Papers

We develop a statistical framework for empirical Bayes learning from selectively reported confidence intervals, and apply it to provide context for interpreting results published in MEDLINE abstracts. We use a collection of 326,060 z-scores from MEDLINE abstracts (2000-2018) as the input for an empirical Bayes analysis, with publication bias as a key methodological challenge. We address publication bias through a selective tilting approach that extends empirical Bayes confidence intervals to truncated sampling. Our framework provides coverage guarantees for functionals including posterior estimands describing idealized replications and the symmetrized posterior mean, which we justify decision-theoretically as optimal among sign-equivariant (odd) estimators.

Covariate adjustment is an approach to improve the precision of trial analyses by adjusting for baseline variables that are prognostic of the primary endpoint. Motivated by the SEARCH Universal HIV Test-and-Treat Trial (2013-2017), we tell our story of developing, evaluating, and implementing a machine learning-based approach for covariate adjustment. We provide the rationale for as well as the practical concerns with such an approach for estimating marginal effects. Using schematics, we illustrate our procedure: targeted machine learning estimation (TMLE) with Adaptive Pre-specification. Briefly, sample-splitting is used to data-adaptively select the combination of estimators of the outcome regression (i.e., the conditional expectation of the outcome given the trial arm and covariates) and known propensity score (i.e., the conditional probability of being randomized to the intervention given the covariates) that minimizes the cross-validated variance estimate and, thereby, maximizes empirical efficiency. We discuss our approach for evaluating finite sample performance with parametric and plasmode simulations, pre-specifying the Statistical Analysis Plan, and unblinding in real-time on video conference with our colleagues from around the world. We present the results from applying our approach in the primary, pre-specified analysis of 8 recently published trials (2022-2024). We conclude with practical recommendations and an invitation to implement our approach in the primary analysis of your next trial.

Above the magnitude of completeness - the minimum threshold for which a 100% detection rate is assumed - earthquake magnitudes are typically modeled as a continuous exponential distribution. In practice, however, earthquake catalogs report magnitudes with finite resolution, resulting in a discrete (geometric) distribution. To determine the magnitude of completeness, the Lilliefors test is commonly applied. Because this test assumes continuous data, it is standard practice to add uniform noise to binned magnitudes prior to testing exponentiality. Here we show analytically that uniform dithering does not recover the underlying continuous exponential distribution from its discretized (geometric) form. It instead returns a piecewise-constant residual lifetime distribution, whose deviation from the exponential model becomes detectable as catalog size or bin width increases. Through numerical experiments, we demonstrate that this deviation yields a systematic overestimation of the magnitude of completeness, with biases exceeding one magnitude unit in large, high-resolution catalogs. We derive the exact noise distribution - a truncated exponential within each magnitude bin - that correctly restores the continuous exponential distribution over the whole magnitude range. Numerical tests show that this correction yields Lilliefors rejection probabilities that are consistent with the significance level across a wide range of bin widths and catalog sizes. Although illustrated for the Lilliefors test, the identified bias and the proposed correction are independent of the specific statistical test and apply generally to exponentiality testing of discretized magnitude data.

This paper tackles the problem of feature selection in a highly challenging setting: $\mathbb{E}(y | \boldsymbol{x}) = G(\boldsymbol{x}_{\mathcal{S}_0})$, where $\mathcal{S}_0$ is the set of relevant features and $G$ is an unknown, potentially nonlinear function subject to mild smoothness conditions. Our approach begins with feature selection in deep neural networks, then generalizes the results to Hölder smooth functions by exploiting the strong approximation capabilities of neural networks. Unlike conventional optimization-based deep learning methods, we reformulate neural networks as index models and estimate $\mathcal{S}_0$ using the second-order Stein's formula. This gradient-descent-free strategy guarantees feature selection consistency with a sample size requirement of $n = \Omega(p^2)$, where $p$ is the feature dimension. To handle high-dimensional scenarios, we further introduce a screening-and-selection mechanism that achieves nonlinear selection consistency when $n = \Omega(s \log p)$, with $s$ representing the sparsity level. Additionally, we refit a neural network on the selected features for prediction and establish performance guarantees under a relaxed sparsity assumption. Extensive simulations and real-data analyses demonstrate the strong performance of our method even in the presence of complex feature interactions.

