Papers

I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often produce unreliable estimates of parameters for the triangle, a key network structure that captures the tendency of two individuals with friends in common to connect. Such unreliable estimates may lead to untrustworthy policy recommendations for networks with triangles. Through a variational mean-field approach, my algorithm addresses the two well-known difficulties when estimating the ERGM, the intractability of its normalizing constant and model degeneracy. In addition, I introduce $\ell_2$ regularization that ensures a unique solution to the mean-field approximation problem under suitable conditions. I provide a non-asymptotic optimization convergence rate analysis for my proposed algorithm under mild regularity conditions. Through Monte Carlo simulations, I demonstrate that my method achieves a perfect sign recovery rate for triangle parameters for small and mid-sized networks under perturbed initialization, compared to a 50% rate for existing algorithms. I provide the sensitivity analysis of estimates of ERGM parameters to hyperparameter choices, offering practical insights for implementation.

Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator Network (PI-DeepONet) designed to learn the solution operator of the Heston model across its entire parameter space. Unlike standard data-driven deep learning (DL) approaches, DeepSVM requires no labelled training data. Rather, we employ a hard-constrained ansatz that enforces terminal payoffs and static no-arbitrage conditions by design. Furthermore, we use Residual-based Adaptive Refinement (RAR) to stabilize training in difficult regions subject to high gradients. Overall, DeepSVM achieves a final training loss of $10^{-5}$ and predicts highly accurate option prices across a range of typical market dynamics. While pricing accuracy is high, we find that the model's derivatives (Greeks) exhibit noise in the at-the-money (ATM) regime, highlighting the specific need for higher-order regularization in physics-informed operator learning.

This paper introduces the Trimmed Functional Empirical Process (TFEP) as a robust framework for statistical inference when dealing with heavy-tailed or skewed distributions, where classical moments such as the mean or variance may be infinite or undefined. Standard approaches including the classical Functional Empirical Process (FEP), break down under such conditions, especially for distributions like Pareto, Cauchy, low degree of freedom Student-t, due to their reliance on finite-variance assumptions to guarantee asymptotic convergence. The TFEP approach addresses these limitations by trimming a controlled proportion of extreme order statistics, thereby stabilizing the empirical process and restoring asymptotic Gaussian behavior. We establish the weak convergence of the TFEP under mild regularity conditions and derive new asymptotic distributions for one-sample and twosample problems. These theoretical developments lead to robust confidence intervals for truncated means, variances, and their differences or ratios. The efficiency and reliability of the TFEP are supported by extensive Monte Carlo experiments and an empirical application to Senegalese income data. In all scenarios, the TFEP provides accurate inference where both Gaussian-based methods and the classical FEP break down. The methodology thus offers a powerful and flexible tool for statistical analysis in heavy-tailed and non-standard environments.

Double Machine Learning is often justified by nuisance-rate conditions, yet finite-sample reliability also depends on the conditioning of the orthogonal-score Jacobian. This conditioning is typically assumed rather than tracked. When residualized treatment variance is small, the Jacobian is ill-conditioned and small systematic nuisance errors can be amplified, so nominal confidence intervals may look precise yet systematically under-cover. Our main result is an exact identity for the cross-fitted PLR-DML estimator, with no Taylor approximation. From this identity, we derive a stochastic-order bound that separates oracle noise from a conditioning-amplified nuisance remainder and yields a sufficiency condition for root-n-inference. We further connect the amplification factor to semiparametric efficiency geometry via the Riesz representer and use a triangular-array framework to characterize regimes as residual treatment variation weakens. These results motivate an out-of-fold diagnostic that summarizes the implied amplification scale. We do not propose universal thresholds. Instead, we recommend reporting the diagnostic alongside cross-learner sensitivity summaries as a fragility assessment, illustrated in simulation and an empirical example.

