Papers

Testing the homogeneity of two distributions is fundamental in statistics, but classical procedures may fail under nonignorable nonresponse. In many surveys, callback data record repeated contact attempts and provide auxiliary information about the response mechanism. We develop a semiparametric framework for two-sample homogeneity testing that explicitly incorporates such information. The response mechanism is modeled by a flexible semiparametric callback model, while the two population distributions are linked through a density ratio model. Within this unified framework, we propose an empirical likelihood ratio test for distributional homogeneity and show that, under the null hypothesis, it has a Wilks-type chi-square limit. To facilitate computation, we develop an efficient expectation-maximization-type algorithm. Simulation results show that the proposed method controls type I error well and achieves substantially higher power than existing methods that ignore nonignorable missingness. An application to real survey income data illustrates its practical value.

As research in causal inference has sought to address more complex scientific questions, the number of specialized estimands in the field has proliferated. Recognition that many of these estimands share a common linear form has generated interest in simplifying estimation procedures using Riesz representers. In this work, we construct a targeted minimum loss-based estimation procedure for nested linear functionals, leveraging Riesz representers of a general recursive form. The proposed method unifies asymptotically efficient estimation for a variety of statistical estimands that originate in causal inference, including the effects of time-varying treatments under treatment-confounder feedback and direct and indirect effects from causal mediation analysis. We demonstrate how our proposal reduces the need for laborious and technically challenging mathematical derivations when constructing estimators of common statistical estimands under complex forms of censoring and sampling. We investigate and validate the properties of the proposed procedures in numerical experiments, discuss open-source software facilitating their implementation, and illustrate their application in a re-analysis of data from an HIV vaccine efficacy trial.

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and performance of neural networks. We pull together major strands of ongoing research in deep learning theory and identify five growing bodies of work that point toward such a theory: (a) solvable idealized settings that provide intuition for learning dynamics in realistic systems; (b) tractable limits that reveal insights into fundamental learning phenomena; (c) simple mathematical laws that capture important macroscopic observables; (d) theories of hyperparameters that disentangle them from the rest of the training process, leaving simpler systems behind; and (e) universal behaviors shared across systems and settings which clarify which phenomena call for explanation. Taken together, these bodies of work share certain broad traits: they are concerned with the dynamics of the training process; they primarily seek to describe coarse aggregate statistics; and they emphasize falsifiable quantitative predictions. We argue that the emerging theory is best thought of as a mechanics of the learning process, and suggest the name learning mechanics. We discuss the relationship between this mechanics perspective and other approaches for building a theory of deep learning, including the statistical and information-theoretic perspectives. In particular, we anticipate a symbiotic relationship between learning mechanics and mechanistic interpretability. We also review and address common arguments that fundamental theory will not be possible or is not important. We conclude with a portrait of important open directions in learning mechanics and advice for beginners. We host further introductory materials, perspectives, and open questions at learningmechanics.pub.

E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well understood, one may need/wish to impose additional structural constraints, including differential privacy, quantization, boundedness, or moment restrictions. We show that under these constraints, log-optimal constrained e-variables can often be constructed by a simple optimize-then-constrain principle: first compute the unconstrained log-optimal e-variable, then impose the constraint via an appropriate transformation. Thus, the constrained growth-rate optimization problem does not require solving for a different LFD pair; the constrained optimal solution is just a post-processing of the unconstrained optimal solution.

Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers. Intersubject correlation (ISC) is the main method for identifying voxelwise shared responses and per-subject variability, but it relies on heavy data summarization and thousands of regional tests, leading to poor uncertainty quantification and multiple testing issues. ISC also does not directly estimate a shared neural response (SNR) function. We propose a model-based alternative applicable to both task-based and naturalistic fMRI that simultaneously identifies spatial regions of shared activity and estimates the SNR function. The model combines sparse Gaussian process estimation of the response function with a Bayesian sparsity prior inspired by the horseshoe prior to detect voxel activation. A spatially structured extension encourages neighboring voxels to exhibit similar activation patterns. We examine the model's properties, evaluate performance via simulations, and analyze two real-world fMRI datasets, including one task-based and one naturalistic dataset. The Bayesian framework provides principled uncertainty quantification for the shared response function and shows improved activation detection and response estimation compared to standard approaches. Model fits demonstrate comparable or superior performance relative to ISC, while the framework opens avenues for clinical applications.

