Papers

Android's Earthquake Alert (AEA) system provided timely early warnings to millions during the Mw 6.2 Marmara Ereglisi, Türkiye earthquake on April 23, 2025. This event, the largest in the region in 25 years, served as a critical real-world test for smartphone-based Earthquake Early Warning (EEW) systems. The AEA system successfully delivered alerts to users with high precision, offering over a minute of warning before the strongest shaking reached urban areas. This study leveraged Large Language Models (LLMs) to analyze more than 500 public social media posts from the X platform, extracting 42 distinct attributes related to user experience and behavior. Statistical analyses revealed significant relationships, notably a strong correlation between user trust and alert timeliness. Our results indicate a distinction between engineering and the user-centric definition of system accuracy. We found that timeliness is accuracy in the user's mind. Overall, this study provides actionable insights for optimizing alert design, public education campaigns, and future behavioral research to improve the effectiveness of such systems in seismically active regions.

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before changing its prediction. However, its applicability is more limited than some of its alternatives, since it requires the use of generative models and restricts the analyses either to specific model architectures or discrete features. In this work, we propose a new robustness metric applicable to any probabilistic discriminative classifier and any type of features. We demonstrate that this new metric is capable of distinguishing between reliable and unreliable predictions, and use this observation to develop new strategies for dynamic classifier selection.

Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to data sparsity, while existing eQTE methods rely on restrictive tail assumptions or on interior-quantile theory. We propose the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, which combines information across quantile levels and anchors the tail using extreme value models within a unified estimating equation approach. We establish asymptotic properties of the resulting estimator and evaluate its performance through simulation under different tail behaviours and model misspecifications. An application to extreme precipitation in the Austrian Alps illustrates how TIEE enables observational causal attribution for very rare events under anthropogenic warming. More broadly, the proposed framework establishes a new foundation for causal inference on rare, high-impact outcomes, with relevance across environmental risk, economics, and public health.

We investigate the problem of matching networks where both edge weights and node features are correlated following a specific node correspondence. While prior work has established sharp thresholds for matching either graphs or features individually, the joint setting has been significantly less explored. In this study, we derive precise information-theoretic thresholds for exact recovery, almost-exact recovery, and partial recovery of the underlying alignment. These are expressed in terms of graph and feature correlation strengths, the number of nodes, and the dimension of the features. Interestingly, whereas an all-or-nothing phase transition is observed in the standard graph-matching scenario, the inclusion of contextual information at the node level introduces a richer structure: the exact-recovery threshold separates from the shared threshold for almost-exact and partial recovery. Closing gaps left by prior works, we provide a sharp characterization of the thresholds governing how structural and contextual information interact in graph matching, and thereby establish a benchmark for designing efficient algorithms in the high-dimensional setting.

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric problem, particularly in multidimensional settings, since the covariance function is defined on a product domain and thus suffers from the curse of dimensionality. This motivates the use of adaptive estimators, such as deep learning estimators. However, existing theoretical results are largely limited to estimators with explicit analytic representations, and the properties of general learning-based estimators remain poorly understood. We establish an oracle inequality for a broad class of learning-based estimators that applies to both sparse and dense observation regimes in a unified manner, and derive convergence rates for deep learning estimators over several classes of covariance functions. The resulting rates suggest that structural adaptation can mitigate the curse of dimensionality, similarly to classical nonparametric regression. We further compare the convergence rates of learning-based estimators with several existing procedures. For a one-dimensional smoothness class, deep learning estimators are suboptimal, whereas local linear smoothing estimators achieve a faster rate. For a structured function class, however, deep learning estimators attain the minimax rate up to polylogarithmic factors, whereas local linear smoothing estimators are suboptimal. These results reveal a distinctive adaptivity-variance trade-off in covariance function estimation.

A model-free measure of Granger causality in expectiles is proposed, generalizing the traditional mean-based measure to arbitrary positions of the conditional distribution. Expectiles are the only law-invariant risk measures that are both coherent and elicitable, making them particularly well-suited for studying distributional Granger causality where risk quantification and forecast evaluation are both relevant. Based on this measure, a test is developed using M-vine copula models that accounts for multivariate Granger causality with $d+1$ series under non-linear and non-Gaussian dependence, without imposing parametric assumptions on the joint distribution. Strong consistency of the test statistic is established under some regularity conditions. In finite samples, simulations show accurate size control and power increasing with sample size. A key advantage is the joint testing capability: causal relationships invisible to pairwise tests can be detected, as demonstrated both theoretically and empirically. Two applications to international stock market indices at the global and Asian regional level illustrate the practical relevance of the proposed framework.