Oysters in Virginia Chesapeake Bay oyster reefs are "age-truncated", possibly due to a combination of historical overfishing, disease epizootics, environmental degradation, and climate change. Research has suggested that oysters exhibit resilience to environmental stressors; however, that evidence is based on the current limited understanding of oyster lifespan. Until this paper, the Virginia Oyster Stock Assessment and Replenishment Archive (VOSARA), a spatially and temporally expansive dataset (222 reefs across 2003-2023) of shell lengths (SL, mm), had yet to be examined comprehensively in the context of resilience. We develop a novel method using Gaussian mixture modeling (GMM) to identify the age groups in each reef using yearly SL data and then link those age groups over time to identify cohorts and estimate their lifespan. Sixty-four reefs (29%) are deemed to have sufficient data (at least 300 oysters sampled for a minimum of 8 consecutive years) for this analysis. We fit univariate GMMs for each year ($t$) and reef ($r$) for each of the seven river strata ($R$) to estimate 1) the mean and standard deviation of SL for each $a_{Rrt}$th age group, and 2) the mixture percentage of each $a_{Rrt}$th age group. We link age groups across time to infer age cohorts by developing a mechanistic algorithm that prevents the shrinking of shell length when an $a_{Rrt}$th group becomes an ($a_{R,r,t+1}$)th group. Our method shows promise in identifying oyster cohorts and estimating lifespan solely using SL data. Our results show signals of resiliency in almost all river systems: oyster cohorts live longer and grow larger in the mid-to-late 2010s compared to the early 2000s.

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they introduce are often known only implicitly through simulations of the detector. Modern machine learning has enabled efficient simulation-based approaches for unfolding high-dimensional data. Among these, one of the first methods successfully deployed on experimental data is the OmniFold algorithm, a classifier-based Expectation-Maximization procedure. In practice, however, the forward model is only approximately specified, and the corresponding uncertainty is encoded through nuisance parameters. Building on the well-studied OmniFold algorithm, we show how to extend machine learning-based unfolding to incorporate nuisance parameters. Our new algorithm, called Profile OmniFold, is demonstrated using a Gaussian example as well as a particle physics case study using simulated data from the CMS Experiment at the Large Hadron Collider.

Given a binary treatment D and a binary mediator M, mediation analysis decomposes the total effect of D on an outcome Y into the direct and indirect effects. Typically, both D and M are assumed to be exogenous, but this paper allows M to be endogenous while maintaining the exogeneity of D, which holds certainly if D is randomized. The endogeneity problem of M is then overcome using a binary instrumental variable Z. We derive a nonparametric "causal reduced form (CRF)" for Y with either (D,Z,DZ) or (D,M,DZ) as the regressors. The CRF enables estimating the direct and indirect effects easily with ordinary least squares or instrumental variable estimator, instead of matching or inverse probability weighting that have difficulties in finding the asymptotic distribution or in dealing with near-zero denominators. Not just this ease in implementation, our approach is applicable to any Y (binary, count, continuous, etc.). Simulation and empirical studies illustrate our approach.

This article examines how authoritarian regimes construct state narratives about politically consequential events. Building on the narrative policy framework and existing research on authoritarian propaganda, we propose two dimensions that shape narrative construction: legitimacy implications – whether events enhance or threaten regime legitimacy, and citizen verification capacity – the extent to which citizens can evaluate official narratives through alternative sources. Using quantitative narrative analysis of Chinese social media posts by government, state media, and celebrity accounts, we extract subject-verb-object (SVO) triplets to map dominant narrative structures across four major events. Our findings show that legitimacy implications of the event shape regime's efforts in storytelling and the beliefs highlighted in the narratives, while citizen's verification capacity could balance the strategic choice between a top-down manipulation and bottom-up responsiveness of state narratives. Together, the results reveal propaganda as a complex process of narrative construction adaptive to specific contexts, offering new insights into how dynamic storytelling sustains authoritarian resilience.

We introduce ideal attribution mechanisms, a formal abstraction for reasoning about attribution decisions over strings. At the core of this abstraction lies the ledger, an append-only log of the prompt-response interaction history between a model and its user. Each mechanism produces deterministic decisions based on the ledger and an explicit selection criterion, making it well-suited to serve as a ground truth for attribution. We frame the design goal of watermarking schemes as faithful representation of ideal attribution mechanisms. This novel perspective brings conceptual clarity, replacing piecemeal probabilistic statements with a unified language for stating the guarantees of each scheme. It also enables precise reasoning about desiderata for future watermarking schemes, even when no current construction achieves them, since the ideal functionalities are specified first. In this way, the framework provides a roadmap that clarifies which guarantees are attainable in an idealized setting and worth pursuing in practice.

