Papers

We propose a novel mixture model for football event data that clusters entire possessions to reveal their temporal, sequential, and spatial structure. Each mixture component models possessions as marked spatio-temporal point processes: event types follow a finite Markov chain with an absorbing state for ball loss, event times follow a conditional Gamma process to account for dispersion, and spatial locations evolve via truncated Brownian motion. To aid interpretation, we derive summary indicators from model parameters capturing possession speed, number of events, and spatial dynamics. Parameters are estimated through maximum likelihood via Generalized Expectation-Maximization algorithm. Applied to StatsBomb data from 38 Ligue 1 matches (2020/2021), our approach uncovers distinct defensive possession patterns faced by Stade Rennais. Unlike previous approaches focusing on individual events, our mixture structure enables principled clustering of full possessions, supporting tactical analysis and the future development of realistic virtual training environments.

Spatial dynamic microsimulations probabilistically project geographically referenced units with individual characteristics over time. Like any projection method, their outcomes are inherently uncertain and sensitive to multiple factors. However, such factors are rarely addressed. Applying variance-based sensitivity analysis to both direct and indirect effects within the employment module of the MikroSim model for Germany, we show that commonly considered sources of uncertainty, namely coefficient and parameter uncertainty, are less influential than qualitative modeling choices. Because dynamic microsimulations are inherently complex and are computationally intensive, it is crucial to consider potential factors of uncertainty and their influence on simulation outputs in order to more carefully design simulation setups and better communicate results. We find, that simple summary measures insufficiently capture overall model uncertainty and urge modelers to account for these broader sources when designing microsimulations and their results.

Covariate adjustment can enhance precision and power in clinical trials, yet its application to the win odds remains unclear. The win odds is an extension of the win ratio that counts ties as half a win for the treatment and the control group, respectively. In their original form, both the win ratio and the win odds rely on comparing each individual from the treatment group to each individual from the control group in a pairwise manner, and count the number of wins, losses, and ties from these pairwise comparisons. A priori, it is not clear how covariate adjustment can be implemented for the win odds. To address this, we establish a connection between the win odds and the marginal probabilistic index, a measure for which covariate adjustment theory is well-developed. Using this connection, we show how covariate adjustment for the win odds is possible, leading to potentially more precise estimators and larger power as compared to the unadjusted win odds. We present the underlying theory for covariate adjustment for the win odds in an accessible way and apply the method on synthetic data based on the CANTOS trial (ClinicalTrials.gov identifier: NCT01327846) characteristics, on a subset of the HF-ACTION trial data (ClinicalTrials.gov identifier: NCT00047437), and on simulated data to study the operating characteristics of the method. We observe that there is indeed a potential gain in power when the win odds is adjusted for baseline covariates if the baseline covariates are prognostic for the outcome. This comes at the cost of a slight inflation of the type I error rate for small sample sizes.

Causal discovery combines data with knowledge provided by experts to learn the DAG representing the causal relationships between a given set of variables. When data are scarce, bagging is used to measure our confidence in an average DAG obtained by aggregating bootstrapped DAGs. However, the aggregation step has received little attention from the specialized literature: the average DAG is constructed using only the confidence in the individual edges of the bootstrapped DAGs, thus disregarding complex higher-order edge structures. In this paper, we introduce a novel theoretical framework based on higher-order structures and describe a new DAG aggregation algorithm. We perform a simulation study, discussing the advantages and limitations of the proposed approach. Our proposal is both computationally efficient and effective, outperforming state-of-the-art solutions, especially in low sample size regimes and under high dimensionality settings.

