Papers

Reinforcement learning algorithms assume that observations satisfy the Markov property, yet real-world sensors frequently violate this assumption through correlated noise, latency, or partial observability. Standard performance metrics conflate Markov breakdowns with other sources of suboptimality, leaving practitioners without tools to detect such violations. This paper introduces a prediction-based Markov Violation Score (MVS) that quantifies non-Markovian structure in observation trajectories. A random forest first removes nonlinear Markov-compliant dynamics; ridge regression then tests whether historical observations reduce prediction error on the residuals beyond what the current observation provides. The resulting score is bounded in [0, 1] and requires no causal graph construction. Evaluation spans six environments (CartPole, Pendulum, Acrobot, HalfCheetah, Hopper, Walker2d), three algorithms (PPO, A2C, SAC), controlled AR(1) noise at six intensity levels, and 10 seeds per condition. In post-hoc detection, 7 of 16 environment-algorithm pairs, primarily high-dimensional locomotion tasks, show significant positive monotonicity between noise intensity and MVS (Spearman rho up to 0.78, confirmed under repeated-measures analysis); under training-time noise, 13 of 16 pairs exhibit statistically significant reward degradation. An inversion phenomenon is documented in low-dimensional environments where the random forest absorbs the noise signal, causing MVS to decrease as true violations grow, a failure mode analyzed in detail. A practical utility experiment demonstrates that MVS correctly identifies partial observability and guides architecture selection, fully recovering performance lost to non-Markovian observations. Source code to reproduce all results is available at https://github.com/NAVEENMN/Markovianes.

This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four stochastics-oriented functionals – risk, deviation, regret, and error, along with an associated statistic, and articulates their revealing and in some ways surprising interrelationships and dualizations. Additions to the RQ framework that have come to light since 2013 are reviewed in a synthesis focused on both theoretical advancements and practical applications. New quadrangles – superquantile, superquantile norm, expectile, biased mean, quantile symmetric average union, and $\varphi$-divergence-based quadrangles – offer novel approaches to risk-sensitive decision-making across various fields such as machine learning, statistics, finance, and PDE-constrained optimization. The theoretical contribution comes in axioms for “subregularity” relaxing “regularity” of the quadrangle functionals, which is too restrictive for some applications. The main RQ theorems and connections are revisited and rigorously extended to this more ample framework. Examples are provided in portfolio optimization, regression, and classification, demonstrating the advantages and the role played by duality, especially in ties to robust optimization and generalized stochastic divergences.

The global network of scientific cooperation has undergone major restructuring over the past two decades, with important implications for geopolitics and science policy. China's integration into this network has redistributed positions of influence in ways that challenge zero-sum views of national competition and security. Drawing on structural holes theory and the Bianconi-Barabasi fitness model, we argue that China's entry accelerated an ongoing process of network maturation. As China's scientific capacity expanded, it formed direct collaborations that reduced reliance on U.S. intermediation. Network analysis shows a large decline in U.S. betweenness centrality, while weighted measures remain stable, indicating a loss of brokerage advantages but continued strong bilateral ties. Granger causality tests suggest that China's early participation predicted later structural changes across fields. Results are consistent across six major domains.

The aim of this article is to determine a new six-parameter Beta Weibull distribution and its various associated functions, namely the cumulative distribution, survival, probability density and hazard functions. Next, we determine the sub-distributions of the new distribution and show that the latter generalizes those of the literature. Finally, numerical simulations were performed and show that the shapes of the density function of the new distribution cover all those in the literature, and the shapes of hazard functions (constant, increasing, decreasing, $\bigcup$-shaped and $\bigcap$-shaped) are represented in the new distribution and encompass all existing distributions.

