Papers

We study the problem of finding confidence ellipsoids for an arbitrary distribution in high dimensions. Given samples from a distribution $D$ and a confidence parameter $\alpha$, the goal is to find the smallest volume ellipsoid $E$ which has probability mass $\mathbb{P}_{D}[E] \ge 1-\alpha$. Ellipsoids are a highly expressive class of confidence sets as they can capture correlations in the distribution, and can approximate any convex set. In statistics, this is the classic minimum volume estimator introduced by Rousseeuw as a robust non-parametric estimator of location and scatter. However in high dimensions, it becomes NP-hard to obtain any non-trivial approximation factor in volume when the condition number $\beta$ of the ellipsoid (ratio of the largest to the smallest axis length) goes to $\infty$. This motivates the focus of our paper: can we efficiently find confidence ellipsoids with volume approximation guarantees when compared to ellipsoids of bounded condition number $\beta$? Our main result is a polynomial time algorithm that finds an ellipsoid $E$ whose volume is within a $O(\beta)^{\gamma d}$ multiplicative factor of the volume of best $\beta$-conditioned ellipsoid while covering at least $1-O(\alpha/\gamma)$ probability mass for any $\gamma \in (0,1)$. In particular, setting $\gamma = o(1)$, this gives a $O(\beta)^{o(d)}$ volume approximation, with a multiplicative loss in miscoverage. We complement this with a computational hardness result that shows that such a dependence on $\beta$ seems necessary, even with some slack in coverage. The algorithm and analysis uses the rich primal-dual structure of the minimum volume enclosing ellipsoid and the geometric Brascamp-Lieb inequality. As a consequence, we obtain the first polynomial time algorithm with approximation guarantees on worst-case instances of the robust subspace recovery problem.

Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm and classical artificial neural networks (ANNs). In this work, we analyze the representational power of SNNs by viewing them as sequence-to-sequence processors of spikes, i.e., systems that transform a stream of input spikes into a stream of output spikes. We establish the universal representation property for a natural class of spike train functions. Our results are fully quantitative, constructive, and near-optimal in the number of required weights and neurons. The analysis reveals that SNNs are particularly well-suited to represent functions with few inputs, low temporal complexity, or compositions of such functions. The latter is of particular interest, as it indicates that deep SNNs can efficiently capture composite functions via a modular design. As an application of our results, we discuss spike train classification. Overall, these results contribute to a rigorous foundation for understanding the capabilities and limitations of spike-based neuromorphic systems.

Treatment noncompliance is pervasive in infectious disease cluster-randomized trials. Although all individuals within a cluster are assigned the same treatment condition, the treatment uptake status may vary across individuals due to noncompliance. We propose a semiparametric framework to evaluate the individual compliance effect and network assignment effect within principal stratum exhibiting different patterns of noncompliance. The individual compliance effect captures the portion of the treatment effect attributable to changes in treatment receipt, while the network assignment effect reflects the pure impact of treatment assignment and spillover among individuals within the same cluster. Unlike prior efforts which either empirically identify or interval identify these estimands, we characterize new structural assumptions for nonparametric point identification. We then develop semiparametrically efficient estimators that combine data-adaptive machine learning methods with efficient influence functions to enable more robust inference. Additionally, we introduce sensitivity analysis methods to study the impact under assumption violations, and apply the proposed methods to reanalyze a cluster-randomized trial in Kenya that evaluated the impact of school-based mass deworming on disease transmission.