We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the covariance estimator and Stein's loss of the precision matrix estimator against all distributions from an ambiguity set centered at the nominal distribution. The radius of the ambiguity set is measured via convex spectral divergence. We demonstrate that the proposed distributionally robust estimation model can be reduced to a convex optimization problem, thereby yielding quasi-analytical estimators. The joint estimators are shown to be nonlinear shrinkage estimators. The eigenvalues of the estimators are shrunk nonlinearly towards a positive scalar, where the scalar is determined by the weight coefficient of the loss terms. By tuning the coefficient carefully, the shrinkage corrects the spectral bias of the empirical covariance/precision matrix estimator. By this property, we call the proposed joint estimator the Spectral concentrated COvariance and Precision matrix Estimator (SCOPE). We demonstrate that the shrinkage effect improves the condition number of the estimator. We provide a parameter-tuning scheme that adjusts the shrinkage target and intensity that is asymptotically optimal. Numerical experiments on synthetic and real data show that our shrinkage estimators perform competitively against state-of-the-art estimators in practical applications.

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions–how the timing of an event would change under a specified intervention–commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to estimate counterfactual hazard trajectories in a panel data setting where multiple units experience potentially different treatments over multiple periods. In such a setting, SSC estimates the counterfactual hazard trajectory for a unit of interest as a weighted combination of the observed trajectories from other units. To provide formal justification, we introduce a panel framework with a low-rank structure for causal survival analysis. Indeed, such a structure naturally arises under classical parametric survival models. Within this framework, for the causal estimand of interest, we establish identification and finite sample guarantees for SSC. We validate our approach using a multi-country clinical dataset of cancer treatment outcomes, where the staggered introduction of new therapies creates a quasi-experimental setting. Empirically, we find that access to novel treatments is associated with improved survival, as reflected by lower post-intervention hazard trajectories relative to their synthetic counterparts. Given the broad relevance of survival analysis across medicine, economics, and public policy, our framework offers a general and interpretable tool for counterfactual survival inference using observational data.

We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses the dynamic Ising model as a special case. We formulate a likelihood-based approach for parameter estimation and statistical inference. We achieve efficient parameter estimation in high-dimensional settings through the use of the pseudo-likelihood method. To perform model selection, a birth-and-death Markov chain Monte Carlo algorithm is proposed to explore the model space and select the most suitable model.

Correlation coefficient is widely used in biomedical and biological literature, yet its frequent misuse and misinterpretation undermine the credibility and reproducibility of the scientific findings. We systematically reviewed 1326 records of correlation analyses across 310 articles published in Science, Nature, and Nature Neuroscience in 2022. Our analysis revealed a troubling pattern of poor statistical reporting and inferring: 58.71% (95% CI: [53.23%, 64.19%], 182/310) of studies did not explicitly report sample sizes, and 98.06% (95% CI: [96.53%, 99.60%], 304/310) failed to provide confidence intervals for correlation coefficients. Among 177 articles inferring correlation strength, 45.25% (95% CI: [38.42%, 53.10%], 81/177) relied solely on point estimates, while 53.63% (95% CI: [46.90%, 61.58%], 96/177) drew conclusions based on null hypothesis significance testing. This widespread omission and misuse highlight a systematic gap in both statistic literacy and editorial standards. We advocate clear reporting guidelines mandating effect sizes and confidence intervals in correlation analyses to enhance the transparency, rigor, and reproducibility of quantitative life sciences research.

Integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) models are a popular framework for modeling serial dependence in count time-series. While convenient for modeling, prediction, and estimation, INGARCH models lack a clear theoretical justification for the evolution step. This limitation not only makes interpretation difficult and complicates the inclusion of covariates, but can also make the handling of missing data computationally burdensome. Consequently, applying such models in an insurance context, where covariates and missing observations are common, can be challenging. In this paper, we first introduce the marginalized state-space model (M-SSM), defined solely through the marginal distribution of the observations, and show that INGARCH models arise as special cases of this framework. The M-SSM formulation facilitates the natural incorporation of covariates and missing data mechanisms, and this representation in turn provides a coherent way to incorporate these elements within the INGARCH model as well. We then demonstrate that an M-SSM can admit an observation-driven state-space model (O-SSM) representation when suitable assumptions are imposed on the evolution of its conditional mean. This lifting from an M-SSM to an O-SSM provides a natural setting for establishing weak stationarity, even in the presence of heterogeneity and missing observations. The proposed ideas are illustrated through the Poisson and the Negative-Binomial INGARCH(1,1) models, highlighting their applicability in predictive analysis for insurance data.

