Papers

When the number of assets is larger than the sample size, the minimum variance portfolio interpolates the training data, delivering pathological zero in-sample variance. We show that if the weights of the zero variance portfolio are learned by a novel “Ridgelet” estimator, in a new test data this portfolio enjoys out-of-sample generalizability. It exhibits the double descent phenomenon and can achieve optimal risk in the overparametrized regime when the number of assets dominates the sample size. In contrast, a “Ridgeless” estimator which invokes the pseudoinverse fails in-sample interpolation and diverges away from out-of-sample optimality. Extensive simulations and empirical studies demonstrate that the Ridgelet method performs competitively in high-dimensional portfolio optimization.

Time-series diagnostic reasoning is essential for many applications, yet existing solutions face a persistent gap: general reasoning large language models (GRLMs) possess strong reasoning skills but lack the domain-specific knowledge to understand complex time-series patterns. Conversely, fine-tuned time-series LLMs (TSLMs) understand these patterns but lack the capacity to generalize reasoning for more complicated questions. To bridge this gap, we propose a hybrid knowledge-injection framework that injects TSLM-generated insights directly into GRLM's reasoning trace, thereby achieving strong time-series reasoning with in-domain knowledge. As collecting data for knowledge injection fine-tuning is costly, we further leverage a reinforcement learning-based approach with verifiable rewards (RLVR) to elicit knowledge-rich traces without human supervision, then transfer such an in-domain thinking trace into GRLM for efficient knowledge injection. We further release SenTSR-Bench, a multivariate time-series-based diagnostic reasoning benchmark collected from real-world industrial operations. Across SenTSR-Bench and other public datasets, our method consistently surpasses TSLMs by 9.1%-26.1% and GRLMs by 7.9%-22.4%, delivering robust, context-aware time-series diagnostic insights.

Networks of interdependent industrial assets (clients) are tightly coupled through physical processes and control inputs, raising a key question: how would the output of one client change if another client were operated differently? This is difficult to answer because client-specific data are high-dimensional and private, making centralization of raw data infeasible. Each client also maintains proprietary local models that cannot be modified. We propose a federated framework for causal representation learning in state-space systems that captures interdependencies among clients under these constraints. Each client maps high-dimensional observations into low-dimensional latent states that disentangle intrinsic dynamics from control-driven influences. A central server estimates the global state-transition and control structure. This enables decentralized counterfactual reasoning where clients predict how outputs would change under alternative control inputs at others while only exchanging compact latent states. We prove convergence to a centralized oracle and provide privacy guarantees. Our experiments demonstrate scalability, and accurate cross-client counterfactual inference on synthetic and real-world industrial control system datasets.

Perceived message effectiveness (PME) by potential intervention end-users is important for selecting and optimizing personalized smoking cessation intervention messages for mobile health (mHealth) platform delivery. This study evaluates whether large language models (LLMs) can accurately predict PME for smoking cessation messages. We evaluated multiple models for predicting PME across three domains: content quality, coping support, and quitting support. The dataset comprised 3010 message ratings (5-point Likert scale) from 301 young adult smokers. We compared (1) supervised learning models trained on labeled data, (2) zero and few-shot LLMs prompted without task-specific fine-tuning, and (3) LLM-based digital twins that incorporate individual characteristics and prior PME histories to generate personalized predictions. Model performance was assessed on three held-out messages per participant using accuracy, Cohen's kappa, and F1. LLM-based digital twins outperformed zero and few-shot LLMs (12 percentage points on average) and supervised baselines (13 percentage points), achieving accuracies of 0.49 (content), 0.45 (coping), and 0.49 (quitting), with directional accuracies of 0.75, 0.66, and 0.70 on a simplified 3-point scale. Digital twin predictions showed greater dispersion across rating categories, indicating improved sensitivity to individual differences. Integrating personal profiles with LLMs captures person-specific differences in PME and outperforms supervised and zero and few-shot approaches. Improved PME prediction may enable more tailored intervention content in mHealth. LLM-based digital twins show potential for supporting personalization of mobile smoking cessation and other health behavior change interventions.