In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a root of a co-coercive operator), a central problem in scientific computing. Our approach leverages both Nesterov's acceleration technique and the Krasnosel'skii-Mann (KM) iteration, while accounting for delayed inexact oracles, a key mechanism in asynchronous algorithms. We also introduce a unified approximate error condition for delayed inexact oracles, which can cover various practical scenarios. Under mild conditions and appropriate parameter updates, we establish both $\mathcal{O}(1/k^2)$ non-asymptotic and $o(1/k^2)$ asymptotic convergence rates in expectation for the squared norm of residual. Our rate significantly improves the $\mathcal{O}(1/k)$ rates in classical KM-type methods, including their asynchronous variants. We also establish $o(1/k^2)$ almost sure convergence rates and the almost sure convergence of iterates to a solution of the problem. Within our framework, we instantiate three settings for the underlying operator: (i) a deterministic universal delayed oracle; (ii) a stochastic delayed oracle; and (iii) a finite-sum structure with asynchronous updates. For each case, we instantiate our framework to obtain a concrete algorithmic variant for which our convergence results still apply, and whose iteration complexity depends linearly on the maximum delay. Finally, we verify our algorithms and theoretical results through two numerical examples on both matrix game and shallow neural network training problems.

Contour location—the process of sequentially training a surrogate model to identify the design inputs that result in a pre-specified response value from a single computer experiment—is a well-studied active learning problem. Here, we tackle a related but distinct problem: identifying the input configuration that returns pre-specified values of multiple computer experiments simultaneously. Motivated by computer experiments of the rotational torques acting upon a vehicle in flight, we aim to identify stable flight conditions that result in zero torque forces. We propose a “joint contour location” (jCL) scheme that strikes a strategic balance between exploring the multiple response surfaces while exploiting learning of the intersecting contours. Rather than working exploration and exploitation into a single acquisition function, we devise two distinct acquisition schemes with a decision rule to choose between the two, which also provides a natural stopping criterion if no solution is present. We employ traditional Gaussian processes (GPs), multitask GPs, and deep GPs, but our jCL procedure is applicable to any surrogate that can provide posterior predictive distributions. Our jCL designs significantly outperform existing (single response) CL strategies, optimization-based alternatives, and previous strategies for targeting joint contours, enabling us to efficiently locate the optimal configurations for our motivating computer experiments.

Statistical learning under distributional drift remains poorly characterized, especially in closed-loop settings where learning alters the data-generating law. We introduce an intrinsic drift budget $C_T$ that quantifies cumulative information-geometric motion of the data distribution along the realized learner-environment trajectory, measured in Fisher-Rao distance. The budget separates exogenous environmental change from policy-sensitive feedback induced by the learner's actions. This gives a rate-based characterization of prequential reproducibility: when performance on the realized stream is used to predict one-step-ahead performance under the next distribution, the drift contribution enters through the average motion rate $C_T/T$, not through cumulative drift alone. We prove a drift-feedback bound of order $T^{-1/2}+C_T/T$, up to controlled second-order remainder terms, and establish a matching sharpness lower bound for the same prequential reproducibility gap on a canonical regular subclass. Thus the dependence on the average Fisher-Rao motion rate is tight up to constants: $C_T/T$ is sufficient for upper control and unavoidable on regular hard subclasses. We further prove an information-theoretic indistinguishability result showing that order-$C/T$ effects on the one-step-ahead target need not be identifiable from the realized performance stream alone. Finally, we show that fixed monitoring channels induce contracted observable Fisher motion, and experiments, including a misspecified real-data feedback setting, indicate that appropriately chosen channels can retain risk-relevant drift signal when the intrinsic data-generating law is unavailable. The resulting theory treats exogenous drift, adaptive data analysis, and performative feedback as different sources of Fisher-Rao motion along the same learner-environment trajectory.