We develop an identifiable reduced-rank spatial multinomial model for categorical data with many classes. The model represents class-specific spatial effects through a low-dimensional set of shared latent factors, substantially reducing parameter dimension while preserving joint dependence across classes. Because standard conjugate and Pólya-Gamma methods fail under this factorization, we propose a Gibbs sampler using Laplace-approximation proposals within Metropolis-Hastings updates. Simulation studies examine dimension selection and the accuracy of the Laplace proposals. An application to dominant tree species mapping in the Blue Ridge Mountains demonstrates scalable inference and flexible joint predictions for individual classes, class unions, and area-level summaries.

We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic objects required for such settings and to establish their first theorem-supporting consequences. The paper develops a regime-varying framework centered on admissible transport, protected-core preservation, and evaluator-aware learning evolution. It records the immediate closure consequences of admissibility, develops a structural obstruction argument for faithful fixed-ontology reduction in genuinely multi-regime settings, and introduces a protected-stability template together with explicit numerical and symbolic witnesses on controlled subclasses, including convex and deductive settings. It also establishes theorem-layer results on evaluator factorization, morphisms, composition, and partial kernel-level alignment across semantically commensurable layers. A worked two-regime example makes the admissibility certificate, protected evaluative core, and regime-variation cost explicit on a controlled subclass. The symbolic component is deliberately restricted in scope: the paper establishes a first kernel-level compatibility result together with a controlled monotonic deductive witness. The manuscript should therefore be read as introducing a structured learning-theoretic framework for regime-varying learning together with its first theorem-supporting layer, not as a complete quantitative theory of all learning systems.

Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.

In this work, we investigate Gaussian Mixture Models (abbrv GMM) and the related problem of non parametric maximum likelihood estimation (abbrv NPMLE) from the perspective of statistical mechanics. In particular, we establish stability guarantees for the NPMLE procedure that extend well beyond the state of the art. Crucially, we obtain guarantees on the Kullback-Leibler divergence between NPMLE estimators and the ground truth, a type of result which has been known to be challenging in the literature on this problem. In particular, we provide high probability upper bounds on the KL divergence between the NPMLE and the true density that are of the order of $\min\big\{\frac{(\log n)^{d+2}}{n} , \frac{\log n}{\sqrt n}\big\}$, which cover a wide range of scenarios for the comparative sizes of $n$ and $d$. We obtain similar guarantees for approximate solutions to the NPMLE problem, addressing realistic situations wherein optimization algorithms need to be stopped in finite time, allowing access only to approximations to the true NPMLE. A cornerstone of our approach is an analysis of the function class complexity of logarithms of gaussian mixture densities, which is able to handle their unboundedness, and could be of wider interest. Our methods lead to novel confidence-interval guarantees for entropy estimation in Gaussian mixtures, demonstrating their wider impact. We also establish correspondences between stability phenomena in the NPMLE problem and concepts such as chaos and multiple valleys in random energy landscapes of statistical mechanics models. While these correspondences are largely of a conceptual nature at this point, we believe that these connections, especially those with concentration phenomena and Langevin dynamics, may be developed into a toolbox for studying a wide variety of random optimization problems in statistics and machine learning.

Despite the success of reinforcement learning from human feedback (RLHF), existing reward modeling methods largely rely on explicit feedback, which is costly to collect and difficult to scale. This work studies implicit reward modeling, learning reward models from implicit user feedback, such as clicks, copies and skips. While scalable and cost-effective, implicit feedback poses two key challenges: It lacks definitive negative samples, which makes standard positive-negative classification methods inapplicable; It suffers from selection bias, where responses have heterogeneous propensities to elicit feedback, which further obscures definitive negative samples. To address these challenges, we propose ImplicitRM, which learns unbiased reward models from implicit feedback. It stratifies training samples into four latent groups using a stratification model and derives a likelihood-maximization objective that is theoretically unbiased, thereby addressing both challenges. Experiments across diverse LLM backbones and benchmark datasets validate that ImplicitRM learns accurate reward models from implicit feedback and improves performance on downstream RLHF tasks.