Mixture models postulate the overall population as a mixture of finite subpopulations with unobserved membership. Fitting mixture models usually requires large sample sizes and combining data from multiple sites can be beneficial. However, sharing individual participant data across sites is often less feasible due to various types of practical constraints, such as data privacy concerns. Moreover, substantial heterogeneity may exist across sites, and locally identified latent classes may not be comparable across sites. We propose a unified modeling framework where a common definition of the latent classes is shared across sites and heterogeneous mixing proportions of latent classes are allowed to account for between-site heterogeneity. To fit the heterogeneous mixture model on multi-site data, we propose a novel distributed Expectation-Maximization (EM) algorithm where at each iteration a density ratio tilted surrogate Q function is constructed to approximate the standard Q function of the EM algorithm as if the data from multiple sites could be pooled together. Theoretical analysis shows that our estimator achieves the same contraction property as the estimators derived from the EM algorithm based on the pooled data.

The legislative output of Colombia's House of Representatives between 2014 and 2025 is analyzed using 4,083 bills. Bipartite networks are constructed between parties and bills, and between representatives and bills, along with their projections, to characterize co-sponsorship patterns, centrality, and influence, and to assess whether political polarization is reflected in legislative collaboration. In parallel, the content of the initiatives is studied through semantic networks based on co-occurrences extracted from short descriptions, and topics by party and period are identified using a stochastic block model for weighted networks, with additional comparison using Latent Dirichlet Allocation. In addition, a Bayesian sociability model is applied to detect terms with robust connectivity and to summarize discursive cores. Overall, the approach integrates relational and semantic structure to describe thematic shifts across administrations, identify influential actors and collectives, and provide a reproducible synthesis that promotes transparency and citizen oversight of the legislative process.

Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition to replacing population expectations by sample averages, one may replace the target distribution itself by a finite-sample surrogate, ranging from the empirical measure to a smoothed estimator. This viewpoint yields a natural hierarchy of empirical FM models. For affine conditional flows, we derive the exact empirical minimizer and identify a smoothed plug-in regime in which the terminal law is exactly a kernel-mixture estimator. This plug-in perspective clarifies several coupled finite-sample biases of empirical FM. First, replacing the target law by a finite-sample surrogate changes the statistical target. Second, the empirical minimizer is generally not a gradient field, even when each conditional flow is. Third, a fixed empirical marginal path does not determine a unique particle dynamics: one may add extra vector fields whose probability flux has zero divergence without changing the marginal path. For Gaussian affine conditional paths, we give explicit families of such flux-null corrections. Finally, the source distribution provides a primary mechanism controlling upper tails of kinetic energy. In particular, Gaussian bases yield exponential upper-tail bounds for instantaneous and integrated kinetic energies, whereas polynomially tailed bases yield corresponding polynomial upper-tail bounds.

We show that for any concave utility, the expected utility of an e-variable can only increase after conditioning on a sufficient statistic, echoing the classic Rao-Blackwell theorem. The simplest form of the result has a straightforward proof using Jensen's inequality, but we prove more sophisticated versions. We provide several applications of this insight, including a derivation of the log-optimal e-variable for testing the variance in a linear regression model.

We study portfolio selection with a Conditional Value-at-Risk (CVaR) constraint under distribution shift and serial dependence. While Wasserstein distributionally robust optimization (DRO) offers tractable protection via an ambiguity ball around empirical data, choosing the ball radius is delicate: large radii are conservative, small radii risk violation under regime change. We propose a shift-aware Gaussian-supremum (GS) validation framework for Wasserstein-DRO CVaR portfolios, building on the work by Lam and Qian (2019). Phase I of the framework generates a candidate path by solving the exact reformulation of the robust CVaR constraint over a grid of Wasserstein radii. Phase II of the framework learns a target deployment law $Q$ by density-ratio reweighting of a time-ordered validation fold, computes weighted CVaR estimates, and calibrates a simultaneous upper confidence band via a block multiplier bootstrap to account for dependence. We select the least conservative feasible portfolio (or abstain if the effective sample size collapses). Theoretically, we extend the normalized GS validator to non-i.i.d. financial data: under weak dependence and regularity of the weighted scores, any portfolio passing our validator satisfies the CVaR limit under $Q$ with probability at least $1-\beta$; the Wasserstein term contributes a deterministic margin $(\delta/\alpha)\|x\|_*$. Empirical results indicate improved return-risk trade-offs versus the naive baseline.