Medication recommendation systems play a crucial role in assisting clinicians with personalized treatment decisions. While existing approaches have made significant progress in learning medication representations, they suffer from two fundamental limitations: (i) treating medical entities as independent features without modeling their synergistic effects on medication selection; (ii) employing static causal relationships that fail to adapt to patient-specific contexts and health states. To address these challenges, we propose CafeMed, a framework that integrates dynamic causal reasoning with cross-modal attention for safe and accurate medication recommendation. CafeMed introduces two key components: the Causal Weight Generator (CWG) that transforms static causal effects into dynamic modulation weights based on individual patient states, and the Channel Harmonized Attention Refinement Module (CHARM) that captures complex interdependencies between diagnoses and procedures. This design enables CafeMed to model how different medical conditions jointly influence treatment decisions while maintaining medication safety constraints. Extensive experiments on MIMIC-III and MIMIC-IV datasets demonstrate that CafeMed significantly outperforms state-of-the-art baselines, achieving superior accuracy in medication prediction while maintaining the lower drug–drug interaction rates. Our results indicate that incorporating dynamic causal relationships and cross-modal synergies leads to more clinically-aligned and personalized medication recommendations. Our code is released publicly at https://github.com/rkl71/CafeMed.

Latent-variable models on spheres and hyperbolic spaces usually draw a Gaussian in the tangent space at a base point and push it onto the manifold. On these spaces the distance from the base point is the coordinate that carries meaning: depth in a hierarchy, the angle of a rotation, the deviation of a protein frame from a reference. We show that the standard construction silently replaces whatever distance distribution the modeler intended with a fixed one, a scaled chi law whose shape no setting of the scale can change. We then solve the reverse problem. Given the intended distance distribution, we derive in closed form the tangent density that realizes it, prove it is the only isotropic choice with chart-independent likelihoods for a broad class of charts, and prove a lower bound with explicit constants on what ignoring the problem costs a variational autoencoder. Experiments backed by an exact per-run normalization audit confirm that the compensated prior is invariant to the chart and stable across scales, every wrapped baseline we train collapses to the boundary of its chart, curvature becomes recoverable where the wrapped prior fails and protein-orientation likelihood improves from 2.58 to 0.87 nats at identical accuracy.

Adaptive learning often diagnoses precisely yet intervenes weakly, yielding help that is mistimed or misaligned. This study presents evidence supporting an instructor-governed feedback loop that converts concept-level assessment evidence into vetted micro-interventions. The adaptive learning algorithm contains three safeguards: adequacy as a hard guarantee of gap closure, attention as a budgeted constraint for time and redundancy, and diversity as protection against overfitting to a single resource. We formalize intervention assignment as a binary integer program with constraints for coverage, time, difficulty windows informed by ability estimates, prerequisites encoded by a concept matrix, and anti-redundancy enforced through diversity. Greedy selection serves low-richness and tight-latency regimes, gradient-based relaxation serves rich repositories, and a hybrid method transitions along a richness-latency frontier. In simulation and in an introductory physics deployment with one thousand two hundred four students, both solvers achieved full skill coverage for essentially all learners within bounded watch time. The gradient-based method reduced redundant coverage by approximately twelve percentage points relative to greedy and harmonized difficulty across slates, while greedy delivered comparable adequacy with lower computational cost in scarce settings. Slack variables localized missing content and supported targeted curation, sustaining sufficiency across subgroups. The result is a tractable and auditable controller that closes the diagnostic-pedagogical loop and delivers equitable, load-aware personalization at classroom scale.