Retrospective causal questions ask what would have happened to an observed individual had they received a different treatment. We study the problem of estimating $\mu(x,y)=\mathbb{E}[Y(1)\mid X=x,Y(0)=y]$, the expected counterfactual outcome for an individual with covariates $x$ and observed outcome $y$, and constructing valid prediction intervals under the Neyman-Rubin superpopulation model. This quantity is generally not identified without additional assumptions. To link the observed and unobserved potential outcomes, we work with a cross-world correlation $\rho(x)=cor(Y(1),Y(0)\mid X=x)$; plausible bounds on $\rho(x)$ enable a principled approach to this otherwise unidentified problem. We introduce retrospective counterfactual estimators $\hat{\mu}_{\rho}(x,y)$ and prediction intervals $C_{\rho}(x,y)$ that asymptotically satisfy $P[Y(1)\in C_{\rho}(x,y)\mid X=x, Y(0)=y]\ge1-\alpha$ under standard causal assumptions. Many common baselines implicitly correspond to endpoint choices $\rho=0$ or $\rho=1$ (ignoring the factual outcome or treating the counterfactual as a shifted factual outcome). Interpolating between these cases through cross-world dependence yields substantial gains in both theory and practice.

Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index increases. However, existing increasing shrinkage priors often possess complex hierarchical structures that complicate posterior inference. To address this issue, we propose using an $L_{1/2}$ shrinkage prior. We demonstrate that by carefully setting the parameters in the hyper prior of its global shrinkage parameters, the increasing shrinkage property is preserved. Our prior specification is simple, facilitating the construction of an efficient Gibbs sampler for exact posterior inference. For faster computation, we also propose a variational approximation algorithm. Through numerical studies, we compare our approaches with current popular Bayesian methods for factor models, demonstrating their merits in terms of accuracy and computational efficiency.

Bayesian inference often relies on Markov chain Monte Carlo (MCMC) methods, particularly required for non-Gaussian data families. When dealing with complex hierarchical models, the MCMC approach can be computationally demanding in workflows that require repeated model fitting or when working with models of large dimensions with limited hardware resources. The Integrated Nested Laplace Approximations (INLA) is a deterministic alternative for models with non-Gaussian data that belong to the class of latent Gaussian models (LGMs), yielding accurate approximations to posterior marginals in many applied settings. The INLA method was implemented in C as a standalone program, inla, that is widely used in R through the INLA package. This paper introduces PyINLA, a dedicated Python package that provides a Pythonic interface directly to the inla program. Therefore, PyINLA enables specifying LGMs, running INLA-based inference, and accessing posterior summaries directly from Python while leveraging the established INLA implementation. We describe the package design and illustrate its use on representative models, including generalized linear mixed models, time series forecasting, disease mapping, and geostatistical prediction, demonstrating how deterministic Bayesian inference can be performed in Python using INLA in a way that integrates naturally with common scientific computing workflows.

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

Many modern products are highly reliable, often exhibiting long lifetimes. As a result, conducting experiments under normal operating conditions can be prohibitively time-consuming to collect sufficient failure data for robust statistical inference. Accelerated life tests (ALTs) offer a practical solution by inducing earlier failures, thereby reducing the required testing time. In step-stress experiments, a stress factor that accelerates product degradation is identified and systematically increased at predetermined time points, while remaining constant between intervals. Failure data collected under these elevated stress levels is analyzed, and the results are then extrapolated to normal operating conditions. Traditional estimation methods for such data, such as the maximum likelihood estimator (MLE), are highly efficient under ideal conditions but can be severely affected by outlying or contaminated observations. To address this, we propose the use of Minimum Density Power Divergence Estimators (MDPDEs) as a robust alternative, offering a balanced trade-off between efficiency and resistance to contamination. The MDPDE framework is extended to mixed distributions and its theoretical properties, including the asymptotic distribution of the model parameters, are derived assuming Weibull lifetimes. The effectiveness of the proposed approach is illustrated through extensive simulation studies, and its practical applicability is further demonstrated using real-world data.