We inspect the deductive connection between the neural scaling law and Zipf's law – two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation model – such as a large language model – changes with respect to the amount of training tokens, parameters, and compute. By contrast, Zipf's law posits that the distribution of tokens exhibits a power law tail. Whereas similar claims have been made in more specific settings, we show that the neural scaling law is a consequence of Zipf's law under certain broad assumptions that we reveal systematically. The derivation steps are as follows: We derive Heaps' law on the vocabulary growth from Zipf's law, Hilberg's hypothesis on the entropy scaling from Heaps' law, and the neural scaling from Hilberg's hypothesis. We illustrate these inference steps by a toy example of the Santa Fe process that satisfies all four statistical laws.

A family of parsimonious ultrametric mixture models with the Manly transformation is developed for clustering high-dimensional data where the clusters may be asymmetric. While advances in Gaussian mixture modeling sufficiently handle high-dimensional data, they often struggle with the common presence of cluster skewness. To address this, we incorporate the extended ultrametric covariance structure and the Manly transformation, resulting in the parsimonious ultrametric Manly mixture model family. The ultrametric covariance structure reduces the number of free parameters while identifying latent groups of variables within a nested hierarchy. This phenomenon enables the visualization of hierarchical relationships within clusters, improving cluster interpretability. Additionally, as with many classes of mixture models, model selection remains a fundamental challenge; to this end, a two-step model selection procedure is proposed herein. Through simulation studies and real data analyses, we demonstrate improved model selection via the proposed two-step method, as well as the effective clustering performance.

Common Method Variance (CMV) is a recurring problem that reduces survey accuracy. Popular fixes such as the Harman single-factor test, correlated uniquenesses, common latent factor models, and marker variable approaches have well known flaws. These approaches either poorly identify issues, rely too heavily on researchers' choices, omit real information, or require special marker items that many datasets lack. This paper introduces a metadata-only Feature-Augmented Method Factor (FAMF-SEM): a single extra method factor with fixed, item-specific weights based on questionnaire details like reverse coding, page and item order, scale width, wording direction, and item length. These weights are set using ridge regression, based on residual correlations in a basic CFA, and remain fixed in the model. The method avoids the need for additional data or marker variables and provides CMV-adjusted results with clear links to survey design features. An AMOS/LISREL-friendly, no-code Excel workflow demonstrates the method. The paper explains the rationale, provides model details, outlines setup, presents step-by-step instructions, describes checks and reliability tests, and notes limitations.

Machine learning models for forecasting solar flares have been trained and evaluated using a variety of data sources, including Space Weather Prediction Center (SWPC) operational and science-quality data. Typically, data from these sources is minimally processed before being used to train and validate a forecasting model. However, predictive performance can be affected if defects and inconsistencies between these data sources are ignored. For a set of commonly used data sources, along with the software that queries and outputs processed data, we identify their defects and inconsistencies, quantify their extent, and show how they can affect predictions from data-driven machine-learning forecasting models. We also outline procedures for fixing these issues or at least mitigating their impacts. Finally, based on thorough comparisons of the effects of data sources on the trained forecasting model's predictive skill scores, we offer recommendations for using different data products in operational forecasting.

While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.

We propose a framework that aligns Conditional Average Treatment Effect (CATE) estimation with profit maximization. Our method recognizes that, for customers with extreme treatment effects, additional estimation accuracy is unlikely to change the recommended actions. In contrast, accuracy is critical near the decision boundary, where treatment effects are close to treatment costs. Our approach optimizes a novel objective function that concentrates learning capacity along this boundary. The proposed objective is Fisher consistent with respect to the original profit function and yields a consistent estimator for CATEs. Theoretically, our framework unifies standard plug-in optimization and direct policy optimization as limiting cases of the same optimization problem. We further show that entropy-regularized policy optimization is a special case of our framework. This result has a direct practical implication: firms can recover consistent CATE estimates from existing profit-maximization pipelines. We use synthetic data to demonstrate how the proposed framework allows firms to explicitly navigate the trade-off between global prediction accuracy and profit maximization.