We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models are illustrated on simulated and real data.

We introduce Stackelberg Learning from Human Feedback (SLHF), a new framework for preference optimization. SLHF frames the alignment problem as a sequential-move game between two policies: a Leader, which commits to an action, and a Follower, which responds conditionally on the Leader's action. This approach decomposes preference optimization into a refinement problem for the Follower and an optimization problem against an adversary for the Leader. Unlike Reinforcement Learning from Human Feedback (RLHF), which assigns scalar rewards to actions, or Nash Learning from Human Feedback (NLHF), which seeks a simultaneous-move equilibrium, SLHF leverages the asymmetry of sequential play to capture richer preference structures. The sequential design of SLHF naturally enables inference-time refinement, as the Follower learns to improve the Leader's actions, and these refinements can be leveraged through iterative sampling. We compare the solution concepts of SLHF, RLHF, and NLHF, and lay out key advantages in consistency, data sensitivity, and robustness to intransitive preferences. Experiments on large language models demonstrate that SLHF achieves strong alignment across diverse preference datasets, scales from 0.5B to 8B parameters, and yields inference-time refinements that transfer across model families without further fine-tuning.

Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann Generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann Generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann Generators, but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.

Wildfires pose an increasingly severe threat to air quality, yet quantifying their causal impact remains challenging due to unmeasured meteorological and geographic confounders. Moreover, wildfire impacts on air quality may exhibit heterogeneous effects across pollution levels, which conventional mean-based causal methods fail to capture. To address these challenges, we develop a Quantile-based Latent Spatial Confounder Model (QLSCM) that substitutes conditional expectations with conditional quantiles, enabling causal analysis across the entire outcome distribution. We establish the causal interpretation of QLSCM theoretically, prove the identifiability of causal effects, and demonstrate estimator consistency under mild conditions. Simulations confirm the bias correction capability and the advantage of quantile-based inference over mean-based approaches. Applying our method to contiguous US wildfire and air quality data, we uncover important heterogeneous effects: fire radiative power exerts significant positive causal effects on aerosol optical depth at high quantiles in Western states like California and Oregon, while insignificant at lower quantiles. This indicates that wildfire impacts on air quality primarily manifest during extreme pollution events. Regional analyses reveal that Western and Northwestern regions experience the strongest causal effects during such extremes. These findings provide critical insights for environmental policy by identifying where and when mitigation efforts would be most effective.

We introduce the most comprehensive publicly available datasets for mixed doubles curling, constructed from eleven top-level tournaments from the CurlIT (https://curlit.com/results) Results Booklets spanning 53 countries, 1,112 games, and nearly 70,000 recorded shots. While curling analytics has grown in recent years, mixed doubles remains under-served due to limited access to data. Using a combined text-scraping and image-processing pipeline, we extract and standardize detailed game- and shot-level information, including player statistics, hammer possession, Power Play usage, stone coordinates, and post-shot scoring states. We describe the data engineering workflow, highlight challenges in parsing historical records, and derive additional contextual features that enable rigorous strategic analysis. Using these datasets, we present initial insights into shot selection and success rates, scoring distributions, and team efficiencies, illustrating key differences between mixed doubles and traditional 4-player curling. We highlight various ways to analyze this type of data including from a shot-, end-, game- or team-level to display its versatilely. The resulting resources provide a foundation for advanced performance modeling, strategic evaluation, and future research in mixed doubles curling analytics, supporting broader analytical engagement with this rapidly growing discipline.