We extend the knockoffs method for selecting predictors to clustered data (cross-sectional or repeated measures). In the setting of clustered data, variable selection is complex because some predictors are measured at the observation level (level 1), whereas others are measured at the cluster level (level 2), so their values are constant within clusters. The solution we propose is to conduct variable selection separately at the two levels. To this end, we suggest a two-step approach: (i) decompose each level 1 predictor into level 2 and level 1 components by replacing it with the cluster mean and the deviation from the cluster mean; (ii) perform variable selection separately at the two levels, where the level 1 data matrix includes the deviations from the cluster means and the level 2 data matrix includes the cluster means of level 1 predictors and the level 2 predictors. To evaluate the performance of the proposed approach, we conduct a simulation study comparing the sequential knockoff, the derandomized knockoff, and the Lasso. The study shows satisfactory results in terms of false discovery rate and power. All methods fail when applied to the complete data matrix, including both level 1 and level 2 predictors. In contrast, all methods perform better when applied to the level 1 and level 2 data matrices separately. Moreover, the sequential knockoffs method performs substantially better than the Lasso and the derandomized knockoffs. Our proposal to implement the knockoffs method in a clustered data framework is feasible, flexible, and effective.

Bridge periodic inspection records contain sensitive information about public infrastructure, making cross-organizational data sharing impractical under existing data governance constraints. We propose a federated framework for estimating a Continuous-Time Markov Chain (CTMC) hazard model of bridge deterioration, enabling municipalities to collaboratively train a shared benchmark model without transferring raw inspection records. Each User holds local inspection data and trains a log-linear hazard model over three deterioration-direction transitions – Good$\to$Minor, Good$\to$Severe, and Minor$\to$Severe – with covariates for bridge age, coastline distance, and deck area. Local optimization is performed via mini-batch stochastic gradient descent on the CTMC log-likelihood, and only a 12-dimensional pseudo-gradient vector is uploaded to a central server per communication round. The server aggregates User updates using sample-weighted Federated Averaging (FedAvg) with momentum and gradient clipping. All experiments in this paper are conducted on fully synthetic data generated from a known ground-truth parameter set with region-specific heterogeneity, enabling controlled evaluation of federated convergence behaviour. Simulation results across heterogeneous Users show consistent convergence of the average negative log-likelihood, with the aggregated gradient norm decreasing as User scale increases. Furthermore, the federated update mechanism provides a natural participation incentive: Users who register their local inspection datasets on a shared technical-standard platform receive in return the periodically updated global benchmark parameters – information that cannot be obtained from local data alone – thereby enabling evidence-based life-cycle planning without surrendering data sovereignty.

Treatment effect heterogeneity is central to policy evaluation, social science, and precision medicine, where interventions can affect individuals differently. In observational studies, covariates, treatment, and outcomes are often only partially observed. When missingness depends on unobserved values (missing not at random; MNAR), standard methods can yield biased estimates of the conditional average treatment effect (CATE). This paper establishes nonparametric identification of the CATE under multivariate MNAR mechanisms that allow covariates, treatment, and outcomes to be MNAR. It also develops nonparametric and parametric estimators and proposes a sensitivity analysis framework for assessing robustness to violations of the missingness assumptions.

Stochastic traffic capacity is used in traffic modelling and control for unidirectional sections of road infrastructure, although some of the estimation methods have recently proved flawed. However, even sound estimation methods require sufficient data. Because breakdowns are rare, the number of recorded breakdowns effectively determines sample size. This is especially relevant for temporary traffic infrastructure, but also for permanent bottlenecks (e.g., on- and off-ramps), where practitioners must know when estimates are reliable enough for control or design decisions. This paper studies this reliability along with the impact of censored data using synthetic data with a known capacity distribution. A corrected maximum-likelihood estimator is applied to varied samples. In total, 360 artificial measurements are created and used to estimate the capacity distribution, and the deviation from the pre-defined distribution is then quantified. Results indicate that at least 50 recorded breakdowns are necessary; 100-200 are the recommended minimum for temporary measurements. Beyond this, further improvements are marginal, with the expected average relative error below 5 %.

Accurately predicting travel time information can be helpful for travelers. This study proposes a framework for predicting network-level travel time index (TTI) using machine learning models. A case study was performed on more than 50,000 TTI data collected from the Washington DC area over 6 years. The proposed approach is also able to identify the effects of weather and seasonality. The performances of the machine learning models were assessed and compared with each other. It was shown that the ridge regression model outperformed the other models in both short-term and long-term predictions.