A common assumption in the spatial analysis of agricultural field trials is stationarity. In practice, however, this assumption is often violated due to unaccounted field effects. For instance, in plant breeding field trials, this can lead to inaccurate estimates of plant performance. Based on such inaccurate estimates, breeders may be impeded in selecting the best performing plant varieties, slowing breeding progress. We propose a method to automatically verify the hypothesis of stationarity. The method is sensitive towards mean as well as variance-covariance nonstationarity. It is specifically developed for the two-dimensional grid-structure of field trials. The method relies on the hypothesis that we can detect nonstationarity by partitioning the field into areas, within which stationarity holds. We applied the method to a large number of simulated datasets and a real-data example. The method reliably points out which trials exhibit quality issues and gives an indication about the severity of nonstationarity. This information can significantly reduce the time spent on manual quality control and enhance its overall reliability. Furthermore, the output of the method can be used to improve the analysis of conducted trials as well as the experimental design of future trials.

This study presents a Bayesian framework for (inverse) uncertainty quantification and parameter estimation in a two-step Chemical Vapor Deposition coating process using production data. We develop an XGBoost surrogate model that maps reactor setup parameters to coating thickness measurements, enabling efficient Bayesian analysis while reducing sampling costs. The methodology handles a mixture of data including continuous, discrete integer, binary, and encoded categorical variables. We establish parameter prior distributions through Bayesian Model Selection and perform Inverse Uncertainty Quantification via weighted Approximate Bayesian Computation with summary statistics, providing robust parameter credible intervals while filtering measurement noise across multiple reactor locations. Furthermore, we employ clustering methods guided by geometry embeddings to focus analysis within homogeneous production groups. This integrated approach provides a validated tool for improving industrial process control under uncertainty.

Explicit "Do not know" responses are treated as missing data, although their accumulation may encode uncertainty. We analysed 502,234 UK Biobank participants to test associations between response uncertainty and incident dementia-related diagnoses. Compared with participants giving 0–1 such responses, those giving more than seven had higher risks of the dementia-related disease composite (hazard ratio 1.62, 95% confidence interval 1.50–1.74), Alzheimer's disease (1.63, 1.48–1.79), and vascular dementia (1.63, 1.42–1.86) after multivariable adjustment. Associations were approximately linear, persisted after a two-year lag, and were directionally reproduced in Scotland and Wales. Polygenic risk scores minimally attenuated these associations. Domain, molecular, and chronic-disease analyses placed response uncertainty within a broader multisystem vulnerability phenotype. Here, we show that explicit response uncertainty provides a scalable behavioural marker of subsequent dementia-related risk.

This paper proposes a parallel-in-time method for computing continuous-time maximum-a-posteriori (MAP) trajectory estimates of the states of partially observed stochastic differential equations (SDEs), with the goal of improving computational speed on parallel architectures. The MAP estimation problem is reformulated as a continuous-time optimal control problem based on the Onsager-Machlup functional. This reformulation enables the use of a previously proposed parallel-in-time solution for optimal control problems, which we adapt to the current problem. The structure of the resulting optimal control problem admits a parallel solution based on parallel associative scan algorithms. In the linear Gaussian special case, it yields a parallel Kalman-Bucy filter and a parallel continuous-time Rauch-Tung-Striebel smoother. These linear computational methods are further extended to nonlinear continuous-time state-space models through Taylor expansions. We also present the corresponding parallel two-filter smoother. The graphics processing unit (GPU) experiments on linear and nonlinear models demonstrate that the proposed framework achieves a significant speedup in computations while maintaining the accuracy of sequential algorithms.

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the number of functional variables is large relative to the length of functional time series, non-asymptotic theory for covariance function estimation has been developed for Gaussian and sub-Gaussian functional linear processes. However, corresponding non-asymptotic results for high-dimensional non-Gaussian and nonlinear functional time series, as well as for spectral density function estimation, are largely unexplored. In this paper, we introduce novel functional dependence measures, based on which we establish systematic non-asymptotic concentration bounds for estimates of (auto)covariance and spectral density functions in high-dimensional and non-Gaussian settings. We then illustrate the usefulness of our convergence results through two applications to dynamic functional principal component analysis and sparse spectral density function estimation. To handle the practical scenario where curves are discretely observed with errors, we further develop convergence rates of the corresponding estimates obtained via a nonparametric smoothing method. Finally, extensive simulation studies are conducted to corroborate our theoretical findings.