Symmetry principles underlie and guide scientific theory and research, from Curie's invariance formulation to modern applications across physics, chemistry, and mathematics. Building on a recent matrix Lie group measurement model, this paper extends the framework to identify additional measurement symmetries implied by Lie group theory. Lie groups provide the mathematics of continuous symmetries, while Lie algebras serve as their infinitesimal generators. Within applied measurement theory, the preservation of symmetries in transformation groups acting on score frequency distributions ensure invariance in transformed distributions, with implications for validity, comparability, and conservation of information. A simulation study demonstrates how breaks in measurement symmetry affect score distribution symmetry and break effect size comparability. Practical applications are considered, particularly in meta analysis, where the standardized mean difference (SMD) is shown to remain invariant across measures only under specific symmetry conditions derived from the Lie group model. These results underscore symmetry as a unifying principle in measurement theory and its role in evidence based research.

Generalizing causal knowledge across diverse environments is challenging, especially when estimates from large-scale datasets must be applied to smaller or systematically different contexts, where external validity is critical. Model-based estimators of individual treatment effects (ITE) from machine learning require large sample sizes, limiting their applicability in domains such as behavioral sciences with smaller datasets. We demonstrate how estimation of ITEs with Treatment Agnostic Representation Networks (TARNet; Shalit et al., 2017) can be improved by leveraging knowledge from source datasets and adapting it to new settings via transfer learning (TL-TARNet; Aloui et al., 2023). In simulations that vary source and sample sizes and consider both randomized and non-randomized intervention target settings, the transfer-learning extension TL-TARNet improves upon standard TARNet, reducing ITE error and attenuating bias when a large unbiased source is available and target samples are small. In an empirical application using the India Human Development Survey (IHDS-II), we estimate the effect of mothers' firewood collection time on children's weekly study time; transfer learning pulls the target mean ITEs toward the source ITE estimate, reducing bias in the estimates obtained without transfer. These results suggest that transfer learning for causal models can improve the estimation of ITE in small samples.

Survival analysis encompasses a broad range of methods for analyzing time-to-event data, with one key objective being the comparison of survival curves across groups. Traditional approaches for identifying clusters of survival curves often rely on computationally intensive bootstrap techniques to approximate the null hypothesis distribution. While effective, these methods impose significant computational burdens. In this work, we propose a novel approach that leverages the k-means and log-rank test to efficiently identify and cluster survival curves. Our method eliminates the need for computationally expensive resampling, significantly reducing processing time while maintaining statistical reliability. By systematically evaluating survival curves and determining optimal clusters, the proposed method ensures a practical and scalable alternative for large-scale survival data analysis. Through simulation studies, we demonstrate that our approach achieves results comparable to existing bootstrap-based clustering methods while dramatically improving computational efficiency. These findings suggest that the log-rank-based clustering procedure offers a viable and time-efficient solution for researchers working with multiple survival curves in medical and epidemiological studies.

Hospital readmission among patients with chronic heart failure (HF) is a major clinical and economic burden. Dynamic prediction models that leverage longitudinal biomarkers may improve risk stratification over traditional static models. This study aims to develop and validate a joint model using longitudinal N-terminal pro-B-type natriuretic peptide (NT-proBNP) measurements to predict the risk of rehospitalization or death in HF patients. We analyzed real-world data from the TriNetX database, including patients with an incident HF diagnosis between 2016 and 2022. The final selected cohort included 1,804 patients. A Bayesian joint modeling framework was developed to link patient-specific NT-proBNP trajectories to the risk of a composite endpoint (HF rehospitalization or all-cause mortality) within a 180-day window following hospital discharge. The model's performance was evaluated using 5-fold cross-validation and assessed with the Integrated Brier Score and Integrated Calibration Index. The joint model demonstrated a strong predictive advantage over a benchmark static model, particularly when making updated predictions at later time points (180-360 days). A joint model trained on patients with more frequent NT-proBNP measurements achieved the highest accuracy. The main joint model showed excellent calibration, suggesting its risk estimates are reliable. Our findings suggest that modeling the full trajectory of NT-proBNP with a joint modeling framework enables more accurate and dynamic risk assessment compared to static, single-timepoint methods. This approach supports the development of adaptive clinical decision-support tools for personalized HF management.