Small and medium-sized enterprises (SMEs) represent 99.9% of U.S. businesses yet remain systematically excluded from AI due to a mismatch between their operational scale and modern machine learning's data requirements. This paper introduces SmallML, a Bayesian transfer learning framework achieving enterprise-level prediction accuracy with datasets as small as 50-200 observations. We develop a three-layer architecture integrating transfer learning, hierarchical Bayesian modeling, and conformal prediction. Layer 1 extracts informative priors from 22,673 public records using a SHAP-based procedure transferring knowledge from gradient boosting to logistic regression. Layer 2 implements hierarchical pooling across J=5-50 SMEs with adaptive shrinkage, balancing population patterns with entity-specific characteristics. Layer 3 provides conformal sets with finite-sample coverage guarantees P(y in C(x)) >= 1-alpha for distribution-free uncertainty quantification. Validation on customer churn data demonstrates 96.7% +/- 4.2% AUC with 100 observations per business – a +24.2 point improvement over independent logistic regression (72.5% +/- 8.1%), with p < 0.000001. Conformal prediction achieves 92% empirical coverage at 90% target. Training completes in 33 minutes on standard CPU hardware. By enabling enterprise-grade predictions for 33 million U.S. SMEs previously excluded from machine learning, SmallML addresses a critical gap in AI democratization. Keywords: Bayesian transfer learning, hierarchical models, conformal prediction, small-data analytics, SME machine learning

We introduce a highly expressive class of function approximators called Splat Regression Models. Model outputs are mixtures of heterogeneous and anisotropic bump functions, termed splats, each weighted by an output vector. The power of splat modeling lies in its ability to locally adjust the scale and direction of each splat, achieving both high interpretability and accuracy. Fitting splat models reduces to optimization over the space of mixing measures, which can be implemented using Wasserstein-Fisher-Rao gradient flows. As a byproduct, we recover the popular Gaussian Splatting methodology as a special case, providing a unified theoretical framework for this state-of-the-art technique that clearly disambiguates the inverse problem, the model, and the optimization algorithm. Through numerical experiments, we demonstrate that the resulting models and algorithms constitute a flexible and promising approach for solving diverse approximation, estimation, and inverse problems involving low-dimensional data.

Using data on 103 recent P4 college football hires, we built a statistical model for predicting a coach's success at their new school. For each hire, we collected data about their background and experiences, the previous success as a head coach or coordinator and their success since hiring. Over 50 variables on these factors were recorded though we used 29 of these in building our predictive model. Our measure of success is based upon Bill Connelly's SP+ team ratings relative to the performance on the same metric of the school in the 15 year prior to their selection as head coach. Using a cross-validated regularized linear regression, we obtain a predictive model for coaching success. Among the important factors for predicting a successful hire are having been a previous college head coach, leaving a job as an Offensive Coordinator, age and quality of the hiring school's team in the previous 15 years. While we do find these factors are important for the prediction of a successful coaching hire, the trends here are weak. With 66% accuracy, the model does identify coaching hires that will outperform team performance in the 15 years before the hire. However, no combination of these factors leads to high predictability of identifying a successful coaching hire. All of the data and code for this paper are available in a Github repository.

Algorithms developed under stationary Markov Decision Processes (MDPs) often face challenges in non-stationary environments, and infinite-horizon formulations may not directly apply to finite-horizon tasks. To address these limitations, we introduce the Non-stationary and Varying-discounting MDP (NVMDP) framework, which naturally accommodates non-stationarity and allows discount rates to vary with time and transitions. Infinite-horizon, stationary MDPs emerge as special cases of NVMDPs for identifying an optimal policy, and finite-horizon MDPs are also subsumed within the NVMDP formulations. Moreover, NVMDPs provide a flexible mechanism to shape optimal policies, without altering the state space, action space, or the reward structure. We establish the theoretical foundations of NVMDPs, including assumptions, state- and action-value formulation and recursion, matrix representation, optimality conditions, and policy improvement under finite state and action spaces. Building on these results, we adapt dynamic programming and generalized Q-learning algorithms to NVMDPs, along with formal convergence proofs. For problems requiring function approximation, we extend the Policy Gradient Theorem and the policy improvement bound in Trust Region Policy Optimization (TRPO), offering proofs in both scalar and matrix forms. Empirical evaluations in a non-stationary gridworld environment demonstrate that NVMDP-based algorithms successfully recover optimal trajectories under multiple reward and discounting schemes, whereas original Q-learning fails. These results collectively show that NVMDPs provide a theoretically sound and practically effective framework for reinforcement learning, requiring only minor algorithmic modifications while enabling robust handling of non-stationarity and explicit optimal policy shaping.