The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to provide guidance for both downstream applications and actionable future improvements. The Item Response Theory (IRT) model with Computerized Adaptive Testing has recently emerged as a promising framework for evaluating LLMs via their response accuracy. Beyond simple response accuracy, LLMs' chain of thought (CoT) lengths serve as a vital indicator of their reasoning ability. To leverage the CoT length information to assist LLM evaluation, we propose the Latency-Response Theory (LaRT) model, which jointly models both the response accuracy and CoT length by introducing a key correlation parameter between the latent ability and the latent speed. We derive an efficient stochastic approximation Expectation-Maximization algorithm for parameter estimation. We establish rigorous identifiability results for the latent ability and latent speed parameters to ensure the statistical validity of their estimation. Through both theoretical asymptotic analyses and simulation studies, we demonstrate LaRT's advantages over IRT in terms of superior estimation accuracy and shorter confidence intervals for latent trait estimation. To evaluate LaRT in real data, we collect responses from diverse LLMs on popular benchmark datasets. We find that LaRT yields different LLM rankings than IRT and outperforms IRT across multiple key evaluation metrics including predictive power, item efficiency, ranking validity, and LLM evaluation efficiency. Code and data are available at https://github.com/Toby-X/Latency-Response-Theory-Model

This paper explores the dynamics of learning in a multi-sector general equilibrium model where firms operate under incomplete information about their production returns to scale. Firms iteratively update their beliefs using maximum a-posteriori estimation, derived from observed production outcomes, to refine their knowledge of their returns to scale. The implications of these learning dynamics for market equilibrium and the conditions under which firms can effectively learn their true returns to scale are the key objects of this study. Our results shed light on how idiosyncratic shocks influence the learning process and demonstrate that input decisions encode all pertinent information for belief updates. Additionally, we show that a long-memory (path-dependent) learning which keeps track of all past estimations ends up having a worse performance than a short-memory (path-independent) approach.

The main objective of this paper is to propose a new approach for estimating the entire collection of Sobol' indices simultaneously. Our approach exploits the fact that Sobol' indices can be rewritten as solutions to an optimisation problem over the simplex of $\R^d$, to construct an online sequence of estimators using a stochastic mirror descent algorithm. We prove that our estimation procedure is consistent and provide a non-asymptotic upper bound for its rate of convergence. Furthermore, we demonstrate the numerical accuracy of our method and compare it with other classical estimation procedures.

We study the classic problem of prediction with expert advice under the constraint of local differential privacy (LDP). In this context, we first show that a classical algorithm naturally satisfies LDP and then design two new algorithms that improve it: RW-AdaBatch and RW-Meta. For RW-AdaBatch, we exploit the limited-switching behavior induced by LDP to provide a novel form of privacy amplification that grows stronger on easier data, analogous to the shuffle model in offline learning. Drawing on the theory of random walks, we prove that this improvement carries essentially no utility cost. For RW-Meta, we develop a general method for privately selecting between experts that are themselves non-trivial learning algorithms, and we show that in the context of LDP this carries no extra privacy cost. In contrast, prior work has only considered data-independent experts. We also derive formal regret bounds that scale inversely with the degree of independence between experts. Our analysis is supplemented by evaluation on real-world data reported by hospitals during the COVID-19 pandemic; RW-Meta outperforms both the classical baseline and a state-of-the-art central DP algorithm by 1.5-3$\times$ on the task of predicting which hospital will report the highest density of COVID patients each week.

