leading to poor generalization. To address these limitations, this paper proposes a dual-level strategy for physics-informed forecasting of dynamical systems. On the first level, input variables are forecast using a hybrid method that integrates a long short-term memory (LSTM) network into probabilistic state transition models (STMs). On the second level, these stochastically predicted inputs are sequentially fed into a physics-informed neural network (PINN) to generate multi-step output predictions. The experimental results of the paper demonstrate that the hybrid input forecasting models achieve a higher log-likelihood and lower mean squared errors (MSE) compared to conventional STMs. Furthermore, the PINNs driven by the input forecasting models outperform their purely data-driven counterparts in terms of MSE and log-likelihood, exhibiting stronger generalization and forecasting performance across multiple test cases.

Outstanding claim liabilities are revised repeatedly as claims develop, yet most modern reserving models are trained as one-shot predictors and typically learn only from settled claims. We formulate individual claims reserving as a claim-level Markov decision process in which an agent sequentially updates outstanding claim liability (OCL) estimates over development, using continuous actions and a reward design that balances accuracy with stable reserve revisions. A key advantage of this reinforcement learning (RL) approach is that it can learn from all observed claim trajectories, including claims that remain open at valuation, thereby avoiding the reduced sample size and selection effects inherent in supervised methods trained on ultimate outcomes only. We also introduce practical components needed for actuarial use – initialisation of new claims, temporally consistent tuning via a rolling-settlement scheme, and an importance-weighting mechanism to mitigate portfolio-level underestimation driven by the rarity of large claims. On CAS and SPLICE synthetic general insurance datasets, the proposed Soft Actor-Critic implementation delivers competitive claim-level accuracy and strong aggregate OCL performance, particularly for the immature claim segments that drive most of the liability.

Individual-specific, time-constant, random effects are often used to model dependence and/or to account for omitted covariates in regression models for longitudinal responses. Longitudinal studies have known a huge and widespread use in the last few years as they allow to distinguish between so-called age and cohort effects; these relate to differences that can be observed at the beginning of the study and stay persistent through time, and changes in the response that are due to the temporal dynamics in the observed covariates. While there is a clear and general agreement on this purpose, the random effect approach has been frequently criticized for not being robust to the presence of correlation between the observed (i.e. covariates) and the unobserved (i.e. random effects) heterogeneity. Starting from the so-called correlated effect approach, we argue that the random effect approach may be parametrized to account for potential correlation between observables and unobservables. Specifically, when the random effect distribution is estimated non-parametrically using a discrete distribution on finite number of locations, a further, more general, solution is developed. This is illustrated via a large scale simulation study and the analysis of a benchmark dataset.

Bridge scour is a complex phenomenon combining hydrological, geotechnical and structural processes. Bridge scour is the leading cause of bridge collapse, which can bring catastrophic consequences including the loss of life. Estimating scour on bridges is an important task for engineers assessing bridge system performance. Overestimation of scour depths during design may lead to excess spendings on construction whereas underestimation can lead to the collapse of a bridge. Many empirical equations have been developed over the years to assess scour depth at bridge piers. These equations have only been calibrated with laboratory data or very few field data. This paper compares eight equations including the UK CIRIA C742 approach to establish their accuracy using the open access USGS pier-scour database for both field and laboratory conditions. A one-at-the-time sensitivity assessment and a global sensitivity analysis were then applied to identify the most significant parameters in the eight scour equations. The paper shows that using a global approach, i.e. one where all parameters are varied simultaneously, provides more insights than a traditional one-at-the-time approach. The main findings are that the CIRIA and Froehlich equations are the most accurate equations for field conditions, and that angle of attack, pier shape and the approach flow depth are the most influential parameters. Efforts to reduce uncertainty of these three parameters would maximise increase of scour estimate precision.