Synthetic tabular data, which are widely used in domains such as healthcare, enterprise operations, and customer analytics, are increasingly evaluated to ensure that they preserve both privacy and utility. While existing evaluation practices typically focus on distributional similarity (e.g., the Kullback-Leibler divergence) or predictive performance (e.g., Train-on-Synthetic-Test-on-Real (TSTR) accuracy), these approaches fail to assess semantic fidelity, that is, whether models trained on synthetic data follow reasoning patterns consistent with those trained on real data. To address this gap, we introduce the SHapley Additive exPlanations (SHAP) Distance, a novel explainability-aware metric that is defined as the cosine distance between the global SHAP attribution vectors derived from classifiers trained on real versus synthetic datasets. By analyzing datasets that span clinical health records with physiological features, enterprise invoice transactions with heterogeneous scales, and telecom churn logs with mixed categorical-numerical attributes, we demonstrate that the SHAP Distance reliably identifies semantic discrepancies that are overlooked by standard statistical and predictive measures. In particular, our results show that the SHAP Distance captures feature importance shifts and underrepresented tail effects that the Kullback-Leibler divergence and Train-on-Synthetic-Test-on-Real accuracy fail to detect. This study positions the SHAP Distance as a practical and discriminative tool for auditing the semantic fidelity of synthetic tabular data, and offers practical guidelines for integrating attribution-based evaluation into future benchmarking pipelines.

Level-based and share-based loss functions are asymptotically equivalent if, in the limit, their averages converge almost surely to a constant ratio. These loss functions take a target value and its realization as arguments and are often used to measure accuracy. The equivalence is proved for a large class of loss functions, the weighted exponentiated functions, when the weights are decomposable as a particular product form. An upshot is that when losses are averaged for a large number of units, differences in ratios and, hence, ranks, are negligible, when the average (or summed) difference between the target values and their realizations is around zero. This implies the almost sure asymptotic convergence of numerical and distributive accuracy when using these loss functions.

We study the running time, in terms of first order oracle queries, of differentially private empirical/population risk minimization of Lipschitz convex losses. We first consider the setting where the loss is non-smooth and the optimizer interacts with a private proxy oracle, which sends only private messages about a minibatch of gradients. In this setting, we show that expected running time $\Omega(\min\{\frac{\sqrt{d}}{\alpha^2}, \frac{d}{\log(1/\alpha)}\})$ is necessary to achieve $\alpha$ excess risk on problems of dimension $d$ when $d \geq 1/\alpha^2$. Upper bounds via DP-SGD show these results are tight when $d>\tilde{\Omega}(1/\alpha^4)$. We further show our lower bound can be strengthened to $\Omega(\min\{\frac{d}{\bar{m}\alpha^2}, \frac{d}{\log(1/\alpha)} \})$ for algorithms which use minibatches of size at most $\bar{m} < \sqrt{d}$. We next consider smooth losses, where we relax the private oracle assumption and give lower bounds under only the condition that the optimizer is private. Here, we lower bound the expected number of first order oracle calls by $\tilde{\Omega}\big(\frac{\sqrt{d}}{\alpha} + \min\{\frac{1}{\alpha^2}, n\}\big)$, where $n$ is the size of the dataset. Modifications to existing algorithms show this bound is nearly tight. Compared to non-private lower bounds, our results show that differentially private optimizers pay a dimension dependent runtime penalty. Finally, as a natural extension of our proof technique, we show lower bounds in the non-smooth setting for optimizers interacting with information limited oracles. Specifically, if the proxy oracle transmits at most $\Gamma$-bits of information about the gradients in the minibatch, then $\Omega\big(\min\{\frac{d}{\alpha^2\Gamma}, \frac{d}{\log(1/\alpha)}\}\big)$ oracle calls are needed. This result shows fundamental limitations of gradient quantization techniques in optimization.