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that allows some neurons to remain unmatched, yielding rotation-sensitive but robust correspondences. This partial soft-matching distance provides theoretical advantages – relaxing strict mass conservation while maintaining interpretable transport costs – and practical benefits through efficient neuron ranking in terms of cross-network alignment without costly iterative recomputation. In simulations, it preserves correct matches under outliers and reliably selects the correct model in noise-corrupted identification tasks. On fMRI data, it automatically excludes low-reliability voxels and produces voxel rankings by alignment quality that closely match computationally expensive brute-force approaches. It achieves higher alignment precision across homologous brain areas than standard soft-matching, which is forced to match all units regardless of quality. In deep networks, highly matched units exhibit similar maximally exciting images, while unmatched units show divergent patterns. This ability to partition by match quality enables focused analyses, e.g., testing whether networks have privileged axes even within their most aligned subpopulations. Overall, partial soft-matching provides a principled and practical method for representational comparison under partial correspondence.

Accurate quantification of the relationship between forest loss and associated carbon emissions is critical for both environmental monitoring and policy evaluation. Although many studies have documented spatial patterns of forest degradation, there is limited understanding of the dynamic elasticity linking tree cover loss to carbon emissions at subnational scales. In this paper, we construct a comprehensive panel dataset of annual forest loss and carbon emission estimates for U.S. subnational administrative units from 2001 to 2023, based on the Hansen Global Forest Change dataset. We apply fixed effects and dynamic panel regression techniques to isolate within-region variation and account for temporal persistence in emissions. Our results show that forest loss has a significant positive short-run elasticity with carbon emissions, and that emissions exhibit strong persistence over time. Importantly, the estimated long-run elasticity, accounting for autoregressive dynamics, is substantially larger than the short-run effect, indicating cumulative impacts of repeated forest loss events. These findings highlight the importance of modeling temporal dynamics when assessing environmental responses to land cover change. The dynamic elasticity framework proposed here offers a robust and interpretable tool for analyzing environmental change processes, and can inform both regional monitoring systems and carbon accounting frameworks.

This paper introduces a scalable causal inference framework for estimating the immediate, session-level effects of on-demand human tutoring embedded within adaptive learning systems. Because students seek assistance at moments of difficulty, conventional evaluation is confounded by self-selection and time-varying knowledge states. We address these challenges by integrating principled analytic sample construction with Deep Knowledge Tracing (DKT) to estimate latent mastery, followed by doubly robust estimation using Causal Forests. Applying this framework to over 5,000 middle-school mathematics tutoring sessions, we find that requesting human tutoring increases next-problem correctness by approximately 4 percentage points and accuracy on the subsequent skill encountered by approximately 3 percentage points, suggesting that the effects of tutoring have proximal transfer across knowledge components. This effect is robust to various forms of model specification and potential unmeasured confounders. Notably, these effects exhibit significant heterogeneity across sessions and students, with session-level effect estimates ranging from $-20.25pp$ to $+19.91pp$. Our follow-up analyses suggest that typical behavioral indicators, such as student talk time, do not consistently correlate with high-impact sessions. Furthermore, treatment effects are larger for students with lower prior mastery and slightly smaller for low-SES students. This framework offers a rigorous, practical template for the evaluation and continuous improvement of on-demand human tutoring, with direct applications for emerging AI tutoring systems.