In the perspective of building statistical tests of divergence between two probability distributions, we study the distribution of empirical relative entropy and derive several types of approximations: concentration inequalities for finite samples, asymptotic distributions, and Berry-Esseen bounds in a pre-asymptotic regime. For the latter, we introduce a new approach to obtain Berry-Esseen inequalities for nonlinear functions of sum statistics under some convexity assumptions. Our theoretical contributions cover both one- and two-sample empirical relative entropies.

Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. Yet, fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic Quantile Forests (TQF), a nonparametric, uncertainty-aware, tree-based regression model for multivariate targets. TQF learns conditional quantiles of directional projections $\mathbf{n}^{\top}\mathbf{y}$ as functions of the input $\mathbf{x}$ and the unit direction $\mathbf{n}$. At inference, it aggregates quantiles across many directions and reconstructs the multivariate conditional distribution by minimizing the sliced Wasserstein distance via an efficient alternating scheme with convex subproblems. Unlike classical directional-quantile approaches that typically produce only convex quantile regions and require training separate models for different directions, TQF covers all directions with a single model without imposing convexity restrictions. We evaluate TQF on synthetic and real-world datasets, and release the source code on GitHub.

We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based on labeled outcomes with auxiliary moment conditions built from predictions, and then optimizing empirical likelihood under these joint constraints. The resulting empirical likelihood-based prediction-powered inference (EPI) estimator is asymptotically normal, has asymptotic variance no larger than the fully supervised estimator, and attains the semiparametric efficiency bound when the auxiliary functions span the predictable component of the supervised score. For hypothesis testing and confidence sets, empirical likelihood ratio statistics admit chi-squared-type limiting distributions. As a by-product, the empirical likelihood weights induce a calibrated empirical distribution that integrates supervised and prediction-based information, enabling estimation and uncertainty quantification for general functionals beyond parameters defined by estimating equations. We present two practical implementations: one based on basis expansions in the predictions and covariates, and one that learns an approximately optimal auxiliary function by cross-fitting. In simulations and applications, EPI reduces mean squared error and shortens confidence intervals while maintaining nominal coverage.

Objectives To investigate the use of a Bayesian joint modelling approach to predict overall survival (OS) from immature clinical trial data using an intermediate biomarker. To compare the results with a typical parametric approach of extrapolation and observed survival from a later datacut. Methods Data were pooled from three phase I/II open-label trials evaluating larotrectinib in 196 patients with neurotrophic tyrosine receptor kinase fusion-positive (NTRK+) solid tumours followed up until July 2021. Bayesian joint modelling was used to obtain patient-specific predictions of OS using individual-level sum of diameter of target lesions (SLD) profiles up to the time at which the patient died or was censored. Overall and tumour site-specific estimates were produced, assuming a common, exchangeable, or independent association structure across tumour sites. Results The overall risk of mortality was 9% higher per 10mm increase in SLD (HR 1.09, 95% CrI 1.05 to 1.14) for all tumour sites combined. Tumour-specific point estimates of restricted mean , median and landmark survival were more similar across models for larger tumour groups, compared to smaller tumour groups. In general, parameters were estimated with more certainty compared to a standard Weibull model and were aligned with the more recent datacut. Conclusions Joint modelling using intermediate outcomes such as tumour burden can offer an alternative approach to traditional survival modelling and may improve survival predictions from limited follow-up data. This approach allows complex hierarchical data structures, such as patients nested within tumour types, and can also incorporate multiple longitudinal biomarkers in a multivariate modelling framework.