Hamiltonian Monte Carlo (HMC) generates efficient Markov transitions by combining Hamiltonian dynamics with a Metropolis correction. This paper develops a geometric \(q\)-analogue of HMC by replacing classical Hamiltonian dynamics with a \(q\)-deformed Hamiltonian system arising from \(q\)-calculus. Starting from a Lagrangian formulation, we derive the corresponding \(q\)-Hamiltonian equations and prove the formal invariance of the associated \(q\)-symplectic form within the \(q\)-deformed differential calculus. To obtain a computable sampler, we introduce a Jackson-derivative realization and construct a Metropolis-corrected \(q\)-HMC algorithm. The proposal reduces to classical HMC as \(q\to1\), while for \(q\neq1\) it replaces ordinary derivatives by \(q\)-Jackson finite differences. We establish detailed balance, which ensures that the resulting Markov transition preserves the target distribution. Numerical experiments examine the computational behavior of the proposed method. For positive-scale black-box targets, the \(q\)-Jackson force has a scale-consistent interpretation: multiplicative perturbations of \(s>0\) correspond to centered finite differences in \(y=\log s\). In such examples, \(q\)-HMC closely tracks log-coordinate finite-difference HMC and the exact-gradient benchmark, whereas raw additive finite differences may produce large force and Hamiltonian errors. These results suggest that the proposed \(q\)-analogue provides a valid HMC-type sampling framework with a visible advantage for positive and multiplicative black-box targets.

Semi-supervised classification leverages both labeled and unlabeled data to improve predictive performance, but existing software support remains fragmented across methods, learning settings, and data modalities. We introduce ModSSC, an open source Python framework for inductive and transductive semi-supervised classification designed to support reproducible and controlled experimentation. ModSSC provides a modular and extensible software architecture centered on reusable semi-supervised learning components, stable abstractions, and fully declarative experiment specification. Experiments are defined through configuration files, enabling systematic comparison across heterogeneous datasets and model backbones without modifying algorithmic code. ModSSC 1.0.0 is released under the MIT license with full documentation and automated tests, and is available at https://github.com/ModSSC/ModSSC. The framework is validated through controlled experiments reproducing established semi-supervised learning baselines across multiple data modalities.

Clinical transfusion-outcomes research faces unique methodological challenges compared with other areas of clinical research. These challenges arise because patients frequently receive multiple transfusions, each unit originates from a different donor, and the probability of receiving specific blood product characteristics is influenced by external, often uncontrollable, factors. These complexities complicate causal inference in observational studies of transfusion effectiveness and safety. This guide addresses key challenges in observational transfusion research, with a focus on time-varying exposure, time-varying confounding, and treatment-confounder feedback. Using the example of donor sex and pregnancy history in relation to recipient mortality, we illustrate the strengths and limitations of commonly used analytical approaches. We compare restriction-based analyses, time-varying Cox regression, and inverse probability weighted marginal structural models using a large observational dataset of male transfusion recipients. In the applied example, restriction and conventional time-varying approaches suggested an increased mortality risk associated with transfusion of red blood cells from ever-pregnant female donors compared with male-only donors (hazard ratio [HR] 1.22; 95% CI 1.05-1.42 and HR 1.21; 95% CI 1.04-1.41, respectively). In contrast, inverse probability of treatment and censoring weighted analyses, which account for treatment-confounder feedback, showed no evidence of an association (HR 1.01; 95% CI 0.85-1.20). These findings demonstrate how conventional methods can yield biased estimates when complex longitudinal structures are not adequately handled. We provide practical guidance on study design, target trial emulation, and the use of g-methods, including a reproducible tutorial and example dataset, to support valid causal inference in clinical transfusion research.