We define a generalized Golomb–Dickman constant $\lambda_{\theta}$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $\theta > 0$. Exploiting the independence properties of Kingman's Poisson process construction of the Poisson–Dirichlet distribution, we obtain an explicit integral representation for $\lambda_{\theta}$ in terms of the exponential integral. The dependence of $\lambda_{\theta}$ on $\theta$ reflects the transition between regimes dominated by long cycles (small $\theta$) and those with many small cycles (large $\theta$). We also derive the asymptotic behavior of $\lambda_{\theta}$ for small and large $\theta$ and illustrate our results with numerical computations, Monte Carlo simulations of the Hoppe urn, and an application.

Drones are becoming popular as a complementary system for Emergency Medical Services (EMS). Although several pilot studies and flight trials have shown the feasibility of drone-assisted Automated External Defibrillator (AED) delivery, running a full-scale operational network remains challenging due to high capital expenditure and environmental uncertainties. In this paper, we formulate a reliability-informed Bayesian learning framework for designing drone-assisted AED delivery networks under environmental and operational uncertainty. We propose our objective function based on the survival probability of Out-off Hospital Cardiac Arrest (OHCA) patients to identify the ideal locations of drone stations. Moreover, we consider the coverage of existing EMS infrastructure to improve the response reliability in remote areas. We illustrate our proposed method using geographically referenced cardiac arrest data from Scotland. The result shows how environmental variability and spatial demand patterns influence optimal drone station placement across urban and rural regions. In addition, we assess the robustness of the network and evaluate its economic viability using a cost-effectiveness analysis based on expected Quality Adjusted Life Year (QALY). The findings suggest that drone-assisted AED delivery is expected to be cost-effective and has the potential to significantly improve the emergency response coverage in rural and urban areas with longer ambulance response times.

Characteristic functions of weighted sums of independent random variables exhibit low-rank structure in the quantized tensor train (QTT) representation, also known as matrix product states (MPS), enabling up to exponential compression of their fully non-Gaussian probability distributions. Under variable independence, the global characteristic function factorizes into local terms. Its low-rank QTT structure arises from intrinsic spectral smoothness in continuous models, or from spectral energy concentration as the number of components $D$ grows in discrete models. We demonstrate this on weighted sums of Bernoulli and lognormal random variables. In the former, despite an adversarial, incompressible small-$D$ regime, the characteristic function undergoes a sharp bond-dimension collapse for $D \gtrsim 300$ components, enabling polylogarithmic time and memory scaling. In the latter, the approach reaches high-resolution discretizations of $N = 2^{30}$ frequency modes on standard hardware, far beyond the $N = 2^{24}$ ceiling of dense implementations. These compressed representations enable efficient computation of Value at Risk (VaR) and Expected Shortfall (ES), supporting applications in quantitative finance and beyond.

Formal model evaluation methods typically certify that a model satisfies a prescribed target key performance indicator (KPI) level. However, in many applications, the relevant target KPI level may not be known a priori, and the user may instead wish to compare candidate models by analyzing the full trade-offs between performance and reliability achievable at test time by the models. This task, requiring the reliable estimate of the test-time KPI distributions, is made more complicated by the fact that the same data must often be used both to pre-select a subset of candidate models and to estimate their KPI distributions, causing a potential post-selection bias. In this work, we introduce post-selection distributional model evaluation (PS-DME), a general framework for statistically valid distributional model assessment after arbitrary data-dependent model pre-selection. Building on e-values, PS-DME controls post-selection false coverage rate (FCR) for the distributional KPI estimates and we establish explicit conditions under which it is provably more sample efficient than a baseline method based on sample splitting. Experiments on synthetic data, text-to-SQL decoding with large language models, and telecom network performance evaluation demonstrate that PS-DME enables reliable comparison of candidate configurations across a range of reliability levels, supporting the statistically reliable exploration of performance–reliability trade-offs.