Background: KRAS mutations are the largest oncogenic subset in NSCLC. While KRAS G12C is now targetable, no approved therapies exist for G12D. We examined time-to-next-treatment (TTNT) and overall survival (OS) differences between G12C and G12D, allowing for time-varying hazard effects. Methods: De-identified data from AACR Project GENIE BPC NSCLC v2.0-public were analyzed. TTNT served as a real-world surrogate for progression-free survival. Co-mutations (TP53, STK11, KEAP1, SMARCA4, MET), TMB, and PD-L1 were harmonized. Kaplan-Meier, multivariable Cox, and a pre-specified piecewise Cox model (split at median TTNT = 23 months) were applied. Schoenfeld residuals assessed proportional hazards; bootstrap resampling (B=1000) evaluated stability. Results: Among 162 TTNT-evaluable patients (G12C n=130; G12D n=32), median TTNT was 28.6 versus 32.0 months (log-rank p=0.79). Adjusted Cox regression showed no overall hazard difference (HR=0.85; 95% CI 0.53-1.37; p=0.50), but Schoenfeld testing indicated borderline non-proportionality (p=0.053). Piecewise Cox modeling revealed time-varying effects: early TTNT hazard favored G12D (HR=0.41; 95% CI 0.17-0.97; p=0.043) with significant KRAS x period interaction (HR=3.33; p=0.021) and late-period attenuation (HR=1.38; 95% CI 0.77-2.47; p=0.285). Bootstrap resampling confirmed this pattern (median HRearly=0.39; HRlate=1.41). Among 278 OS-evaluable patients (133 deaths), G12D showed improved OS (adjusted HR=0.63; 95% CI 0.39-0.99; p=0.048). G12C tumors exhibited higher TMB (9.79 vs 7.83 mut/Mb; p=0.002) and greater STK11/KEAP1 enrichment. Conclusions: KRAS G12D demonstrated early TTNT advantage and improved OS. Late-period TTNT differences were non-significant (post-hoc power: 12.3%). These exploratory findings require validation in larger cohorts but support allele-specific therapeutic development for G12D.

Regression discontinuity and kink designs are typically analyzed through mean effects, even when treatment changes the shape of the entire outcome distribution. To address this, we introduce distributional discontinuity designs, a framework for estimating causal effects for a scalar outcome at the boundary of a discontinuity in treatment assignment. Our estimand is the Wasserstein distance between limiting conditional outcome distributions; a single scale-interpretable measure of distribution shift. We show that this weakly bounds the average treatment effect, where equality holds if and only if the treatment effect is purely additive; thus, departure from equality measures effect heterogeneity. To further encode effect heterogeneity we show that the Wasserstein distance admits an orthogonal decomposition into squared differences in $L$-moments, thereby quantifying the contribution from location, scale, skewness, and higher-order shape components to the overall distributional distance. Next, we extend this framework to distributional kink designs by evaluating the Wasserstein derivative at a policy kink; this describes the flow of probability mass through the kink. In the case of fuzzy kink designs, we derive new identification results. Finally, we apply our methods on real data by re-analyzing two natural experiments to compare our distributional effects to traditional causal estimands.

We propose a localized conformal model selection framework that integrates local adaptivity with post-selection validity for distribution-free prediction. By performing model selection symmetrically across calibration points using upper and lower surrogate intervals, we construct a data-dependent safe index set that contains the oracle model and preserves exchangeability. The resulting ensemble procedure retains exact finite-sample marginal coverage while adapting to spatial heterogeneity and model complexity. Simulations demonstrate substantial reductions in interval length compared to the best fixed model, especially in heterogeneous and low-noise settings.

Modern manufacturing systems often experience multiple and unpredictable failure behaviors, yet most existing prognostic models assume a fixed, known set of failure modes with labeled historical data. This assumption limits the use of digital twins for predictive maintenance, especially in high-mix or adaptive production environments, where new failure modes may emerge, and the failure mode labels may be unavailable. To address these challenges, we propose a novel Bayesian nonparametric framework that unifies a Dirichlet process mixture module for unsupervised failure mode discovery with a neural network-based prognostic module. The key innovation lies in an iterative feedback mechanism to jointly learn two modules. These modules iteratively update one another to dynamically infer, expand, or merge failure modes as new data arrive while providing high prognostic accuracy. Experiments on both simulation and aircraft engine datasets show that the proposed approach performs competitively with or significantly better than existing approaches. It also exhibits robust online adaptation capabilities, making it well-suited for digital-twin-based system health management in complex manufacturing environments.

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that quantization impacts effective model and data capacities or acts as an additive error, the theoretical mechanisms governing these effects remain largely unexplored. In this work, we initiate a theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework. By analyzing multiplicative (signal-dependent) and additive (signal-independent) quantization, we identify a critical dichotomy in their scaling behaviors. Our analysis reveals that while both schemes introduce an additive error and degrade the effective data size, they exhibit distinct effects on effective model size: multiplicative quantization maintains the full-precision model size, whereas additive quantization reduces the effective model size. Numerical experiments validate our theoretical findings. By rigorously characterizing the complex interplay among model scale, dataset size, and quantization error, our work provides a principled theoretical basis for optimizing training protocols under practical hardware constraints.