Recent years have witnessed significant advancements in machine learning methods on graphs. However, transferring knowledge effectively from one graph to another remains a critical challenge. This highlights the need for algorithms capable of applying information extracted from a source graph to an unlabeled target graph, a task known as unsupervised graph domain adaptation (GDA). One key difficulty in unsupervised GDA is conditional shift, which hinders transferability. In this paper, we show that conditional shift can be observed only if there exists local dependencies among node features. To support this claim, we perform a rigorous analysis and also further provide generalization bounds of GDA when dependent node features are modeled using markov chains. Guided by the theoretical findings, we propose to improve GDA by decorrelating node features, which can be specifically implemented through decorrelated GCN layers and graph transformer layers. Our experimental results demonstrate the effectiveness of this approach, showing not only substantial performance enhancements over baseline GDA methods but also clear visualizations of small intra-class distances in the learned representations. Our code is available at https://github.com/TechnologyAiGroup/DFT

The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as it runs, the classical theory of SGD provides guarantees only at pre-specified iteration horizons and offers no valid way to decide, based on the observed trajectory, when further computation is justified. We address this longstanding gap by developing anytime-valid confidence sequences for stochastic gradient methods, which remain valid under continuous monitoring and directly induce statistically valid, trajectory-dependent stopping rules: stop as soon as the current upper confidence bound on an appropriate performance measure falls below a user-specified tolerance. The confidence sequences are constructed using nonnegative supermartingales, are time-uniform, and depend only on observable quantities along the SGD trajectory, without requiring prior knowledge of the optimization horizon. In convex optimization, this yields anytime-valid certificates for weighted suboptimality of projected SGD under general stepsize schedules, without assuming smoothness or strong convexity. In nonconvex optimization, it yields time-uniform certificates for weighted first-order stationarity under smoothness assumptions. We further characterize the stopping-time complexity of the resulting stopping rules under standard stepsize schedules. To the best of our knowledge, this is the first framework that provides statistically valid, time-uniform stopping rules for SGD across both convex and nonconvex settings based solely on its observed trajectory.

We develop a unified geometric framework for nonparametric estimation based on the notion of Twin Kernel Spaces, defined as orbits of a reproducing kernel under a group action. This structure induces a family of transported RKHS geometries in which classical orthogonal polynomial estimators, kernel estimators, and spectral smoothing methods arise as projections onto transported eigenfunction systems. Our main contribution is a Spectral Equivariance Theorem showing that the eigenfunctions of any transported kernel are obtained by unitary transport of the base eigenfunctions. As a consequence, orthogonal polynomial estimators are equivariant under geometric deformation, kernel estimators correspond to soft spectral filtering in a twin space, and minimax rates and bias–variance tradeoffs are invariant under transport. We provide examples based on Hermite and Legendre polynomials, affine and Gaussian groups, and illustrate the effectiveness of twin transport for adaptive and multimodal estimation. The framework reveals a deep connection between group actions, RKHS geometry, and spectral nonparametrics, offering a unified perspective that encompasses kernel smoothing, orthogonal series, splines, and multiscale methods.

Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of multi-fidelity strategies that leverage inexpensive low-fidelity information without compromising accuracy. Addressing this challenge, this work presents a multi-fidelity deep learning framework that combines autoencoder-based transfer learning with a newly developed Multi-Split Conformal Prediction (MSCP) strategy to achieve uncertainty-aware aerodynamic data fusion under extreme data scarcity. The methodology leverages abundant Low-Fidelity (LF) data to learn a compact latent physics representation, which acts as a frozen knowledge base for a decoder that is subsequently fine-tuned using scarce HF samples. Tested on surface-pressure distributions for NACA airfoils (2D) and a transonic wing (3D) databases, the model successfully corrects LF deviations and achieves high-accuracy pressure predictions using minimal HF training data. Furthermore, the MSCP framework produces robust, actionable uncertainty bands with pointwise coverage exceeding 95%. By combining extreme data efficiency with uncertainty quantification, this work offers a scalable and reliable solution for aerodynamic regression in data-scarce environments.