This paper proposes tds mgtwr, a multiscale geographically and temporally weighted regression (MGTWR) model with covariate-specific spatial and temporal scales. The approach combines a separable spatio-temporal kernel with a Top-Down Scale (TDS) calibration scheme, where spatial and temporal bandwidths are selected for each covariate through a coordinate-wise search over ordered grids guided by the corrected Akaike Information Criterion (AICc). By avoiding unconstrained multidimensional optimization, this strategy extends to the spatio-temporal setting the stabilizing properties of TDS calibration scheme Geniaux (2026). The multiscale backfitting procedure combines the Top-Down Scale calibration scheme with an adaptive, importance-driven update schedule that prioritizes covariates according to their current scale-normalized contribution to the fitted signal, thereby limiting the number of local recalibrations required and accelerating convergence while maintaining estimator fidelity. We also introduce a generic prediction method for MGWR and MGTWR based on kernel sharpening. Monte Carlo experiments show that modeling both space and time improves coefficient recovery and predictive accuracy relative to purely spatial multiscale models when temporal variation is present and sufficiently supported by the data. Gains increase with sample size and signal-to-noise ratio. Two empirical applications illustrate the method under contrasting regimes. For Beet Yellows severity, a plant epidemiology and pest management problem, multiscale spatial modeling is essential, while spatio-temporal extensions yield additional gains when temporal information is rich. In modeling house prices, MGTWR consistently outperforms spatial local and STVC models. In both cases, predictive performance rivals flexible machine-learning benchmarks while preserving interpretable spatio-temporal scales.

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

We study the theoretical behavior of denoising score matching–the learning task associated to diffusion models–when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network. We derive asymptotically exact expressions for the test, train, and score errors in the high-dimensional limit. Our analysis reveals that, for linear manifolds the sample complexity required to learn the score function scales linearly with the intrinsic dimension of the manifold, rather than with the ambient dimension. Perhaps surprisingly, the benefits of low-dimensional structure starts to diminish once we have a non-linear manifold. These results indicate that diffusion models can benefit from structured data; however, the dependence on the specific type of structure is subtle and intricate.

We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of trees built from copulas, where more complex latent dependence can be modeled with increasing number of trees. We propose to estimate the vine copula approximate posterior in a stepwise fashion, tree by tree along the vine structure. Further, we show that the usual backward Kullback-Leibler divergence cannot recover the correct parameters in the vine copula model, thus the evidence lower bound is defined based on the Rényi divergence. Finally, an intuitive stopping criterion for adding further trees to the vine eliminates the need to pre-define a complexity parameter of the variational distribution, as required for most other approaches. Thus, our method interpolates between mean-field VI (MFVI) and full latent dependence. In many applications, in particular sparse Gaussian processes, our method is parsimonious with parameters, while outperforming MFVI.

System outputs such as eigenfrequencies or strain data, often used in structural health monitoring (SHM), not only react to damage but also depend on environmental conditions. When trying to correct for these confounding effects, it is often (at least implicitly) assumed that only the expected, i.e., mean, output values are affected by environmental conditions. However, the evaluation of real-world SHM data indicates that environmental conditions may influence not only the mean output but also higher-order statistical moments, particularly the variances of and the covariances and correlations between the output quantities, such as eigenfrequencies of different modes or strain sensors at different locations. To address these issues, we discuss two approaches for identifying and quantifying multivariate confounding effects on output covariances and correlations: a random forest and a nonparametric, kernel-based approach. We compare the two competing methods on both artificial and real-world SHM data, finding that the kernel-based approach achieves higher accuracy, but the random forest produces estimates that are more robust and sometimes easier to interpret.

Single-index models or time-to-event models are frequently applied in empirical research. These models are non-identifiable in presence of unknown (dependent) censoring or competing risks and do not give informative results in empirical analysis unless rather strong, non-testable restrictions hold. Little is known, whether the known robustness properties of the single-index model carry over to models with dependent censoring or competing risks. This paper shows that the ratio of partial covariate effects on the margins is identifiable in nonparametric models with unknown dependent censoring or nonparametric competing risks models with nonparametric dependence structure, provided an exclusion restriction holds. Commonly used (semi)parametric models for the margin and independent censoring, such as Cox proportional hazards, accelerated failure time or proportional odds models, can be used to obtain relative covariate effects despite their misspecified censoring mechanism. Several nonparametric estimators for the general model are introduced and their numerical properties are studied.