The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when specified parametrically, can only capture limited shapes. To overcome this limitation, we propose a general class of parametric survival regression models obtained by modelling the hazard function using autonomous systems of ordinary differential equations (ODEs). Covariate information is incorporated via transformed linear predictors on the parameters of the ODE system. Our framework capitalises on the interpretability of parameters in common ODE systems, enabling the identification of covariate values that produce qualitatively distinct hazard shapes associated with different attractors of the system of ODEs. This provides deeper insights into how covariates influence survival dynamics. We develop efficient Bayesian computational tools, including parallelised evaluation of the log-posterior, which facilitates integration with general-purpose Markov Chain Monte Carlo samplers. We also derive conditions for posterior asymptotic normality, enabling fast approximations of the posterior. A central contribution of our work lies in the case studies. We demonstrate the methodology using clinical trial data with crossing survival curves, and a study of cancer recurrence times where our approach reveals how the efficacy of interventions (treatments) on hazard and survival are influenced by patient characteristics.

Mixture regression models are powerful tools for capturing heterogeneous covariate-response relationships, yet classical finite mixtures and Bayesian nonparametric alternatives often suffer from instability or overestimation of clusters when component separability is weak. Recent repulsive priors improve parsimony in density mixtures by discouraging nearby components, but their direct extension to regression is nontrivial since separation must respect the predictive geometry induced by covariates. We propose a repulsive g-prior for regression mixtures that enforces separation in the Mahalanobis metric, penalizing components indistinguishable in the predictive mean space. This construction preserves conjugacy-like updates while introducing geometry-aware interactions, enabling efficient blocked-collapsed Gibbs sampling. Theoretically, we establish tractable normalizing bounds, posterior contraction rates, and shrinkage of tail mass on the number of components. Simulations under correlated and overlapping designs demonstrate improved clustering and prediction relative to independent, Euclidean-repulsive, and sparsity-inducing baselines.

Educational videos are widely used across various instructional models in higher education to support flexible and self-paced learning. However, student engagement with these videos varies significantly depending on how they are designed. While several studies have identified potential influencing factors, there remains a lack of scalable tools and open datasets to support large-scale, data-driven improvements in video design. This study aims to advance data-driven approaches to educational video design. Its core contributions include: (1) a workflow model for analysing educational videos; (2) an open-source implementation for extracting video metadata and features; (3) an accessible, community-driven database of video attributes; (4) a case study applying the approach to two engineering courses; and (5) an initial machine learning-based analysis to explore the relative influence of various video characteristics on student engagement. This work lays the groundwork for a shared, evidence-based approach to educational video design.

We investigate the distributed online economic dispatch problem for power systems with time-varying coupled inequality constraints. The problem is formulated as a distributed online optimization problem in a multi-agent system. At each time step, each agent only observes its own instantaneous objective function and local inequality constraints; agents make decisions online and cooperate to minimize the sum of the time-varying objectives while satisfying the global coupled constraints. To solve the problem, we propose an algorithm based on the primal-dual approach combined with constraint-tracking. Under appropriate assumptions that the objective and constraint functions are convex, their gradients are uniformly bounded, and the path length of the optimal solution sequence grows sublinearly, we analyze theoretical properties of the proposed algorithm and prove that both the dynamic regret and the constraint violation are sublinear with time horizon T. Finally, we evaluate the proposed algorithm on a time-varying economic dispatch problem in power systems using both synthetic data and Australian Energy Market data. The results demonstrate that the proposed algorithm performs effectively in terms of tracking performance, constraint satisfaction, and adaptation to time-varying disturbances, thereby providing a practical and theoretically well-supported solution for real-time distributed economic dispatch.

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern applications, however, feature complex structure, like arrays, spatial processes, or covariates. We propose a generalized approach to empirical Bayes based on probabilistic symmetry. Our method pairs a simultaneous inference problem with an unknown prior to a symmetry assumption on the joint distribution of the latent variables. Each symmetry implies an ergodic decomposition, which we use to derive a corresponding empirical Bayes method. We call this method Bayesian empirical Bayes (BEB). BEB recovers classical empirical Bayes methods, which implicitly assume exchangeability. We extend EB to other probabilistic symmetries: (i) EB matrix recovery for arrays and graphs; (ii) covariate-informed EB for conditional data; and (iii) EB spatial regression under shift invariance. We develop scalable algorithms based on variational inference and neural networks. In simulations, BEB outperforms existing denoising methods. On real data, we demonstrate BEB on cancer gene-expression and brain-connectivity matrices and NYC air-quality data.