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing conditional validity is challenging, as standard stratification methods suffer from the curse of dimensionality. We propose Conformal Prediction Assessment (CPA), a framework that reframes the evaluation of conditional coverage as a supervised learning task by training a reliability estimator that predicts instance-level coverage probabilities. Building on this estimator, we introduce the Conditional Validity Index (CVI), which decomposes reliability into safety (undercoverage risk) and efficiency (overcoverage cost). We establish convergence rates for the reliability estimator and prove the consistency of CVI-based model selection. Extensive experiments on synthetic and real-world datasets demonstrate that CPA effectively diagnoses local failure modes and that CC-Select, our CVI-based model selection algorithm, consistently identifies predictors with superior conditional coverage performance.

We study the recovery of geometric structure from data generated by convolving the uniform measure on a smooth compact submanifold $M\subset\mathbb{R}^D$ with ambient Gaussian noise. Our main result is that several fundamental Riemannian quantities of $M$, including tangent spaces, the intrinsic dimension, and the second fundamental form, are identifiable from derivatives of the noisy density. We first derive uniform small-noise expansions of the data density and its derivatives in a tubular neighborhood of $M$. These expansions show that, at the population level, tangent spaces can be recovered from the density Hessian with $O(\sigma^2)$ error, while the intrinsic dimension can be estimated consistently. We further construct estimators for the second fundamental form from density derivatives, obtaining $O(d(y,M)+\sigma)$ and $O(d(y,M)+\sigma^2)$ errors for hypersurfaces and submanifolds with arbitrary codimension. At the sample level, we estimate the density and its derivatives by kernel methods in the ambient space and plug them into the population constructions, yielding uniform nonparametric rates in the ambient dimension. Finally, we show that these density-based constructions admit a geometric interpretation through density-induced ambient metrics, linking the geometry of $M$ to ambient geodesic structure.

Time-series analysis is often affected by missing data, a common problem across several fields, including healthcare and environmental monitoring. Multiple Imputation by Chained Equations (MICE) has been prominent for imputing missing values through "fully conditional specification". We extend MICE using the Bayesian framework (tBayes-MICE), utilising Bayesian inference to impute missing values via Markov Chain Monte Carlo (MCMC) sampling to account for uncertainty in MICE model parameters and imputed values. We also include temporally informed initialisation and time-lagged features in the model to respect the sequential nature of time-series data. We evaluate the tBayes-MICE method using two real-world datasets (AirQuality and PhysioNet), and using both the Random Walk Metropolis (RWM) and the Metropolis-Adjusted Langevin Algorithm (MALA) samplers. Our results demonstrate that tBayes-MICE reduces imputation errors relative to the baseline methods over all variables and accounts for uncertainty in the imputation process, thereby providing a more accurate measure of imputation error. We also found that MALA mixed better than RWM across most variables, achieving comparable accuracy while providing more consistent posterior exploration. Overall, these findings suggest that the tBayes-MICE framework represents a practical and efficient approach to time-series imputation, balancing increased accuracy with meaningful quantification of uncertainty in various environmental and clinical settings.

We propose a control-theoretic framework for evolutionary clustering based on quasi-stationary Mean Field Games. Each cluster is represented by a probability density whose evolution is governed by a Fokker–Planck equation, while the associated velocity field is determined through a stationary Hamilton–Jacobi equation. The general formulation does not prescribe a finite-dimensional statistical shape for the component densities, although the number of components is fixed. In the Gaussian specialization, we show that suitable affine dynamics reproduce the mean and covariance trajectories generated by the classical Expectation–Maximization procedure. To improve temporal coherence in the presence of noise and temporary cluster overlaps, we introduce causal and non-causal time-averaged log-likelihood objectives. We also develop a fully density-based numerical implementation for non-Gaussian components. The proposed formulations are assessed on synthetic and real time-dependent datasets and compared with independent snapshot Expectation–Maximization and with the same method applied to temporally smoothed observations. In the two-dimensional benchmark, an established evolutionary \(k\)-means method is also included as an external dynamic-clustering baseline.