Large language models can follow complex procedures yet fail at a seemingly trivial final step: reporting a value they themselves computed moments earlier. We study this phenomenon as procedural hallucination: failure to execute a verifiable, prompt-grounded specification even when the correct value is present in context. In long-context binding tasks with a known single-token candidate set, we find that many errors are readout-stage routing failures. Specifically, failures decompose into Stage~2A (gating) errors, where the model does not enter answer mode, and Stage~2B (binding) errors, where it enters answer mode but selects the wrong candidate (often due to recency bias). In the hard regime, Stage~2B accounts for most errors across model families in our tasks (Table~1). On Stage~2B error trials, a linear probe on the final-layer residual stream recovers the correct value far above chance (e.g., 74% vs.\ 2% on Qwen2.5-3B; Table~2), indicating that the answer is encoded but not used. We formalize “present but not used” via available vs.\ used mutual information and pseudo-prior interventions, yielding output-computable diagnostics and information-budget certificates. Finally, an oracle checkpointing intervention that restates the true binding near the query can nearly eliminate Stage~2B failures at long distance (e.g., Qwen2.5-3B $0/400 \rightarrow 399/400$ at $k = 1024$; Table~8).

Mixed-effects models are fundamental tools for analyzing clustered and repeated-measures data, but existing high-dimensional methods largely focus on penalized estimation with vector-valued covariates. Bayesian alternatives in this regime are limited, with no sampling-based mixed-effects framework that supports tensor-valued fixed- and random-effects covariates while remaining computationally tractable. We propose the Compressed Mixed-Effects Tensor (CoMET) model for high-dimensional repeated-measures data with scalar responses and tensor-valued covariates. CoMET performs structured, mode-wise random projection of the random-effects covariance, yielding a low-dimensional covariance parameter that admits simple Gaussian prior specification and enables efficient imputation of compressed random-effects. For the mean structure, CoMET leverages a low-rank tensor decomposition and margin-structured Horseshoe priors to enable fixed-effects selection. These design choices lead to an efficient collapsed Gibbs sampler whose computational complexity grows approximately linearly with the tensor covariate dimensions. We establish high-dimensional theoretical guarantees by identifying regularity conditions under which CoMET's posterior predictive risk decays to zero. Empirically, CoMET outperforms penalized competitors across a range of simulation studies and two benchmark applications involving facial-expression prediction and music emotion modeling.

Matched case-control studies are commonly employed in epidemiological research for their convenience and efficiency. Analysis of secondary outcomes can yield valuable insights into biological pathways and help identify genetic variants of importance. Naive analysis using standard statistical methods, such as least-squares regression for quantitative traits, can be misleading because they fail to account for unequal sampling induced by the case-control design and matching. In this paper, we propose novel statistical methods that appropriately reflect the study design and sampling scheme in the analysis of secondary outcome data. The new methods provide consistent estimation and accurate coverage probabilities for the confidence interval estimators. We demonstrate the advantages of the new methods through simulation studies and a real application with diabetes patients. R code implementing the proposed methods is publicly available.

Aspect-Based Sentiment Analysis (ABSA) provides a fine-grained understanding of opinions by linking sentiment to specific aspects in text. While transformer-based models excel at this task, their black-box nature limits their interpretability, posing risks in real-world applications without labeled data. This paper introduces a statistical, model-agnostic framework to assess the behavioral transparency and trustworthiness of ABSA models. Our framework relies on several metrics, such as the entropy of polarity distributions, soft-count-based dominance scores, and sentiment divergence between sources, whose robustness is validated through bootstrap resampling and sensitivity analysis. A case study on environmentally focused Reddit communities illustrates how the proposed indicators provide interpretable diagnostics of model certainty, decisiveness, and cross-source variability. The results show that statistical indicators computed on soft outputs can complement traditional approaches, offering a computationally efficient methodology for validating, monitoring, and interpreting ABSA models in contexts where labeled data are unavailable.