Optimizing survival outcomes, such as patient survival or customer retention, is a critical objective in data-driven decision-making. Off-Policy Evaluation~(OPE) provides a powerful framework for assessing such decision-making policies using logged data alone, without the need for costly or risky online experiments in high-stakes applications. However, typical estimators are not designed to handle right-censored survival outcomes, as they ignore unobserved survival times beyond the censoring time, leading to systematic underestimation of the true policy performance. To address this issue, we propose a novel framework for OPE and Off-Policy Learning~(OPL) tailored for survival outcomes under censoring. Specifically, we introduce IPCW-IPS and IPCW-DR, which employ the Inverse Probability of Censoring Weighting technique to explicitly deal with censoring bias. We theoretically establish that our estimators are unbiased and that IPCW-DR achieves double robustness, ensuring consistency if either the propensity score or the outcome model is correct. Furthermore, we extend this framework to constrained OPL to optimize policy value under budget constraints. We demonstrate the effectiveness of our proposed methods through simulation studies and illustrate their practical impacts using public real-world data for both evaluation and learning tasks.

We study boundary inference at $H=3/4$ for mixed fractional Brownian motion and mixed fractional Ornstein–Uhlenbeck models under high-frequency observation. This boundary is economically important because it separates the critical and supercritical regimes of mixed fractional dynamics. We make three contributions. First, we identify the exact critical first-order scaling and show that, after removing the explicit linear component in the $H$-score, the transformed $(\sigma,H)$ block is already non-degenerate. Second, we establish critical score central limit theorems (CLT) and derive local asymptotic normality (LAN) with fully explicit leading information constants for both models. Third, we construct boundary-calibrated one-sided score tests for detecting entry into the supercritical region $H>3/4$ and discuss feasible implementation through restricted nuisance estimation. Monte Carlo evidence shows that the feasible statistic has the correct directional power but conservative null calibration. Finally, an intraday illustration on one-minute SPY data finds no persistent evidence in favor of $H>3/4$.

Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and heavy-tailed noise. In this paper, we propose DROP (Distributionally Robust Optimization), a robust estimation method formulated within a multi-task nodewise regression framework. The proposed estimator enforces structural sparsity while resisting the influence of corrupted observations. Theoretically, we establish error bounds for the DROP estimator under general contamination. Through extensive high-dimensional simulations, we demonstrate that DROP consistently controls the rate of false positive edges and outperforms conventional non-robust estimators when data deviate from standard Gaussian assumptions. Furthermore, in a functional MRI (fMRI) application, DROP maintains a stable graph structure and preserves network modularity even when subjected to severe data perturbations, whereas competing methods yield excessively dense networks. To facilitate reproducible research, the DROP R package will be made publicly available on GitHub.

We study layer-specific community detection in an $L$-layer network $\{A^{(l)}\}_{l\in[L]}$ on a common set of $n$ nodes. Because modern networks are constructed from multi-modal data or with different contexts, the community labels $\pi^{(l)}\in[K]^n$ are layer-dependent and the degree heterogeneity parameters $\theta_i^{(l)}$ vary widely across nodes and layers. The inhomogeneity and extreme sparsity raise a challenge for classical community detection methods. We propose a multilayer-assisted regularized spectral method (MARS-CD) to address this challenge. For layer $l$, MARS-CD first constructs $X^{(l)}$ from the remaining layers, so that the problem is transformed into a network-with-covariates clustering problem on $(A^{(l)}, X^{(l)})$. Then we recover $\pi^{(l)}$ by NAC in Hu and Wang (2024) that allows misalignment. The key component is to construct $X^{(l)}$, where we stack regularized embeddings. Building upon this, we establish the first theoretical guarantees for the quality of $X^{(l)}$ under multilayer networks with extreme sparsity. These further lead to weak and strong consistency for recovering $\pi^{(l)}$. We further develop an optional label alignment step to interpret the shared community structure across layers. Simulations demonstrate the superior performance of our MARS-CD method. Applying MARS-CD to international food trading networks provides an interpretable product-specific community structure.