We address network structure learning from zero-inflated count data by casting each node as a zero-inflated generalized linear model and optimizing a smooth, score-based objective under a directed acyclic graph constraint. Our Zero-Inflated Continuous Optimization (ZICO) approach uses node-wise likelihoods with canonical links and enforces acyclicity through a differentiable surrogate constraint combined with sparsity regularization. ZICO achieves superior performance with faster runtimes on simulated data. It also performs comparably to or better than common algorithms for reverse engineering gene regulatory networks. ZICO is fully vectorized and mini-batched, enabling learning on larger variable sets with practical runtimes in a wide range of domains.

In many settings, robust data analysis involves computational methods for uncertainty quantification and statistical inference. To design frequentist studies that leverage robust analysis methods, suitable sample sizes to achieve desired power are often found by estimating sampling distributions of p-values via intensive simulation. Moreover, most sample size recommendations rely heavily on assumptions about a single data-generating process. Consequently, robustness in data analysis does not by itself imply robustness in study design, as examining sample size sensitivity to data-generating assumptions typically requires further simulations. We propose an economical alternative for determining sample sizes that are robust to multiple data-generating mechanisms. Applying our theoretical results that model p-values as a function of the sample size, we assess power across the sample size space using simulations conducted at only two sample sizes for each data-generating mechanism. We demonstrate the broad applicability of our methodology to study design based on M-estimators in both experimental and observational settings through a varied set of clinical examples.

This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large number of samples to achieve accurate results. We propose a novel estimator, BayesSum, which is an extension of Bayesian quadrature to discrete domains. It is more sample efficient than alternatives due to its ability to make use of prior information about the integrand through a Gaussian process. We show this through theory, deriving a convergence rate significantly faster than Monte Carlo in a broad range of settings. We also demonstrate empirically that our proposed method does indeed require fewer samples on several synthetic settings as well as for parameter estimation for Conway-Maxwell-Poisson and Potts models.

Inhomogeneous phase-type (IPH) distributions extend classical phase-type (PH) models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed distributions or time-dependent absorption phenomena. Statistical inference for these models has largely assumed that absorption times, or entire trajectories, are observed exactly. In many applications, however, the process is observed only at discrete, irregularly spaced time points, so that transition and absorption times are unknown and estimation becomes a missing-data problem. We address this setting for the subclass with time-scaled sub-intensity matrices $\boldsymbol{\Lambda}(t) = h_{\beta}(t)\boldsymbol{\Lambda}$, which admits a time transformation to a homogeneous Markov jump process (MJP). We develop an inference framework that combines Markov-bridge data augmentation with a Stochastic Expectation-Maximization (SEM) algorithm: at each iteration the latent continuous-time trajectories are simulated conditionally on the discrete observations, and the parameters are then updated by maximizing the resulting complete-data likelihood. The baseline sub-intensity matrix $\boldsymbol{\Lambda}$ is updated by its closed-form complete-data maximum-likelihood estimator, while the time-scaling parameter $\beta$ is refined by gradient ascent on the same complete-data log-likelihood. The reported estimators are thus obtained from complete-data maximum-likelihood updates, avoiding constrained nonlinear optimization of the observed-data likelihood. Through simulation studies for the matrix-Gompertz and matrix-Weibull families, and a real-data application to coronary allograft vasculopathy (CAV) progression, we demonstrate that the proposed approach provides an accurate and computationally tractable tool for fitting time-scaled IPH models to irregular multi-state data.