Estimation of differences in conditional independence graphs (CIGs) of two time series Gaussian graphical models (TSGGMs) is investigated where the two TSGGMs are known to have similar structure. The TSGGM structure is encoded in the inverse power spectral density (IPSD) of the time series. In several existing works, one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data consisting of independent and identically distributed (i.i.d.) observations. In this paper we consider estimation of the difference in two IPSDs to characterize the underlying changes in conditional dependencies of two sets of time-dependent data. Our approach accounts for data time dependencies unlike past work. We analyze a penalized D-trace loss function approach in the frequency domain for differential graph learning, using Wirtinger calculus. We consider both convex (group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm) and graph recovery. Both synthetic and real data examples are presented in support of the proposed approaches. In synthetic data examples, our log-sum-penalized differential time-series graph estimator significantly outperformed our lasso based differential time-series graph estimator which, in turn, significantly outperformed an existing lasso-penalized i.i.d. modeling approach, with $F_1$ score as the performance metric.

Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state–action pairs. A long-standing difficulty in classical IRL is the non-uniqueness of the recovered reward: many reward functions can induce the same optimal policy, rendering the inverse problem ill-posed. In this paper, we develop a statistical framework for Inverse Entropy-regularized Reinforcement Learning that resolves this ambiguity by combining entropy regularization with a least-squares reconstruction of the reward from the soft Bellman residual. This combination yields a unique and well-defined so-called least-squares reward consistent with the expert policy. We model the expert demonstrations as a Markov chain with the invariant distribution defined by an unknown expert policy $\pi^\star$ and estimate the policy by a penalized maximum-likelihood procedure over a class of conditional distributions on the action space. We establish high-probability bounds for the excess Kullback–Leibler divergence between the estimated policy and the expert policy, accounting for statistical complexity through covering numbers of the policy class. These results lead to non-asymptotic minimax optimal convergence rates for the least-squares reward function, revealing the interplay between smoothing (entropy regularization), model complexity, and sample size. Our analysis bridges the gap between behavior cloning, inverse reinforcement learning, and modern statistical learning theory.

The challenge of imbalanced regression arises when standard Empirical Risk Minimization (ERM) biases models toward high-frequency regions of the data distribution, causing severe degradation on rare but high-impact “tail” events. Existing strategies uch as loss re-weighting or synthetic over-sampling often introduce noise, distort the underlying distribution, or add substantial algorithmic complexity. We introduce PARIS (Pruning Algorithm via the Representer theorem for Imbalanced Scenarios), a principled framework that mitigates imbalance by optimizing the training set itself. PARIS leverages the representer theorem for neural networks to compute a closed-form representer deletion residual, which quantifies the exact change in validation loss caused by removing a single training point without retraining. Combined with an efficient Cholesky rank-one downdating scheme, PARIS performs fast, iterative pruning that eliminates uninformative or performance-degrading samples. We use a real-world space weather example, where PARIS reduces the training set by up to 75% while preserving or improving overall RMSE, outperforming re-weighting, synthetic oversampling, and boosting baselines. Our results demonstrate that representer-guided dataset pruning is a powerful, interpretable, and computationally efficient approach to rare-event regression.

Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty quantification is therefore a critical but still underexplored challenge, especially within the framework of conformal prediction (CP). While CP methods can generate individual prediction sets from each model, combining them into a single, more informative set remains a challenging problem. To address this, we propose SACP (Symmetric Aggregated Conformal Prediction), a novel method that aggregates nonconformity scores from multiple predictors. SACP transforms these scores into e-values and combines them using any symmetric aggregation function. This flexible design enables a robust, data-driven framework for selecting aggregation strategies that yield sharper prediction sets. We also provide theoretical insights that help justify the validity and performance of the SACP approach. Extensive experiments on diverse datasets show that SACP consistently improves efficiency and often outperforms state-of-the-art model aggregation baselines.

Adaptive experimental designs have gained increasing attention across a range of domains. In this paper, we propose a new methodological framework, surrogate-leveraged online adaptive causal inference (SLOACI), which integrates predictive surrogate outcomes into adaptive designs to enhance efficiency. For downstream analysis, we construct the adaptive augmented inverse probability weighting estimator for the average treatment effect using collected data. Our procedure remains robust even when surrogates are noisy or weak. We provide a comprehensive theoretical foundation for SLOACI. Under the asymptotic regime, we show that the proposed estimator attains the semiparametric efficiency bound. From a non-asymptotic perspective, we derive a regret bound to provide practical insights. We also develop a toolbox of sequential testing procedures that accommodates both asymptotic and non-asymptotic regimes, allowing experimenters to choose the perspective that best aligns with their practical needs. Extensive simulations and a synthetic case study are conducted to showcase the superior finite-sample performance of our method.