Text-to-time-series generation is particularly important in meteorology, where natural language offers intuitive control over complex, multi-scale atmospheric dynamics. Existing approaches are constrained by the lack of large-scale, physically grounded multimodal datasets and by architectures that overlook the spectral-temporal structure of weather signals. We address these challenges with a unified framework for text-guided meteorological time-series generation. First, we introduce MeteoCap-3B, a billion-scale weather dataset paired with expert-level captions constructed via a Multi-agent Collaborative Captioning (MACC) pipeline, yielding information-dense and physically consistent annotations. Building on this dataset, we propose MTransformer, a diffusion-based model that enables precise semantic control by mapping textual descriptions into multi-band spectral priors through a Spectral Prompt Generator, which guides generation via frequency-aware attention. Extensive experiments on real-world benchmarks demonstrate state-of-the-art generation quality, accurate cross-modal alignment, strong semantic controllability, and substantial gains in downstream forecasting under data-sparse and zero-shot settings. Additional results on general time-series benchmarks indicate that the proposed framework generalizes beyond meteorology.

Precision mental health requires treatment decisions that account for heterogeneous symptoms reflecting multiple clinical domains. However, existing methods for estimating individualized treatment effects (ITE) rely on a single summary outcome or a specific set of observed symptoms or measures, which are sensitive to symptom selection and limit generalizability to unmeasured yet clinically relevant domains. We propose DRIFT, a new maximin framework for estimating robust ITEs from high-dimensional item-level data by leveraging latent factor representations and adversarial learning. DRIFT learns latent constructs via generalized factor analysis, then constructs an anchored on-target uncertainty set that extrapolates beyond the observed measures to approximate the broader hyper-population of potential outcomes. By optimizing worst-case performance over this uncertainty set, DRIFT yields ITEs that are robust to underrepresented or unmeasured domains. We further show that DRIFT is invariant to admissible reparameterizations of the latent factors and admits a closed-form maximin solution, with theoretical guarantees for identification and convergence. In analyses of a randomized controlled trial for major depressive disorder (EMBARC), DRIFT demonstrates superior performance and improved generalizability to external multi-domain outcomes, including side effects and self-reported symptoms not used during training.

Generating chemically valid 3D molecules is hindered by discrete bond topology: small local bond errors can cause global failures (valence violations, disconnections, implausible rings), especially for drug-like molecules with long-range constraints. Many unconditional 3D generators emphasize coordinates and then infer bonds or rely on post-processing, leaving topology feasibility weakly controlled. We propose Hierarchy-Guided Latent Topology Flow (HLTF), a planner-executor model that generates bond graphs with 3D coordinates, using a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures. On QM9, HLTF achieves 98.8% atom stability and 92.9% valid-and-unique, improving PoseBusters validity to 94.0% (+0.9 over the strongest reported baseline). On GEOM-DRUGS, HLTF attains 85.5%/85.0% validity/valid-unique-novel without post-processing and 92.2%/91.2% after standardized relaxation, within 0.9 points of the best post-processed baseline. Explicit topology generation also reduces "false-valid" samples that pass RDKit sanitization but fail stricter checks.

Identifying the causal effects of socioeconomic determinants on population health is of many great interests - from statistical methodology development to public health practitioners and policy developments. The statistical side of the problem needs to address several questions: spatial autocorrelation in both exposures and outcomes, confounding between treatments and covariates, and the need for geographically logical inference. We address these jointly by using spectral basis functions - Moran Eigenvector Maps and ICAR precision matrix eigenvectors - within a doubly robust generalized propensity score estimator for continuous treatments. Applied to 2022 county health data across the U.S. counties, the framework identifies the effect of six chosen predictors on the average physically unhealthy days per month. Possible further applications and methodological extensions are also discussed as future directions from this research.

In large-scale biomedical research, it's common to gather ultra-high dimensional data that includes right-censored survival times. Feature screening has emerged as a crucial statistical technique for handling such data. In this paper, we introduce a straightforward and robust feature screening approach, leveraging the modified Chatterjee's rank correlation, suitable for a broad range of survival models. With reasonably mild regularity assumptions, we establish the properties of sure screening and ranking consistency. The computation involved in our proposed method is quite direct and simple. Through simulation studies and real gene expression data analysis, we demonstrate the superior efficacy of our proposed approach.

Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the future observation and the declared information set equals the maximum achievable reduction in expected loss. This paper develops the consequences of that identity. Forecastability, defined as this mutual information evaluated across horizons, forms a profile whose shape reflects the dependence structure of the process and need not be monotone. Three structural properties are derived: compression of the information set can only reduce forecastability; the gap between the profile under a finite lag window and the full history gives an exact truncation error budget; and for processes with periodic dependence, the profile inherits the periodicity. Predictive loss decomposes into an irreducible component fixed by the information structure and an approximation component attributable to the method; their ratio defines the exploitation ratio, a normalised diagnostic for method adequacy. The exact equality is specific to log loss, but when forecastability is near zero, classical inequalities imply that no method under any loss can materially improve on the unconditional baseline. The framework provides a theoretical foundation for assessing, prior to any modelling, whether the declared information set contains sufficient predictive information at the horizon of interest.

Weight decay is ubiquitous in training deep neural network architectures. Its empirical success is often attributed to capacity control; nonetheless, our theoretical understanding of its effect on the loss landscape and the set of minimizers remains limited. In this paper, we show that $\ell^2$-regularized deep matrix factorization/deep linear network training problems with squared-error loss admit a unique end-to-end minimizer for all target matrices subject to factorization, except for a set of Lebesgue measure zero formed by the depth and the regularization parameter. This observation reveals fundamental properties of the loss landscape of regularized deep matrix factorization problems: the Hessian spectrum is constant across all minimizers of the regularized deep scalar factorization problem with squared-error loss. Moreover, we show that, in regularized deep matrix factorization problems with squared-error loss, if the target matrix does not belong to the Lebesgue measure-zero set, then the Frobenius norm of each layer is constant across all minimizers. This, in turn, yields a global lower bound on the trace of the Hessian evaluated at any minimizer of the regularized deep matrix factorization problem. Furthermore, we establish a critical threshold for the regularization parameter above which the unique end-to-end minimizer collapses to zero.

Signal Temporal Logic (STL) inference learns interpretable logical rules for temporal behaviors in dynamical systems. To ensure the correctness of learned STL formulas, recent approaches have incorporated conformal prediction as a statistical tool for uncertainty quantification. However, most existing methods rely on the assumption that calibration and testing data are identically distributed and exchangeable, an assumption that is frequently violated in real-world settings. This paper proposes a conformalized STL inference framework that explicitly addresses covariate shift between training and deployment trajectories dataset. From a technical standpoint, the approach first employs a template-free, differentiable STL inference method to learn an initial model, and subsequently refines it using a limited deployment side dataset to promote distribution alignment. To provide validity guarantees under distribution shift, the framework estimates the likelihood ratio between training and deployment distributions and integrates it into an STL-robustness-based weighted conformal prediction scheme. Experimental results on trajectory datasets demonstrate that the proposed framework preserves the interpretability of STL formulas while significantly improving symbolic learning reliability at deployment time.

AI-assisted task delegation is increasingly common, yet human effort in such systems is costly and typically unobserved. Recent work by Bastani and Cachon (2025); Sambasivan et al. (2021) shows that accuracy-based payment schemes suffer from incentive collapse: as AI accuracy improves, sustaining positive human effort requires unbounded payments. We study this phenomenon in a budget-constrained principal-agent framework with strategic human agents whose output accuracy depends on unobserved effort. Our first contribution is a general impossibility result showing that incentive collapse is not merely a limitation of simple linear payments, but arises for any payment rule based only on observed task accuracy.To overcome this barrier, we propose a sentinel-auditing payment mechanism that enforces a strictly positive and controllable level of human effort at finite cost, independent of AI accuracy. Building on this incentive-robust foundation, we develop an incentive-aware active statistical inference framework that jointly optimizes (i) the auditing rate and (ii) active sampling and budget allocation across tasks of varying difficulty to minimize the final statistical loss under a single budget. Experiments demonstrate improved cost-error tradeoffs relative to standard active learning and auditing-only baselines.