Mutational signatures describe the pattern of mutations over the different mutation types. Each mutation type is determined by a base substitution and the flanking nucleotides to the left and right of that base substitution. Due to the widespread interest in mutational signatures, several efforts have been devoted to the development of methods for robust and stable signature estimation. Here, we combine various extensions of the standard framework to estimate mutational signatures. These extensions include (a) incorporating opportunities to the analysis, (b) allowing for extended sequence contexts, (c) using the Negative Binomial model, and (d) parametrizing the signatures. We show that the combination of these four extensions gives very robust and reliable mutational signatures. In particular, we highlight the importance of including mutational opportunities and parametrizing the signatures when the mutation types describe an extended sequence context with two or three flanking nucleotides to each side of the base substitution.

In observational studies, accurately characterizing variance is critical for sample size determination, yet unaccounted-for variability from propensity score estimation and the resulting weights limit the accuracy of standard variance approximations for design. Existing approaches often rely on heuristics or randomized controlled trial (RCT) formulas that treat weights as fixed, potentially misaligning prospective design with the causal estimator used at analysis. We propose an estimator-aligned framework for prospective sample size determination based on generalized estimating equations (GEE) and stacked M-estimation. By merging the propensity score model and marginal structural model (MSM) into a single system of estimating equations, the method propagates nuisance-model uncertainty and directly targets the large-sample variance of the IPTW estimator. For study planning, we estimate a pilot-based large-sample variance factor and introduce a bootstrap stabilization procedure that accounts for both within- and between-pilot variability. The framework applies uniformly across binary, count, and continuous outcomes through link-specific GEE representations under a common design principle. Simulation studies motivated by post-marketing safety and healthcare cost applications demonstrate that anchoring design to this variance improves power calibration relative to conventional RCT-style formulas, particularly in settings with weight instability, outcome sparsity, or heavy-tailed variability.

Concurrent floods and concurrent droughts in nearby catchments pose challenges to risk assessment and water management. Climate change is affecting extremely high and low discharge, but the complex interplay between changes in individual catchments and in the dependence across catchments make it difficult to provide accurate assessments of the occurrence probabilities of concurrent extremes. In this work, we use a contemporary statistical deep learning model (the deep SPAR framework) to capture concurrent river floods and droughts in four catchments in the Upper Danube basin, based on discharge simulated by a hydrological model driven with large ensemble climate model output. The statistical model is able to accurately capture the multivariate extremes of the simulated discharge, which we assess by making use of the large available sample size. We subsequently use our statistical model to study changes in joint tail behaviour of discharge over time, finding that both compound flooding and drought-like conditions are becoming increasingly likely towards the end of the 21st century under a high-emission scenario. In particular, our results highlight that changes in the dependence structure of extremes strongly contribute to the detected changes, an aspect that would be difficult to capture with traditional approaches. This work paves the way for highly flexible, general inference on compound extremes in hydrological applications, and demonstrates key advantages of using statistical deep learning in this setting.

Causal discovery in multivariate extremes is challenging because extreme observations are sparse, dependent, and often affected by latent common shocks. Existing approaches focus on undirected extremal dependence, require prior graph restriction, and do not scale beyond small systems. We introduce tail-induced asymmetry as a principle for causal directionality in heavy-tailed systems, where extreme events propagate asymmetrically so that forward tail prediction is systematically easier than backward prediction. We show that this asymmetry yields identifiable causal direction under a canonical max-linear model and provides a basis for score-based structure learning in the tail regime. Building on this, we propose Sparse Structure diScovery in Multivariate Extremes (S3ME), a two-stage data-driven framework for causal discovery. The first stage performs proxy-adjusted penalized neighbourhood selection to recover a sparse candidate skeleton under latent confounding. The second stage orients edges by minimizing tail prediction risk based on max-linear envelope models, exploiting directional asymmetry. We establish high-dimensional guarantees for skeleton screening and consistency of the score-based estimator under population separation conditions. Simulations demonstrate robustness to latent confounding and favourable scaling relative to existing extremal methods. Applications to river network data and financial tail-risk networks show that the approach recovers sparse, interpretable propagation structures without prespecified graph structure.