This article develops a moderate-deviation limit theory for autoregressive models with jointly persistent mean and volatility dynamics. The autoregressive coefficient is allowed to drift toward unity slower than the classical 1/n rate, while the volatility persistence parameter also converges to one at an even slower, logarithmic order, so that the conditional variance process is itself nearly nonstationary and its unconditional moments may diverge. This double localization allows the variance process to be nearly nonstationary and to evolve slowly, as observed in financial data and during asset price bubble episodes. Under standard regularity conditions, we establish consistency and distributional limits for the OLS estimator of the autoregressive coefficient that remains valid in the presence of highly persistent stochastic volatility. We show that the effective normalization for least squares inference is governed by an average volatility scale, and we derive martingale limit theorems for the OLS estimator under joint drift and volatility dynamics. In a mildly stationary regime (where the autoregressive root approaches one from below), the OLS estimator is asymptotically normal. In a mildly explosive regime (where the root approaches one from above), an OLS based self normalized statistic converges to a Cauchy limit. Strikingly, in both regimes, the limiting laws of our statistics are invariant to the detailed specification of the volatility process, even though the conditional variance is itself nearly nonstationary. Overall, the results extend moderate-deviation asymptotics to settings with drifting volatility persistence, unify local to unity inference with nearly nonstationary stochastic volatility, and deliver practically usable volatility robust statistics for empirical work in settings approaching instability and exhibiting bubbles.

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the evolution of token distributions across layers of large language models. While the targeted applications differ (samples, weights, tokens), their mathematical descriptions share a common structure. A key idea is to switch from the Eulerian representation of densities to their Lagrangian counterpart through vector fields that advect particles. This dual view introduces challenges, notably the non-uniqueness of Lagrangian vector fields, but also opportunities to craft density evolutions and flows with favorable properties in terms of regularity, stability, and computational tractability. This survey presents an overview of these methods, with emphasis on two complementary approaches: diffusion methods, which rely on stochastic interpolation processes and underpin modern generative AI, and optimal transport, which defines interpolation by minimizing displacement cost. We illustrate how both approaches appear in applications ranging from sampling, neural network optimization, to modeling the dynamics of transformers for large language models.

Adam is a widely used optimizer in neural network training due to its adaptive learning rate. However, because different data samples influence model updates to varying degrees, treating them equally can lead to inefficient convergence. To address this, a prior work proposed adapting the sampling distribution using a bandit framework to select samples adaptively. While promising, the bandit-based variant of Adam suffers from limited theoretical guarantees. In this paper, we introduce Adam with Combinatorial Bandit Sampling (AdamCB), which integrates combinatorial bandit techniques into Adam to resolve these issues. AdamCB is able to fully utilize feedback from multiple samples at once, enhancing both theoretical guarantees and practical performance. Our regret analysis shows that AdamCB achieves faster convergence than Adam-based methods including the previous bandit-based variant. Numerical experiments demonstrate that AdamCB consistently outperforms existing methods.

This paper fully characterizes the geometrical structure of the class of distributions of three-dimensional Bernoulli random variables with equal means, $p$. We find all the geometrical generators in closed form as functions of $p$. This result stems from an algebraic representation of the class that encodes the statistical properties of Bernoulli distributions. We study extremal negative dependence within the class and provide an application example by finding the impact of negative dependence to minimal aggregate risk. The application relies on a game theory approach.