The measurement of human behavior remains a central challenge across the behavioral sciences. Traditional approaches typically rely on passive observation of responses collected under static or weakly controlled conditions, limiting the identifiability of the underlying generative processes. As a result, different behavioral mechanisms may produce indistinguishable observations, constraining both inference and theoretical development. In this paper, we propose a methodological framework for behavioral measurement based on controlled perturbations. From this perspective, behavior is conceptualized as the observable output of a dynamical system, and measurement is reframed as a problem of system identification. Experimental environments act as measurement instruments that apply structured inputs (perturbations) and record behavioral trajectories as outputs over time. We outline the core components of this framework, including the design of perturbations, the role of temporal resolution, and the integration of multimodal data streams. We further discuss how advances in immersive technologies, programmable environments, and computational modeling enable the implementation of closed-loop experimental systems, where perturbation, observation, and model updating are tightly coupled. The proposed approach provides a principled basis for moving from descriptive and predictive models toward the identification of generative behavioral mechanisms. By integrating psychometrics, experimental design, and dynamical modeling, this framework contributes to the development of a more rigorous and reproducible methodology for the measurement of human behavior.

When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional densities are ill-defined, considering that for a continuous random variable $Y$, the event $\{Y=y\}$ has probability zero, meaning the formula $\mathbb{P}(A|B)=\mathbb{P}(A\cap B)/\mathbb{P}(B)$ is inapplicable. In reality, when we work with conditional densities, we never condition directly on the zero-probability event $\{Y=y\}$; rather, we first condition on the random variable $Y$, and then we may plug in an observed value $y$. The first purpose of our article is to provide an exposition on conditional densities that elaborates on this point. While we have aimed to make this explanation accessible, we follow it with a roadmap of the measure theory needed to make it rigorous. A recent preprint (arXiv:2411.13570) has expressed the concern that probability densities are ill-defined and that as a result Bayes' theorem cannot be used, and they provide examples that allegedly demonstrate inconsistencies in the Bayesian framework. The second purpose of our article is to investigate their claims. We contend that the examples given in their work do not demonstrate any inconsistencies; we find that there are mathematical errors and that they deviate significantly from the Bayesian framework.

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we leverage the Wiener Chaos Expansion (WCE), a spectral decomposition technique that projects the stochastic solution onto an orthogonal basis of Hermite polynomials. This transformation effectively maps the stochastic dynamics into a hierarchical system of deterministic functions, termed the propagator. By reducing the stochastic inference task to a deterministic optimization problem, our framework circumvents the heavy computational burden and sampling requirements of traditional simulation-based methods like MCMC or MLE. The robustness and scalability of the proposed approach are demonstrated through numerical experiments on various non-linear SDEs, including models for individual biological growth. Results show that the WCE-SGD framework provides accurate parameter recovery even from discrete, noisy observations, offering a significant paradigm shift in the efficient modeling of complex stochastic systems.

When treatment policy estimands are of interest, clinical trials often attempt to collect patient data after intercurrent events (ICEs), although such data are often limited. Retrieved dropout imputation methods, which use pre-ICE and available post-ICE data to impute missing post-ICE outcomes, are commonly applied but often yield treatment effect estimates with large standard errors (SEs) and may encounter convergence issues when post-ICE data are sparse. Reference-based imputation methods are also used, but they rely on strong assumptions about post-ICE outcomes, which can lead to biased estimates if these assumptions are incorrect. To address these limitations, we previously proposed the reference-based Bayesian causal model (BCM), which incorporates a prior on the maintained effect parameter to reflect uncertainty in reference-based assumptions for missing post-ICE data. Our earlier work assumed no post-ICE data were observed. Here, we extend the BCM to incorporate available post-ICE outcomes, providing an approach that mitigates limitations of both retrieved-dropout and standard reference-based methods. We propose both a fully Bayesian model and an imputation-based approach. A simulation study was conducted to evaluate the frequentist properties of the proposed methods in settings with partially observed post-ICE data and to compare performance with existing approaches. Retrieved-dropout methods produced higher estimated SEs than the BCM, particularly when post-ICE data were sparse. Under the BCM, treatment effect SEs increased as post-ICE data became more limited for both modelling approaches. Importantly, this increase can be controlled through the prior variance of the maintained effect parameter, with more informative priors stabilising estimation when post-ICE data are scarce.