Missing data is an universal problem in statistics. We develop a unified framework for estimating parameters defined by general estimating equations under a missing-at-random (MAR) mechanism, based on generalized entropy calibration weighting. We construct weights by minimizing a convex entropy subject to (i) balancing constraints on a data-adaptive calibration function, estimated using flexible machine-learning predictors with cross-fitting, and (ii) a debiasing constraint involving the fitted propensity score (PS) model. The resulting estimator is doubly robust, remaining consistent if either the outcome regression (OR) or the PS model is correctly specified, and attains the semiparametric efficiency bound when both models are correctly specified. Our formulation encompasses classical inverse probability weighting (IPW) and augmented IPW (AIPW) as special cases and accommodates a broad class of entropy functions. We illustrate the versatility of the approach in three important settings: semi-supervised learning with unlabeled outcomes, regression analysis with missing covariates, and causal effect estimation in observational studies. Extensive simulation studies and real-data applications demonstrate that the proposed estimators achieve greater efficiency and numerical stability than existing methods. In particular, the proposed estimator outperforms the classical AIPW estimator under the OR model misspecification.

This paper develops an asymptotic and inferential theory for fixed-effects panel quantile regression (FEQR) that delivers inference robust to pervasive common shocks. Such shocks induce cross-sectional dependence that is central in many economic and financial panels but largely ignored in existing FEQR theory, which typically assumes cross-sectional independence and requires $T \gg N$. We show that the standard FEQR estimator remains asymptotically normal under the mild condition $(\log N)^2/T \to 0$, thereby accommodating empirically relevant regimes, including those with $T \ll N$. We further show that common shocks fundamentally alter the asymptotic covariance structure, rendering conventional covariance estimators inconsistent, and we propose a simple covariance estimator that remains consistent both in the presence and absence of common shocks. The proposed procedure therefore provides valid robust inference without requiring prior knowledge of the dependence structure, substantially expanding the applicability of FEQR methods in realistic panel data settings.

This paper studies simple transformers trained on a high-order Markov chain, where the model must incorporate information from multiple past positions, each with different statistical importance. We show that transformers learn the task incrementally, with each stage corresponding to learning how to copy information from a subset of positions via a sparse attention pattern. Notably, the learning dynamics transition from a competitive phase, where all heads focus on the statistically most important positions, to a cooperative phase, where different heads specialize in different patterns. We model these dynamics with simplified differential equations and prove stage-wise convergence of the resulting system. Functionally, these stages correspond to a sequence of increasingly expressive misspecified models, with the full model class reached only at the end. Overall, we give a theoretical account of how structured attention patterns and head specialization emerge in stages without an explicit curriculum, with implications for generalization in sequential tasks.

Multilayer networks have become increasingly ubiquitous across diverse scientific fields, yet their inferential theory remains underdeveloped. We propose a flexible latent space model for directed multilayer networks with various edge types, where each node has sender and receiver latent positions capturing its sending and receiving behaviors, together with layer-varying out- and in-degree parameters and layer-specific connection matrices. Through nonlinear link functions, the model induces a Tucker low-rank tensor structure in which the structural latent spaces are intertwined with the degree-effect subspaces, creating challenges for estimation and inference. To address these challenges, we develop a novel unfolding and fusion method, coupled with two-sided centering to partial out degree effects. We establish consistency and asymptotic normality for the latent-position estimators. For the connection matrices, we uncover a non-negligible second-order bias induced by fusing two separately estimated unfolding components, derive its explicit representation, and construct a feasible plug-in correction. The resulting debiased estimator is asymptotically normal. Together, these results enable confidence regions for latent positions and tests of whether two network layers share the same structure. Extensive simulation studies validate the proposed method, and a real-world data analysis demonstrates its practical utility.

We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between ridge-regularized RF training and Bayesian inference with Gaussian priors and likelihoods, we replace the single prior and likelihood with $\epsilon$- and $\eta$-contaminated credal sets, respectively, and perform inference using pessimistic generalized Bayesian updating. We derive explicit and tractable bounds for the resulting lower and upper posterior predictive densities. These bounds show that, when contamination is moderate, prior and likelihood ambiguity effectively acts as a direct contamination of the posterior predictive distribution, yielding uncertainty envelopes around the classical Gaussian predictive. We introduce an Imprecise Highest Density Region (IHDR) for robust predictive uncertainty quantification and show that it admits an efficient approximation via an adjusted Gaussian credible interval. We further obtain predictive variance bounds (under a mild truncation approximation for the upper bound) and prove that they preserve the leading-order proportional-growth asymptotics known for RF models. Together, these results establish a robustness theory for Bayesian random features: predictive uncertainty remains computationally tractable, inherits the classical double-descent phase structure, and is improved by explicit worst-case guarantees under bounded prior and likelihood misspecification.