The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet the relationship between Popper's eliminative view of theory testing and Bayesian model comparison remains insufficiently articulated. This paper develops a unified account in which falsification is reinterpreted as a Bayesian process of model elimination. A theory is not rejected because it contradicts an observation in a logical sense; it is eliminated because it assigns vanishing integrated probability to the data in comparison with an alternative model. This reinterpretation resolves the difficulties raised by the Duhem-Quine thesis, clarifies the status of auxiliary hypotheses, and explains why ad hoc modifications reduce rather than increase theoretical credibility. The analysis is illustrated through two classical episodes in celestial mechanics, the discovery of Neptune and the anomalous precession of Mercury. In the Neptune case, an auxiliary hypothesis internal to Newtonian gravity dramatically increases the marginal likelihood of the theory, preserving it from apparent refutation. In the Mercury case, no permissible auxiliary modification can rescue the Newtonian model, while general relativity assigns high probability to the anomaly without adjustable parameters. The resulting posterior collapse provides a quantitative realisation of Popper's eliminative criterion. Bayesian model comparison therefore supplies the mathematical structure that Popper's philosophy lacked and offers a coherent account of scientific theory change as a process of successive eliminations within a space of competing models.

Potable water utilities are currently making great efforts to reduce leakage rates and assure long-term supply to the population due to the challenges of climate change, growing population and water shortage scenarios that have been on them over the last years. One of the most employed methods to reduce leakage includes the installation of pressurereducing valves along the water distribution network and the utilization of pressure management schemes. Pressure management includes different types of control models, which are applied according to the requirements of each site. The most advanced and sophisticated scheme is critical point control, which relies on a flow signal from a measuring device or online communication between the critical point and the valve. This paper proposes the utilization of a seasonal autoregressive integrated moving average, or the SARIMA model, to correlate pressure at the outlet of the valve and pressure on the critical point of the area supplied, aiming to set a fixed pressure in the critical point. The SARIMA model is developed according to historical data logged in the field and then validated. Later, the SARIMA model was tested on a real location in the village of Noja, Spain. The analysis of the field test results prove that the proposed model is feasible to be used since there is no significance difference between the target values set in the critical point and the real values measured in the field. The research proves that the SARIMA model can be used as an alternative for critical point control in water distribution networks when no flow signal is available or when communication between the critical point and the pressure reducing valve is not an option.

In many engineering systems, proper predictive maintenance and operational control are essential to increase efficiency and reliability while reducing maintenance costs. However, one of the major challenges is that many sensors are used for system monitoring. Analyzing these sensors simultaneously for better predictive maintenance optimization is often very challenging. In this paper, we propose a systematic decision-making framework to improve the system performance in manufacturing practice, considering the real-time degradation signals generated by multiple sensors. Specifically, we propose a partially observed Markov decision process (POMDP) model to generate the optimal capacity and predictive maintenance policies, given the fact that the observation of the system state is imperfect. Such work provides a systematic approach that focuses on jointly controlling the operating conditions and preventive maintenance utilizing the real-time machine deterioration signals by incorporating the degradation constraint and non-observable states. We apply this technique to the bearing degradation data and NASA aircraft turbofan engine dataset, demonstrating the effectiveness of the proposed method.

VR in the treatment of clinical concerns such as generalized anxiety disorder or social anxiety. VR has created additional pathways to support patient well-being and care. Understanding online discussion of what users think about this technology may further support its efficacy. The purpose of this study was to employ a corpus linguistic methodology to identify the words and word networks that shed light on the online discussion of virtual reality and anxiety. Using corpus linguistics, frequently used words in discussion along with collocation were identified by utilizing Sketch Engine software. The results of the study, based upon the English Trends corpus, identified VR, Oculus, and headset as the most frequently discussed within the VR and anxiety subcorpus. These results point to the development of the virtual system, along with the physical apparatus that makes viewing and engaging with the virtual environment possible. Additional results point to collocation of prepositional phrases such as of virtual reality, in virtual reality, and for virtual reality relating to the design, experience, and development, respectively. These findings offer new perspective on how VR and anxiety together are discussed in general discourse and offer pathways for future opportunities to support counseling needs through development and accessibility. Keywords: anxiety disorders, corpus linguistics, Sketch Engine, and virtual reality VR