This technical note studies the reliability limits of LLM-based multi-agent planning as a delegated decision problem. We model the LLM-based multi-agent architecture as a finite acyclic decision network in which multiple stages process shared model-context information, communicate through language interfaces with limited capacity, and may invoke human review. We show that, without new exogenous signals, any delegated network is decision-theoretically dominated by a centralized Bayes decision maker with access to the same information. In the common-evidence regime, this implies that optimizing over multi-agent directed acyclic graphs under a finite communication budget can be recast as choosing a budget-constrained stochastic experiment on the shared signal. We also characterize the loss induced by communication and information compression. Under proper scoring rules, the gap between the centralized Bayes value and the value after communication admits an expected posterior divergence representation, which reduces to conditional mutual information under logarithmic loss and to expected squared posterior error under the Brier score. These results characterize the fundamental reliability limits of delegated LLM planning. Experiments with LLMs on a controlled problem set further demonstrate these characterizations.

Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or sparse rewards. In this paper, we propose a framework to perform statistical online inference for a sample-averaged Q-learning approach. We adapt the functional central limit theorem (FCLT) for the modified algorithm under some general conditions and then construct confidence intervals for the Q-values via random scaling. We conduct experiments to perform inference on both the modified approach and its traditional counterpart, Q-learning using random scaling and report their coverage rates and confidence interval widths on two problems: a grid world problem as a simple toy example and a dynamic resource-matching problem as a real-world example for comparison between the two solution approaches.

Understanding the interplay between high-dimensional data from different views is essential in biomedical research, particularly in fields such as genomics, neuroimaging and biobank-scale studies involving high-dimensional features. Existing statistical tests for the association between two random vectors often do not fully capture dependencies between views due to limitations in modeling within-view dependencies, particularly in high-dimensional data without clear dependency patterns, which can lead to a potential loss of statistical power. In this work, we propose a novel approach termed devariation which is considered a simple yet effective preprocessing method to address the limitations by adopting a penalized low-rank factor model to flexibly capture within-view dependencies. Theoretical analysis of asymptotic power shows that devariation increases statistical power, especially when within-view correlations impact signal-to-noise ratios, while maintaining robustness in scenarios without strong internal correlations. Simulation studies demonstrate devariation's superior performance over existing methods in various scenarios. We further validate devariation in multimodal neuroimaging data from the UK Biobank study, examining the associations between imaging-derived phenotypes (IDPs) from functional, structural, and diffusion magnetic resonance imaging (MRI).

Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by atypical brain connectivity. One of the crucial steps in addressing ASD is its early detection. This study introduces a novel computational framework that employs an Attention-Based Graph Convolutional Network, referred to as the GATGraphClassifier, for detecting ASD. We utilize Functional Magnetic Resonance Imaging (fMRI) data from the Autism Brain Imaging Data Exchange (ABIDE) repository to construct functional connectivity matrices using Pearson correlation, which captures interactions between various brain regions. These matrices are then transformed into graph representations, where the nodes and edges represent the brain regions and functional connections, respectively. The GATGraphClassifier employs attention mechanisms to identify critical connectivity patterns, thereby enhancing the model's interpretability and diagnostic accuracy. Our proposed framework demonstrates superior performance across all standard classification metrics compared to existing state-of-the-art methods. Notably, we achieved an average accuracy of 88.79% on the test data over 30 independent runs, surpassing the benchmark model's performance by 12.27%. In addition, we identified the crucial brain regions associated with ASD, consistent with the previous studies, and a few novel regions. This study not only contributes to the advancement of ASD detection but also shows the potential for broader adaptability of GATGraphClassifier in analyzing complex relational data in various fields, where understanding intricate connectivity and interaction patterns is essential.