We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are typically viewed as less competitive than the Adaptive Sufficient Statistics Perturbation (AdaSSP) method \citep{wang_adassp}, which directly perturbs the sufficient statistics $(X^{\top}X, X^{\top}Y)$. This method was shown to be close to information-theoretically optimal, while also exhibiting strong empirical performance. In this work, we propose the Iterative Hessian Mixing (IHM), an algorithm that builds on Gaussian sketching approaches to DP-OLS and is inspired by the Iterative Hessian Sketch of \citet{pilanci_hessiansketch}. We prove that IHM is differentially private and provide utility guarantees in the form of excess empirical risk bounds. These bounds improve upon those of AdaSSP by removing a multiplicative factor that can be as large as the square root of the data dimension. The design of the IHM is based on new accuracy guarantees that we present for prior Gaussian sketching approaches for DP-OLS, which clarify when these methods are expected to perform well and how IHM circumvents their inherent limitations. We also conduct a rigorous empirical evaluation on a large suite of datasets, demonstrating that IHM consistently outperforms prior baselines, including AdaSSP.

The synthetic control method (SCM) is a widely used tool for evaluating causal effects of policy changes in panel data settings. Recent studies have extended its framework to accommodate complex outcomes that take values in metric spaces, such as distributions, functions, networks, covariance matrices, and compositional data. However, due to the lack of linear structure in general metric spaces, theoretical guarantees for estimation and inference within these extended frameworks remain underdeveloped. In this study, we propose the functional synthetic control (FSC) method as an extension of the SCM for metric space-valued outcomes. To address challenges arising from the nonlinearlity of metric spaces, we leverage isometric embeddings into Hilbert spaces. Building on this approach, we develop the FSC and augmented FSC estimators for counterfactual outcomes, with the latter being a bias-corrected version of the former. We then derive their finite-sample error bounds to establish theoretical guarantees for estimation, and construct prediction sets based on these estimators to conduct inference on causal effects. We demonstrate the usefulness of the proposed framework through simulation studies and three empirical applications.

Clustering with bandit feedback refers to the problem of partitioning the arms of an $N$-armed stochastic bandit according to their underlying distributions, based on noisy observations collected sequentially and adaptively. This setting has attracted growing interest for its applicability in recommendation systems, crowdsourcing, and adaptive trials. Existing works rely on the strong assumption that arm distributions are sub-Gaussian, which can only distinguish arms whose distributions differ in mean - missing realistic settings where distributional differences lie in shape or higher moments. % We introduce a framework of nonparametric clustering with bandit feedback, free of any parametric assumptions regarding the arm distributions. We adopt a kernel-based approach and reformulate the problem as clustering arms according to their kernel mean embeddings in a reproducing kernel Hilbert space (RKHS). Building on this formulation, we introduce the \kabc\ algorithm, prove that it is $\delta$-PAC, and derive a non-asymptotic high-probability upper bound on its sampling complexity. The bound is governed by a variance-aware signal-to-noise ratio defined as the minimum over pairs of arms in distinct clusters of the ratio between their squared MMD and their RKHS variance. \kabc\ achieves instance-dependent guarantees while being adaptive to this unknown ratio. We validate our approach empirically on synthetic and real-world datasets, demonstrating that \kabc\ succeeds in distributional clustering settings where mean-based methods fail.

This paper proposes a novel statistical approach that aims at the identification of valid and useful patterns in handwriting examination via Bayesian modeling. Starting from a sample of characters selected among 13 French native writers, an accurate loop reconstruction can be achieved through Fourier analysis. The contour shape of handwritten characters can be described by the first four pairs of Fourier coefficients and by the surface size. Six Bayesian models are considered for such handwritten features. These models arise from two likelihood structures: (a) a multivariate Normal model, and (b) a MANOVA model that accounts for character-level variability. For each likelihood, three different prior formulations are examined, resulting in distinct Bayesian models: (i) a conjugate Normal-Inverse-Wishart prior, (ii) a hierarchical Normal-Inverse-Wishart prior, and (iii) a Normal-LogNormal-LKJ prior specification. The hierarchical prior formulations are of primary interest because they can incorporate the between-writers variability, a distinguishing element that sets writers apart. These approaches do not allow calculation of the marginal likelihood in a closed-form expression. Therefore, bridge sampling is used to estimate it. The Bayes factor is estimated to compare the performance of the proposed models and to evaluate their efficiency for discriminating purposes. Bayesian MANOVA with Normal-LogNormal-LKJ prior showed an overall better performance, in terms of discriminatory capacity and model fitting. Finally, a sensitivity analysis for the elicitation of the prior distribution parameters is performed.