Bayes factor sensitivity analysis examines how the evidence for one hypothesis over another depends on the prior distribution. In complex models, the standard approach refits the model at each hyper-parameter value, and the total computational cost scales linearly in the grid size. We propose a method that recovers the entire sensitivity curve from a single additional model fit. The key identity decomposes the Bayes factor at any hyper-parameter value $\gamma_x$ into an “anchor” Bayes factor at a fixed reference $\gamma_0$ and a Savage–Dickey density ratio in an extended model that places a hyper-prior on $\gamma$. Once this extended model is fit, the Bayes factor at any $\gamma_x$ follows from the anchor value and a ratio of two posterior density ordinates. To approximate this ratio, we employ the importance-weighted marginal density estimator (IWMDE). Because the sensitivity parameter enters the model only through the prior distribution on the model parameters, the data likelihood cancels in the IWMDE, reducing it to a simple ratio of prior density evaluations on the MCMC draws, without any additional likelihood computation. The resulting estimator is fast, remains accurate even with small MCMC samples, and substantially outperforms kernel density estimation across the full sensitivity range. The method extends naturally to simultaneous sensitivity over multiple hyper-parameters and to Bayesian model averaging. We illustrate it on a univariate Bayesian $t$-test with exact Bayes factors for validation, a bivariate informed $t$-test, and a Bayesian model-averaged meta-analysis, obtaining accurate sensitivity curves at a fraction of the brute-force cost.

Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS) that produces prediction regions that explicitly adapt to this geometry. We show that the proposed score resembles the Gaussian process posterior variance, unifying Bayesian uncertainty quantification with the coverage guarantees of frequentist-type. Moreover, the MKS can be decomposed into an anisotropic Maximum Mean Discrepancy (MMD) that interpolates between kernel density estimation and covariance-weighted distance. We prove finite-sample coverage guarantees and establish convergence rates that depend on the effective rank of the kernel-based covariance operator rather than the ambient dimension, enabling dimension-free adaptation. On regression tasks, the MKS reduces the volume of prediction region significantly, compared to ellipsoidal baselines while maintaining nominal coverage, with larger gains at higher dimensions and tighter coverage levels.

Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications – estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM – demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.

Treatment effect distributions are not identified without restrictions on the joint distribution of potential outcomes. Existing approaches either impose rank preservation – a strong assumption – or derive partial identification bounds that are often wide. We show that a single scalar parameter, rank stickiness, suffices for nonparametric point identification while permitting rank violations. The identified joint distribution – the coupling that maximizes average rank correlation subject to a relative entropy constraint, which we call the Bregman-Sinkhorn copula – is uniquely determined by the marginals and rank stickiness. Its conditional distribution is an exponential tilt of the marginal with a Bregman divergence as the exponent, yielding closed-form conditional moments and rank violation probabilities; the copula nests the comonotonic and Gaussian copulas as special cases. The empirical Bregman-Sinkhorn copula converges at the parametric $\sqrt{n}$-rate with a Gaussian process limit, despite the infinite-dimensional parameter space. We apply the framework to estimate the full treatment effect distribution, derive a variance estimator for the average treatment effect tighter than the Fréchet–Hoeffding and Neyman bounds, and extend to observational studies under unconfoundedness.

Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models. Many Bayesian implementations of these models involve a trade-off between computational efficiency and full posterior inference. We propose instead a Bayesian approach able to provide both aspects. The method fixes the total number of components to a large value and employs an asymmetric Dirichlet prior on the mixture weights. The asymmetric Dirichlet hyperparameters are elicited using the popular Penalized Complexity prior framework, which provides an intuitive way for users to inform the induced distribution of the number of clusters. An efficient MCMC algorithm is then developed to fit the model. Simulations and real-world applications demonstrate that the method is competitive with existing alternatives and can outperform them in certain settings. The proposal is illustrated using an ecological dataset about presence-absence of species across multiple sites, where cluster-specific parameters are modelled on the basis of environmental conditions. Overall, the proposed method provides a computationally efficient, fully Bayesian, and interpretable framework for clustering multivariate binary data, with potential applications across diverse scientific domains.

Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an Itô stochastic differential equation (SDE) and observations arrive at discrete times. We propose a novel class of constrained PFs that enforce compact support on the state at each observation instant, thereby limiting exploration to plausible regions of the state space. Unlike earlier approaches that truncate the likelihood, the proposed method constrains the dynamics directly, yielding improved numerical stability. Under standard regularity assumptions, we prove convergence of the constrained filter, derive uniform-in-time error estimates, and extend the analysis to account for discretisation errors arising from numerical SDE solvers. A numerical study on a stochastic Lorenz-96 system demonstrates the practical application of the methodology when the constraint is implemented via barrier functions.

Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the design of assistive technologies. We analyze experimental data in which blind, low-vision, and sighted participants performed spatial updating tasks under five sensory conditions, with signed angular error as the response. To model these data, we propose a nonparametric circular regression framework that accommodates both continuous and categorical predictors via a product-kernel estimator. Bandwidth selection is crucial in this setting, yet developing practical data-driven methods remains challenging. We derive asymptotic bias and variance expressions for the estimator, though these results do not directly lead to a feasible plug-in bandwidth selector. To address this, we develop a bootstrap bandwidth selection criterion tailored to the cosine loss and compare it with cross-validation and rule-of-thumb approaches in simulation studies. Applied to the spatial updating data, the proposed framework reveals nonlinear, condition-specific patterns and quantifies uncertainty via simultaneous bootstrap confidence bands. Across the scenarios considered, the proposed bootstrap selector achieves a favorable bias-variance trade-off and yields stable inference relative to the competing methods. An implementation is available in the R package circMixedReg.

Differential privacy (DP) is a mathematical framework that guarantees individual privacy; however, systematic evaluation of its impact on statistical utility in survival analyses remains limited. In this study, we systematically evaluated the impact of DP mechanisms (Laplace mechanism and Randomized Response) with data-driven clipping bounds on the Cox proportional hazards model, using 5 clinical datasets ($n = 168$–$6{,}524$), 15 levels of $\varepsilon$ (0.1–1000), and $B = 1{,}000$ Monte Carlo iterations. The data-driven clipping bounds used here are observed min/max and therefore do not provide formal $\varepsilon$-DP guarantees; the results represent an optimistic lower bound on utility degradation under formal DP. We compared three types of input perturbations (covariates only, all inputs, and the discrete-time model) with output perturbations (dfbeta-based sensitivity), using loss of significance rate (LSR), C-index, and coefficient bias as metrics. At standard DP levels ($\varepsilon \leq 1$), approximately 90% (90–94%) of the significant covariates lost significance, even in the largest dataset ($n = 6{,}524$), and the predictive performance approached random levels (test C-index $\approx 0.5$) under many conditions. Among the input perturbation approaches, perturbing only covariates preserved the risk-set structure and achieved the best recovery, whereas output perturbation (dfbeta-based sensitivity) maintained near-baseline performance at $\varepsilon \geq 5$. At $n \approx 3{,}000$, the significance recovered rapidly at $\varepsilon = 3$–10; however, in practice, $\varepsilon \geq 10$ (for predictive performance) to $\varepsilon \geq 30$–60 (for significance preservation) is required. In the moderate-to-high $\varepsilon$ range, false-positive rates increased for variables whose baseline $p$-values were near the significance threshold.