Purpose: Prior research has established perceived pressure and life satisfaction as important correlates of depression, yet their causal interplay remains insufficiently identified. This study aims to disentangle whether satisfaction acts as an independent protective factor or operates by buffering pressure, and to identify population-specific risk profiles across students and workers. Methods: We applied a causal machine learning framework to harmonized data from India, China, and Malaysia (total N=28,243). We integrated random forests and logistic regression with Causal Mediation Analysis and Causal Forests. To resolve theoretical ambiguity regarding directionality, we validated the causal pathway between pressure and satisfaction using numerical simulation benchmarks. Results: Pressure emerged as the dominant predictor across all cohorts. Simulation-validated analysis confirmed a causal pathway flowing from Life Satisfaction -> Pressure -> Depression, rejecting the reverse hypothesis. Satisfaction mitigated depression partially through pressure reduction (proportion mediated around 15.1%), rather than functioning exclusively as a direct mechanism. A distinct developmental reversal was observed: younger age predicted vulnerability in students, whereas older age predicted risk in workers. Causal forests further revealed that the depressogenic impact of pressure was significantly amplified in students with high anxiety. Conclusion: Pressure acts as the proximal bottleneck for depression risk, while life satisfaction functions as an antecedent buffer. These findings challenge uniform risk models by highlighting age-related context dependence and suggest that precision interventions targeting stress reduction and high-anxiety subgroups offer the most effective pathway for breaking the causal cycle of depression.

The monotone data augmentation (MDA) algorithm has been widely used to impute missing data for longitudinal continuous outcomes. Compared to a full data augmentation approach, the MDA scheme accelerates the mixing of the Markov chain, reduces computational costs per iteration, and aids in missing data imputation under nonignorable dropouts. We extend the MDA algorithm to the multivariate probit (MVP) model for longitudinal binary and ordinal outcomes. The MVP model assumes the categorical outcomes are discretized versions of underlying longitudinal latent Gaussian outcomes modeled by a mixed effects model for repeated measures. A parameter expansion strategy is employed to facilitate the posterior sampling, and expedite the convergence of the Markov chain in MVP. The method enables the sampling of the regression coefficients and covariance matrix for longitudinal continuous, binary and ordinal outcomes in a unified manner. This property aids in understanding the algorithm and developing computer codes for MVP. We also introduce independent Metropolis-Hasting samplers to handle complex priors, and evaluate how the choice between flat and diffuse normal priors for regression coefficients influences parameter estimation and missing data imputation. Numerical examples are used to illustrate the methodology.

Score-based generative models commonly employ linear forward diffusions with Gaussian reference distributions, limiting their ability to directly incorporate structural information into the noising dynamics. We introduce latent nonlinear denoising score matching (LNDSM), which combines nonlinear, structure-informed latent diffusions with the variational autoencoder (VAE) training framework. In our construction, the forward diffusion is designed to admit a prescribed reference distribution, such as a Gaussian mixture model, that reflects qualitative features of the latent data distribution. We derive a computable approximation to a cross-entropy upper bound in the VAE objective using Euler-Maruyama discretization and the resulting Gaussian conditional transitions. To stabilize training, we remove two zero-mean control variates whose variances become large for small time steps. The resulting objective enables joint training of the encoder, decoder, and latent score network. Numerical experiments on benchmark image datasets demonstrate the effectiveness of LNDSM in learning structured distributions, outperforming conventional latent score-based generative modeling in sample quality and mode balance across several settings, while achieving improved training efficiency. These results highlight the potential of nonlinear, structure-informed latent diffusions for generative modeling.

We provide an approach to exploratory data analysis in observational studies with a single intervention and multiple endpoints. In such settings, the researcher would like to explore evidence for actual treatment effects while accounting for both false discoveries and the potential impact of unmeasured confounding. For any candidate subset of hypotheses about these outcomes, we provide sensitivity sets for the proportion of the hypotheses within the subset which are true. The resulting sensitivity statements are valid simultaneously over all possible choices for the rejected set, allowing the researcher to search for promising subsets of hypotheses that maintain a large estimated fraction of true discoveries even if hidden bias is present. The approach is well suited to sensitivity analysis, as conclusions that some fraction of outcomes are affected by the treatment exhibit larger robustness to unmeasured confounding than findings that any particular outcome is affected. For Rosenbaum's sensitivity model in matched observational studies, we show how a sequence of integer programs, in tandem with screening steps, facilitate the efficient computation of the required sensitivity sets. We illustrate the practical utility of our method through both simulation studies and a data example on the long-term impacts of childhood abuse.