Indirect treatment comparisons (ITCs) are essential in Health Technology Assessment (HTA) when head-to-head clinical trials are absent. A common challenge arises when attempting to compare a treatment with available individual patient data (IPD) against a competitor with only reported aggregate-level data (ALD), particularly when trial populations differ in effect modifiers. While methods such as Matching-Adjusted Indirect Comparison (MAIC) exist to adjust for these cross-trial differences, they are increasingly being superseded by regression-based marginalization methods. Historically, software implementations for these methods have often been fragmented or limited in scope. This article introduces outstandR, an R package designed to provide a comprehensive and unified framework for population-adjusted indirect comparison (PAIC). outstandR implements advanced G-computation methods - within both maximum likelihood and Bayesian frameworks, and Multiple Imputation Marginalization (MIM) to address non-collapsibility. By streamlining the workflow of covariate simulation, model standardization, and contrast estimation, outstandR enables robust and compatible evidence synthesis in complex decision-making scenarios.

We consider in this paper a stochastic process that mixes in time, according to a nonobserved stationary Markov selection process, two separate sources of randomness: i) a stationary process which distribution is accessible (gold standard); ii) a pure i.i.d. sequence which distribution is unknown (poisoning process). In this framework we propose to estimate, with two different approaches, the transition of the hidden Markov selection process along with the distribution, not supposed to belong to any parametric family, of the unknown i.i.d. sequence, under minimal (identifiability, stationarity and dependence in time) conditions. We show that both estimators provide consistent estimations of the Euclidean transition parameter, and also prove that one of them, which is $\sqrt$ n-consistent, allows to establish a functional central limit theorem about the unknown poisoning sequence cumulative distribution function. The numerical performances of our estimators are illustrated through various challenging examples.

Traditional reinforcement learning usually assumes either episodic interactions with resets or continuous operation to minimize average or cumulative loss. While episodic settings have many theoretical results, resets are often unrealistic in practice. The infinite-horizon setting avoids this issue but lacks non-asymptotic guarantees in online scenarios with unknown dynamics. In this work, we move towards closing this gap by introducing a reset-free framework called the periodic framework, where the goal is to find periodic policies: policies that not only minimize cumulative loss but also return the agents to their initial state distribution after a fixed number of steps. We formalize the problem of finding optimal periodic policies and identify sufficient conditions under which it is well-defined for tabular Markov decision processes. To evaluate algorithms in this framework, we introduce the periodic regret, a measure that balances cumulative loss with the terminal law constraint. We then propose the first algorithms for computing periodic policies in two multi-agent settings and show they achieve sublinear periodic regret of order $\tilde O(T^{3/4})$. This provides the first non-asymptotic guarantees for reset-free learning in the setting of $M$ homogeneous agents, for $M > 1$.

Penalised estimation methods for point processes usually rely on a large amount of independent repetitions for cross-validation purposes. However, in the case of a single realisation of the process, existing cross-validation methods may be impractical depending on the chosen model. To overcome this issue, this paper presents a Ridge-penalised spectral least-squares estimation method for second-order stationary point processes. This is achieved through two novel approaches: a p-thinning-based cross-validation method to tune the penalisation parameter, relying on the spectral representation of the process; and the introduction of a spectral least-squares contrast based around the asymptotic properties of the periodogram of the sample. The proposed method is then illustrated by a simulation study on linear Hawkes processes in the context of parametric estimation, highlighting its performances against more traditional approaches, specifically when working with short observation windows.