Implicit bias induced by gradient-based algorithms is essential to the generalization of overparameterized models, yet its mechanisms can be subtle. This work leverages the Normalized Steepest Descent} (NSD) framework to investigate how optimization geometry shapes solutions on multiclass separable data. We introduce NucGD, a geometry-aware optimizer designed to enforce low rank structures through nuclear norm constraints. Beyond the algorithm itself, we connect NucGD with emerging low-rank projection methods, providing a unified perspective. To enable scalable training, we derive an efficient SVD-free update rule via asynchronous power iteration. Furthermore, we empirically dissect the impact of stochastic optimization dynamics, characterizing how varying levels of gradient noise induced by mini-batch sampling and momentum modulate the convergence toward the expected maximum margin solutions.Our code is accessible at: https://github.com/Tsokarsic/observing-the-implicit-bias-on-multiclass-seperable-data.

Active learning reduces labeling costs by selecting samples that maximize information gain. A dominant framework, Query-by-Committee (QBC), typically relies on perturbation-based diversity by inducing model disagreement through random feature subsetting or data blinding. While this approximates one notion of epistemic uncertainty, it sacrifices direct characterization of the plausible hypothesis space. We propose the complementary approach: Rashomon Ensembled Active Learning (REAL) which constructs a committee by exhaustively enumerating the Rashomon Set of all near-optimal models. To address functional redundancy within this set, we adopt a PAC-Bayesian framework using a Gibbs posterior to weight committee members by their empirical risk. Leveraging recent algorithmic advances, we exactly enumerate this set for the class of sparse decision trees. Across synthetic and established active learning baselines, REAL outperforms randomized ensembles, particularly in moderately noisy environments where it strategically leverages expanded model multiplicity to achieve faster convergence.

Generating samples from a continuous probability density is a central algorithmic problem across statistics, engineering, and the sciences. For high-dimensional settings, Hamiltonian Monte Carlo (HMC) is the default algorithm across mainstream software packages. However, despite the extensive line of work on HMC and its widespread empirical success, it remains unclear how many iterations of HMC are required as a function of the dimension $d$. On one hand, a variety of results show that Metropolized HMC converges in $O(d^{1/4})$ iterations from a warm start close to stationarity. On the other hand, Metropolized HMC is significantly slower without a warm start, e.g., requiring $\Omega(d^{1/2})$ iterations even for simple target distributions such as isotropic Gaussians. Finding a warm start is therefore the computational bottleneck for HMC. We resolve this issue for the well-studied setting of sampling from a probability distribution satisfying strong log-concavity (or isoperimetry) and third-order derivative bounds. We prove that non-Metropolized HMC generates a warm start in $\tilde{O}(d^{1/4})$ iterations, after which we can exploit the warm start using Metropolized HMC. Our final complexity of $\tilde{O}(d^{1/4})$ is the fastest algorithm for high-accuracy sampling under these assumptions, improving over the prior best of $\tilde{O}(d^{1/2})$. This closes the long line of work on the dimensional complexity of MHMC for such settings, and also provides a simple warm-start prescription for practical implementations.

Driver heterogeneity is often reduced to labels or discrete regimes, compressing what is inherently dynamic into static categories. We introduce quantum-inspired representation that models each driver as an evolving latent state, presented as a density matrix with structured mathematical properties. Behavioral observations are embedded via non-linear Random Fourier Features, while state evolution blends temporal persistence of behavior with context-dependent profile activation. We evaluate our approach on empirical driving data, Third Generation Simulation Data (TGSIM), showing how driving profiles are extracted and analyzed.

Integrative analysis of multivariate functional time series (MFTS) is both critical and challenging across many scientific domains. Such data often exhibit complex multi-way dependencies arising from within-curve structures, temporal correlations across curves, and cross-subject interactions, underscoring the need for efficient methods that can jointly capture these dependencies and support accurate downstream analyses. In this work, we propose a novel frequency-domain framework based on a marginal dynamic Karhunen–Loève expansion. The key idea is to integrate individual spectral densities of the MFTS to construct a marginal spectral operator, whose eigenfunctions yield optimal functional filters. These filters transform complex functional observations into a structured multivariate time series representation, providing a powerful foundation for joint modeling and estimation. Through extensive simulation studies, we demonstrate the superior performance of the proposed approach. We further validate its practical utility through an application to the imputation and forecasting of air pollutant concentration trajectories in China.