Spatio-temporal forecasting is fundamental to intelligent systems in transportation, climate science, and urban planning. However, training deep learning models on the massive, often redundant, datasets from these domains presents a significant computational bottleneck. Existing solutions typically focus on optimizing model architectures or optimizers, while overlooking the inherent inefficiency of the training data itself. This conventional approach of iterating over the entire static dataset each epoch wastes considerable resources on easy-to-learn or repetitive samples. In this paper, we explore a novel training-efficiency techniques, namely learning from complexity with dynamic sample pruning, ST-Prune, for spatio-temporal forecasting. Through dynamic sample pruning, we aim to intelligently identify the most informative samples based on the model's real-time learning state, thereby accelerating convergence and improving training efficiency. Extensive experiments conducted on real-world spatio-temporal datasets show that ST-Prune significantly accelerates the training speed while maintaining or even improving the model performance, and it also has scalability and universality.

Background: Phase I dose-finding trials increasingly encounter delayed-onset toxicities, especially with immunotherapies and targeted agents. The time-to-event continual reassessment method (TITE-CRM) handles incomplete follow-up using fixed linear weights, but this ad hoc approach doesn't reflect actual delay patterns and may expose patients to excessive risk during dose escalation. Methods: We replace TITE-CRM's fixed weights with adaptive weights, posterior predictive probabilities derived from the evolving toxicity delay distribution. Under a Weibull timing model, we get closed-form weight updates through maximum likelihood estimation, making real-time implementation straightforward. We tested our method (AW-TITE) against TITE-CRM and standard designs (3+3, mTPI, BOIN) across three dose-toxicity scenarios through simulation (N = 30 patients, 2,000 replications). We also examined robustness across varying accrual rates, sample sizes, shape parameters, observation windows, and priors. Results: Our AW-TITE reduced patient overdosing by 40.6% compared to TITE-CRM (mean fraction above MTD: 0.202 vs 0.340; 95% CI: -0.210 to -0.067, p < 0.001) while maintaining comparable MTD selection accuracy (mean difference: +0.023, p = 0.21). Against algorithm-based methods, AW-TITE achieved higher MTD identification: +32.6% vs mTPI, +19.8% vs 3+3, and +5.6% vs BOIN. Performance remained robust across all sensitivity analyses. Conclusions: Adaptive weighting offers a practical way to improve Phase I trial safety while preserving MTD selection accuracy. The method requires minimal computation and is ready for real-time use.

We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the total number of parameters exceeds the number of training samples, we prove that SMD with matrix mirror functions $\psi(\cdot)$ converges exponentially to a global interpolator. Furthermore, we generalize classical implicit bias results of vector SMD by demonstrating that the matrix SMD algorithm converges to the unique solution minimizing the Bregman divergence induced by $\psi(\cdot)$ from initialization subject to interpolating the data. These findings reveal how matrix mirror maps dictate inductive bias in high-dimensional, multi-output problems.

Recurrent binary outcomes within individuals, such as hospital readmissions, often reflect latent risk processes that evolve over time. Conventional methods like generalized linear mixed models and generalized estimating equations estimate average risk but fail to capture temporal changes in variability, asymmetry, and tail behavior. We introduce two statistical frameworks that model each binary event as the outcome of a thresholded value drawn from a time-varying latent distribution defined by its location, scale, skewness, and kurtosis. Rather than treating these four quantities as nonparametric moment estimators, we model them as interpretable latent moments within a flexible latent distributional family. The first, BLaS-Recurrent, is a Bayesian model using the sinh-arcsinh distribution (a parametric family that provides explicit control over asymmetry and tail weight) to estimate latent moment trajectories; the second, QuaD-Recurrent, is a quasi-distributional approach that maps simulated moment vectors to event probabilities using a flexible nonparametric surface. Both models support time-dependent covariates, serial correlation, and multiple membership structures. Simulation studies show improved calibration, interpretability, and robustness over standard models. Applied to ICU readmission data from the MIMIC-IV database, both approaches uncover clinically meaningful patterns in latent risk, such as right-skewed escalation and widening dispersion, that are missed by traditional methods. These models provide interpretable, distribution-sensitive tools for longitudinal binary outcomes in healthcare while explicitly acknowledging that latent "moments" summarize but do not uniquely determine the underlying distribution.