The identification of patient subgroups with comparable event-risk dynamics plays a key role in supporting informed decision-making in clinical research. In such settings, it is important to account for the inherent dependence that arises when individuals are nested within higher-level units, such as hospitals. Existing survival models account for group-level heterogeneity through frailty terms but do not uncover latent patient subgroups, while most clustering methods ignore hierarchical structure and are not estimated jointly with survival outcomes. In this work, we introduce a new framework that simultaneously performs patient clustering and shared-frailty survival modeling through a penalized likelihood approach. The proposed methodology adaptively learns a patient-to-patient similarity matrix via a modified version of spectral clustering, enabling cluster formation directly from estimated risk profiles while accounting for group membership. A simulation study highlights the proposed model's ability to recover latent clusters and to correctly estimate hazard parameters. We apply our method to a large cohort of heart-failure patients hospitalized with COVID-19 between 2020 and 2021 in the Lombardy region (Italy), identifying clinically meaningful subgroups characterized by distinct risk profiles and highlighting the role of respiratory comorbidities and hospital-level variability in shaping mortality outcomes. This framework provides a flexible and interpretable tool for risk-based patient stratification in hierarchical data settings.

Over-smoothing and over-squashing have been extensively studied in the literature on Graph Neural Networks (GNNs) over the past years. We challenge this prevailing focus in GNN research, arguing that these phenomena are less critical for practical applications than assumed. We suggest that performance decreases often stem from uninformative receptive fields rather than over-smoothing. We support this position with extensive experiments on several standard benchmark datasets, demonstrating that accuracy and over-smoothing are mostly uncorrelated and that optimal model depths remain small even with mitigation techniques, thus highlighting the negligible role of over-smoothing. Similarly, we challenge that over-squashing is always detrimental in practical applications. Instead, we posit that the distribution of relevant information over the graph frequently factorises and is often localised within a small k-hop neighbourhood, questioning the necessity of jointly observing entire receptive fields or engaging in an extensive search for long-range interactions. The results of our experiments show that architectural interventions designed to mitigate over-squashing fail to yield significant performance gains. This position paper advocates for a paradigm shift in theoretical research, urging a diligent analysis of learning tasks and datasets using statistics that measure the underlying distribution of label-relevant information to better understand their localisation and factorisation.

Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series model, while the latter employs (locally) time-varying models to describe smooth changes in dependence structure of a time series. However, in some applications, abrupt and smooth changes can co-exist, and neither of the two approaches alone can model the data adequately. In this paper, we propose a novel likelihood-based procedure for the inference of multiple change-points in locally stationary time series. In contrast to traditional change-point analysis where an abrupt change occurs in a real-valued parameter, a change in locally stationary time series occurs in a parameter curve, and can be classified as a jump or a kink depending on whether the curve is discontinuous or not. We show that the proposed method can consistently estimate the number, locations, and the types of change-points. Two different asymptotic distributions corresponding respectively to jump and kink estimators are also established. Extensive simulation studies and a real data application to financial time series are provided.

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint distribution, but instead define a family of admissible distributions that share the same pairwise dependence while potentially differing in higher-order interactions. In this paper, we introduce a geometric framework to describe the entire feasible set of such joint distributions with uniform margins. We show that this admissible set forms a convex polytope, analyze its symmetry properties, and characterize its extreme rays. These extremal distributions provide fundamental insights into how higher-order dependence structures may vary while preserving the prescribed pairwise information. Unlike traditional methods for table generation, which return a single table, our framework makes it possible to explore and understand the full admissible space of dependence structures, enabling more flexible choices for modeling and simulation. We illustrate the usefulness of our theoretical results through examples and a real case study on rater agreement.

We introduce the $\widetilde{\rho}$-posterior, a modified version of the $\rho$-posterior, obtained by replacing the supremum over competitor parameters with a softmax aggregation. This modification allows a PAC-Bayesian analysis of the $\widetilde{\rho}$-posterior. This yields finite-sample oracle inequalities with explicit convergence rates that inherit the key robustness properties of the original framework, in particular, graceful degradation under model misspecification and data contamination. Crucially, the PAC-Bayesian oracle inequalities extend to variational approximations of the $\widetilde{\rho}$-posterior, providing theoretical guarantees for tractable inference. Numerical experiments on exponential families, regression, and real-world datasets confirm that the resulting variational procedures achieve robustness competitive with theoretical predictions at computational cost comparable to standard variational Bayes.