We develop an empirical likelihood (EL) framework for random forests and related ensemble methods, providing a likelihood-based approach to quantify their statistical uncertainty. Exploiting the incomplete $U$-statistic structure inherent in ensemble predictions, we construct an EL statistic that is asymptotically chi-squared when subsampling induced by incompleteness is not overly sparse. Under sparser subsampling regimes, the EL statistic tends to over-cover due to loss of pivotality; we therefore propose a modified EL that restores pivotality through a simple adjustment. Our method retains key properties of EL while remaining computationally efficient. Theory for honest random forests and simulations demonstrate that modified EL achieves accurate coverage and practical reliability relative to existing inference methods.

Despite recent progress in predicting biomarker trajectories from real clinical data, uncertainty in the predictions poses high-stakes risks (e.g., misdiagnosis) that limit their clinical deployment. To enable safe and reliable use of such predictions in healthcare, we introduce a conformal method for uncertainty-calibrated prediction of biomarker trajectories resulting from randomly-timed clinical visits of patients. Our approach extends conformal prediction to the setting of randomly-timed trajectories via a novel nonconformity score that produces prediction bands guaranteed to cover the unknown biomarker trajectories with a user-prescribed probability. We apply our method across a wide range of standard and state-of-the-art predictors for two well-established brain biomarkers of Alzheimer's disease, using neuroimaging data from real clinical studies. We observe that our conformal prediction bands consistently achieve the desired coverage, while also being tighter than baseline prediction bands. To further account for population heterogeneity, we develop group-conditional conformal bands and test their coverage guarantees across various demographic and clinically relevant subpopulations. Moreover, we demonstrate the clinical utility of our conformal bands in identifying subjects at high risk of progression to Alzheimer's disease. Specifically, we introduce an uncertainty-calibrated risk score that enables the identification of 17.5% more high-risk subjects compared to standard risk scores, highlighting the value of uncertainty calibration in real-world clinical decision making. Our code is available at github.com/vatass/ConformalBiomarkerTrajectories.

This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can lead to biased causal estimands when mis-specified. We focus on directly estimating time–unit–specific causal effects and use generalised Bayesian inference to quantify model mis-specification and adjust for it, while retaining interpretable posterior inference. We select the learning rate~$\omega$ based on a proper scoring rule that jointly evaluates point and interval accuracy of the causal estimand, thus providing a coherent, decision-theoretic foundation for tuning~$\omega$. Simulation studies and applications to real data demonstrate improved calibration, sharpness, and robustness in estimating causal effects.

This paper investigates how market competition influences poverty dynamics using a functional econometric framework that captures both contemporaneous and lagged effects. Using annual data for 48 countries from 1991-2017, we estimate function-on-function regressions linking poverty headcount ratios to market concentration and other macroeconomic indicators. The results show that, based on the entire sample, stronger competition initially increased poverty during structural adjustment phases, but its adverse impact weakened after 2010 as economies adapted and efficiency gains emerged. The estimated bivariate surfaces reveal that the effect of competition on poverty often persists over multiple years (around 5 years), highlighting the importance of intertemporal transmission. Then, functional clustering based on market capitalization (MCAP) uncovers strong heterogeneity: pro-poor 5-years lagged effect of competition in low- and medium-MCAP economies, while it remains insignificant to weakly negative in high-MCAP countries. Overall, the findings underscore the value of functional data methods in uncovering evolving and lag-dependent poverty-competition linkages that static panel models fail to capture.

Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations that exploit locality in the distributions. These methods approximate high-dimensional couplings using low-order marginals and sparse moment statistics, yielding semidefinite programs that provide lower bounds on the OT cost with greatly reduced complexity. For Gaussian measures with sparse correlations, we prove an exponential convergence rate for the cluster moment relaxation and an improved statistical error bound. We also establish approximation error bounds for the marginal relaxation when the reference measures are local perturbations of mean-field measures. In addition, we demonstrate how to extract transport maps from our relaxations, offering a simpler and interpretable alternative to neural networks in generative modeling. Extensive numerical experiments demonstrate strong empirical performance across a range of distributions. Our results suggest that convex relaxations can provide a promising path for dimension reduction in high-dimensional OT.