Timely population displacement estimates are critical for humanitarian response during disasters, but traditional surveys and field assessments are slow. Mobile phone data enables near real-time tracking, yet existing approaches apply uniform displacement definitions regardless of individual mobility patterns, misclassifying regular commuters as displaced. We present a methodological framework addressing this through three innovations: (1) mobility profile classification distinguishing local residents from commuter types, (2) context-aware between-municipality displacement detection accounting for expected location by user type and day of week, and (3) operational uncertainty bounds derived from baseline coefficient of variation with a disaster adjustment factor, intended for humanitarian decision support rather than formal statistical inference. The framework produces three complementary metrics scaled to population with uncertainty bounds: displacement rates, origin-destination flows, and return dynamics. An Aparri case study following Super Typhoon Nando (2025, Philippines) applies the framework to vendor-provided daily locations from Globe Telecom. Context-aware detection reduced estimated between-municipality displacement by 1.6-2.7 percentage points on weekdays versus naive methods, attributable to the commuter exception but not independently validated. The method captures between-municipality displacement only. Within-municipality evacuation falls outside scope. The single-case demonstration establishes proof of concept. External validity requires application across multiple events and locations. The framework provides humanitarian actors with operational displacement information while preserving individual privacy through aggregation.

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.

When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target. This raises the question: Under which conditions can we recover characteristics of the target despite misspecification? In this work, we extend previous theoretical results on robust VI with location-scale families under target symmetries in two substantial ways: (1) We open them up to a wider range of divergences by providing sufficient conditions for exact recovery of the target mean and correlation matrix when using the forward Kullback-Leibler divergence and $\alpha$-divergences. (2) By doing so, we find that we can drop the restrictive assumption of a log-concave target made in previous work, allowing us to give guarantees for a wider range of targets, including multi-modal ones. In our experiments, we show how our guarantees can serve as guidelines for the choice of the variational family and $\alpha$-value and we illustrate on a diverse set of examples how and why optimization can fail in the absence of our sufficient conditions.

Parametric insurance contracts translate index measurements to compensation for policyholders' losses using predefined payment schemes. These need to be designed carefully to keep basis risk, i.e. the disparity between payouts and true damages, small. Previous research has motivated the use of conditional expectiles as payment schemes, whose compensation is impacted by the policyholder's potentially unknown attitude towards basis risk. To alleviate this model uncertainty and to investigate the impact of (hidden) influencing factors, we characterize existence and uniqueness of the optimal basis risk weighting in a utility-maximization framework through a set of boundary conditions. In the absence of an optimal solution, we provide comparisons to the utility of no insurance and full indemnity coverage. We establish a link between location-scale distributions and separability of conditional expectiles' derivatives, thus improving the understanding of these statistical functionals. A simulation study on parametric hurricane insurance visualizes our results, investigates the influence of premium loading and risk aversion on the optimal weighting, and comments on the challenge of (spatial) loss dependence.

It is well-known in industrial data science that large values of real-life time series tend to be structured and often follow concrete and visible patterns. In this paper, we use ideas from additive combinatorics and discrete Fourier analysis to give this heuristic a mathematical foundation. Our main tool is the Fourier ratio, a complexity measure previously used in compressed sensing, combined with a generalized version of Chang's lemma from additive combinatorics. Together, these yield a precise prediction: when the Fourier ratio of a time series is small, the set of its largest values can be additively generated by a very small set using only $\{-1,0,1\}$ coefficients. We test this prediction on US inflation data and Delhi climate data, both in their original form and after mean-centering. The numerical results confirm the predicted structure: a generating set of size $4$–$7$ suffices to span large spectra containing dozens of points, even when the Fourier ratio is large enough that our theoretical bounds become loose. These findings provide a rigorous explanation for why extreme values in real-world data are information-rich and structurally significant.

There has been remarkable progress over the past decade in establishing finite-sample, non-asymptotic bounds on recovering unknown system parameters from observed system behavior. Surprisingly, however, we show that the current state-of-the-art bounds do not accurately capture the statistical complexity of system identification, even in the most fundamental setting of estimating a discrete-time linear dynamical system (LDS) via ordinary least-squares regression (OLS). Specifically, we utilize asymptotic normality to identify classes of problem instances for which current bounds overstate the squared parameter error, in both spectral and Frobenius norm, by a factor of the state-dimension of the system. Informed by this discrepancy, we then sharpen the OLS parameter error bounds via a novel second-order decomposition of the parameter error, where crucially the lower-order term is a matrix-valued martingale that we show correctly captures the CLT scaling. From our analysis we obtain finite-sample bounds for both (i) stable systems and (ii) the many-trajectories setting that match the instance-specific optimal rates up to constant factors in Frobenius norm, and polylogarithmic state-dimension factors in spectral norm.

We study semisupervised mean estimation with a small labeled sample, a large unlabeled sample, and a black-box prediction model whose output may be miscalibrated. A standard approach in this setting is augmented inverse-probability weighting (AIPW) [Robins et al., 1994], which protects against prediction-model misspecification but can be inefficient when the prediction score is poorly aligned with the outcome scale. We introduce Calibrated Prediction-Powered Inference, which post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation. This simple step requires no retraining and can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference. We study both linear and isotonic calibration. For isotonic calibration, we establish first-order optimality guarantees: isotonic post-processing can improve predictive accuracy and estimator efficiency relative to the original score and simpler post-processing rules, while no further post-processing of the fitted isotonic score yields additional first-order gains. For linear calibration, we show first-order equivalence to PPI++. We also clarify the relationship among existing estimators, showing that the original PPI estimator is a special case of AIPW and can be inefficient when the prediction model is accurate, while PPI++ is AIPW with empirical efficiency maximization [Rubin et al., 2008]. In simulations and real-data experiments, our calibrated estimators often outperform PPI and are competitive with, or outperform, AIPW and PPI++. We provide an accompanying Python package, ppi_aipw, at https://larsvanderlaan.github.io/ppi-aipw/.

Multimodal clinical records contain structured measurements and clinical notes recorded over time, offering rich temporal information about the evolution of patient health. Yet these observations are sparse, and whether they are recorded depends on the patient's latent condition. Observation patterns also differ across modalities, as structured measurements and clinical notes arise under distinct recording processes. While prior work has developed methods that accommodate missingness in clinical time series, how to extract and use the information carried by the observation process itself remains underexplored. We therefore propose a patient representation learning framework for multimodal clinical time series that explicitly leverages informative missingness. The framework combines (1) a multimodal encoder that captures signals from structured and textual data together with their observation patterns, (2) a Bayesian filtering module that updates a latent patient state over time from observed multimodal signals, and (3) downstream modules for offline treatment policy learning and patient outcome prediction based on the learned patient state. We evaluate the framework on ICU sepsis cohorts from MIMIC-III, MIMIC-IV, and eICU. It improves both offline treatment policy learning and adverse outcome prediction, achieving FQE 0.679 versus 0.528 for clinician behavior and AUROC 0.886 for post-72-hour mortality prediction on MIMIC-III.

We analyze the filing-side legal infrastructure of eviction using 755,004 Philadelphia Municipal Court landlord-tenant records filed between 1969 and 2022, of which 747,125 are residential. Eviction in Philadelphia is organized upstream by a concentrated plaintiff-side bar, durable plaintiff-attorney dependence, repeated use of the same properties, and recurring tenant-name exposure. Between 1983 and 2022, the ten most active plaintiff attorneys handled 82.2% of represented plaintiff-side cases per year on average, compared with 14.8% for the ten most active plaintiffs. Large plaintiffs depend heavily on a single attorney: among plaintiffs filing at least 101 cases, 78.3% of each plaintiff's filings are handled by that plaintiff's most-used attorney, on average. Repetition is likewise central to the docket. Across the residential filing universe, 48.8% of cases occur at addresses with a prior filing in the preceding year, and 23.6% at addresses with six or more prior filings; these repeats are usually filed by the same plaintiff and follow a more default-heavy, less agreement-heavy pathway. We further examine a narrower mechanism: strict switches into specialist plaintiff-side counsel, defined as a plaintiff changing attorney to one in the prior-year top ten. Filing counts rise around the switch with non-flat pre-trends, indicating organizational reconfiguration rather than a clean exogenous shock. Within-plaintiff and within-plaintiff-property comparisons yield more stable estimates: judgment by agreement, fee share, waiver language, and corrected lockout-trigger language decline, while deadline language rises. We interpret eviction as a layered upstream process in which concentrated counsel, repeated places, and recurring tenants produce filings before any courtroom bargaining or adjudication occurs.