A decision-theoretic characterization of perfect calibration is that an agent seeking to minimize a proper loss in expectation cannot improve their outcome by post-processing a perfectly calibrated predictor. Hu and Wu (FOCS'24) use this to define an approximate calibration measure called calibration decision loss ($\mathsf{CDL}$), which measures the maximal improvement achievable by any post-processing over any proper loss. Unfortunately, $\mathsf{CDL}$ turns out to be intractable to even weakly approximate in the offline setting, given black-box access to the predictions and labels. We suggest circumventing this by restricting attention to structured families of post-processing functions $K$. We define the calibration decision loss relative to $K$, denoted $\mathsf{CDL}_K$ where we consider all proper losses but restrict post-processings to a structured family $K$. We develop a comprehensive theory of when $\mathsf{CDL}_K$ is information-theoretically and computationally tractable, and use it to prove both upper and lower bounds for natural classes $K$. In addition to introducing new definitions and algorithmic techniques to the theory of calibration for decision making, our results give rigorous guarantees for some widely used recalibration procedures in machine learning.

We present a method for computing optimal fixed-width confidence intervals for a single, bounded parameter, extending a method for the binomial due to Asparaouhov and Lorden, who called it the Push algorithm. The method produces the shortest possible non-decreasing confidence interval for a given confidence level, and if the Push interval does not exist for a given width and level, then no such interval exists. The method applies to any bounded parameter that is discrete, or is continuous for which interval probabilities are quasiconcave. We demonstrate the method on the binomial, hypergeometric, and normal distributions with our available R package. In each of these distributions the proposed method outperforms the standard ones, and in the latter case even improves upon the $z$-interval. We apply the proposed method to World Health Organization (WHO) data on tobacco use.

Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that efficiently manage massive datasets while preserving essential physical features and quantities of interest. In many scientific workflows, it is also crucial to enable data recovery from compressed representations - a task known as super-resolution - with guarantees on the preservation of key physical characteristics. A notable example is checkpointing and restarting, which is essential for long-running simulations to recover from failures, resume after interruptions, or examine intermediate results. In this work, we introduce a novel framework for scientific data compression and super-resolution, grounded in recent advances in learning exponential families. Our method preserves and quantifies uncertainty in physical quantities of interest and supports flexible trade-offs between compression ratio and reconstruction fidelity.

Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal in-control signal probability at a prescribed level by employing the finite Markov chain imbedding technique combined with random permutation and conditioning arguments. To elucidate the methodology, we examine two popular runs- and patterns-type statistics: the number of success runs and the scan statistic. Numerical results indicate that the performance of our proposed control charts is comparable to that of existing Phase I nonparametric control charts for individual observations.

We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for direct implementation. After establishing these estimators, we derive closed-form expressions for probability estimates over regions of the circle and the sphere. Then, the proposed theories are supported by extensive simulation studies. The considered settings naturally arise when analyzing phenomena on the Earth's surface or in the sky (sphere), as well as directional or periodic phenomena (circle). The proposed approaches are broadly applicable, and we illustrate their usefulness through case studies in zoology, climatology, geophysics, and astronomy, which may be of independent interest. The methodologies developed here can be readily applied across a wide range of scientific domains.

We seek to design novel multiple testing procedures, which take into account a relevant notion of ”power” or true discovery on the one hand, and allow computationally efficient test design and application on the other. Towards this end we characterize the optimal procedures that strongly control the family-wise error rate, for a range of power objectives measuring the success of multiple testing procedures in making true individual discoveries, and under a reasonable set of assumptions. While we cannot generally find these optimal solutions in practice, we propose the bottom-up approach, which constructs consonant closed testing procedures, while taking into account the overall power objective in designing the tests on every level of the closed testing hierarchy. This leads to a general recipe, yielding novel procedures which are computationally practical and demonstrate substantially improved power in both simulations and a real data study, compared to existing procedures.