We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible second-order (Hessian) information or suffer from slow convergence. To address these challenges, we propose a novel, fully online de-biased covariance estimator that eliminates the need for second-order derivatives while significantly improving estimation accuracy. Our method employs a bias-reduction technique to achieve a convergence rate of $n^{(\alpha-1)/2} \sqrt{\log n}$, outperforming existing Hessian-free alternatives.

According to the United Nations Office for Disaster Risk Reduction (2025), the average annual cost of natural catastrophes increased from 70–80 billion USD between 1970 and 2000 to 180–200 billion USD between 2001 and 2020. Reports from organizations such as the IFOA and the WWF highlight the need for the insurance sector to adapt to this rapidly evolving context by developing medium- to long-term strategies that go beyond the one-year horizon of prudential regulations such as Solvency II. This paper introduces an artificial intelligence framework based on Conditional Generative Adversarial Networks (Conditional GANs) to generate future spatio-temporal trajectories of climatic indices. The approach focuses on the Soil Wetness Index (SWI), a key indicator used in France to assess drought severity. Drought accounts for approximately 30% of the indemnities paid under the French natural catastrophe insurance scheme. The proposed model, SwiGAN, simulates plausible drought propagation patterns up to 2050 for a region of France particularly exposed to this hazard. By generating realistic sequences of SWI maps, SwiGAN provides insights into drought dynamics under climate change scenarios and supports the design of adaptive risk management and insurance strategies. The methodology is also generalizable to other climate-related perils and actuarial applications such as economic scenario generation.

Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced matrix AMP, complex AMP, and AMP for non-separable functions independently, a unified state evolution theory for complex AMP with non-separable denoisers has been lacking. This article fills that gap by establishing state evolution in the setting of complex, non-separable denoising functions. The proposed approach constructs an augmented real-valued system that lifts the problem to a higher-dimensional space, then recovers the complex domain through a many-to-one canonical transformation. Under this construction, the Onsager correction naturally involves Wirtinger derivatives, and the resulting state evolution reduces to scalar complex recursions despite the non-separable structure of the denoisers. The framework extends to the matrix-valued setting, accommodating multiple feature vectors simultaneously. This generalization enables AMP to exploit joint structural constraints, such as simultaneous group and element sparsity, in complex-valued recovery problems. The complex sparse group least absolute shrinkage and selection operator (LASSO) serves as a key instantiation, motivated by preamble detection in Orthogonal Time-Frequency Space (OTFS)-based unsourced random access. Numerical experiments confirm that state evolution accurately predicts performance and show that complex non-separable denoising can produce significant gains over separable and real-valued alternatives.

Logistic regression is widely used to model the propensity score in the analysis of nonignorable missing data. However, goodness-of-fit testing for this propensity score model has received limited attention in the literature. In this paper, we propose a new goodness-of-fit testing procedure for the logistic propensity score model under nonignorable missing data. The proposed test is based on an unweighted sum-of-squared residuals constructed from the marginal missingness mechanism and accommodates the partial observability of the outcome. We establish the asymptotic distribution of the test statistic under both the null hypothesis and general alternatives, and develop a bootstrap procedure with theoretical guarantees to approximate its null distribution. We show that the resulting bootstrap test attains asymptotically correct size and is consistent, with power converging to one under model misspecification. Simulation studies and a real data application demonstrate that the proposed method performs well in finite samples.