We study group-averaged Markov chains obtained by augmenting a $\pi$-stationary kernel $P$ with orbit kernels induced by a group action. We analyse the Gibbs ($G$), Metropolis–Hastings ($M$), and Barker ($B$) kernels, their sandwiches $QPQ$, and mixtures $\tfrac{1}{2}(P+Q)$, where $Q\in\{G,M,B\}$. Under suitable conditions, $M^t$ and $B^t$ converge blockwise to $G$. The projection chains of $GPG$ and $P$ coincide, while every sandwich $QPQ$ has absolute spectral gap no smaller than that of reversible $P$. For $GPG$, we derive an additive asymptotic-variance bound, prove monotonicity for $G$-invariant observables, and identify it as the Kullback–Leibler (KL) information projection of $P$ onto the $G$-invariant kernels. For a fixed orbit partition, the spectral and KL properties of $GPG$ reduce to those of a lower-dimensional orbit-space chain. Among Gibbs projections with a prescribed number of orbits, we identify the partition minimizing KL divergence to stationarity and characterize exact stationarity. Finally, alternating group projections converge at a rate determined by singular values of an overlap matrix and, in structured cases, can yield exact sampling with logarithmically many group actions. These results motivate tuning heuristics and yield polynomial mixing for a Curie–Weiss example in a regime where Glauber dynamics is exponentially slow.

While short-term models such as the Short-Term Earthquake Probability (STEP) and Epidemic-Type Aftershock Sequence (ETAS) are well established and supported by open-source software, medium- to long-term models, notably the Every Earthquake a Precursor According to Scale (EEPAS) and Proximity to Past Earthquakes (PPE), remain under-documented and largely inaccessible. Despite outperforming time-invariant models in regional studies, their mathematical foundations are often insufficiently formalized. This study addresses these gaps by formally deriving the EEPAS and PPE models within the framework of inhomogeneous Poisson point processes and clarifying the connection between empirical $\Psi$-scaling regressions and likelihood-based inference. We introduce a fully automated, open-source Python implementation of EEPAS that combines analytical modeling with Numba JIT acceleration, NumPy vectorization, and joblib parallelization, all configured via modular JSON files for usability and reproducibility. Integration with pyCSEP enables standardized evaluation and comparison. When applied to the Italy HORUS dataset, our system reproduces published results within one hour using identical initialization settings. It also provides a comprehensive pipeline from raw catalog to parameter estimation, achieving improved log-likelihoods and passing strict consistency tests without manual $\Psi$ identification. We position our framework as part of a growing open-source ecosystem for seismological research that spans the full workflow from data acquisition to forecast evaluation. Our framework fills a key gap in this ecosystem by providing robust tools for medium- to long-term statistical modeling of earthquake catalogs, which is an essential but underserved component in probabilistic seismic forecasting.

Out-of-distribution (OOD) detection is essential for determining when a supervised model encounters inputs that differ meaningfully from its training distribution. While widely studied in classification, OOD detection for regression and survival analysis remains limited due to the absence of discrete labels and the challenge of quantifying predictive uncertainty. We introduce a framework for OOD detection that is simultaneously model aware and subspace aware, and that embeds variable prioritization directly into the detection step. The method uses the fitted predictor to construct localized neighborhoods around each test case that emphasize the features driving the model's learned relationship and downweight directions that are less relevant to prediction. It produces OOD scores without relying on global distance metrics or estimating the full feature density. The framework is applicable across outcome types, and in our implementation we use random forests, where the rule structure yields transparent neighborhoods and effective scoring. Experiments on synthetic and real data benchmarks designed to isolate functional shifts show consistent improvements over existing methods. We further demonstrate the approach in an esophageal cancer survival study, where distribution shifts related to lymphadenectomy identify patterns relevant to surgical guidelines.

Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the latent subpopulation distributions may be unrealistic, which motivates the need for nonparametric modeling of the mixture components themselves. In this paper, we study finite mixtures with nonparametric mixture components, using a Bayesian nonparametric modeling approach. In particular, it is assumed that the data population is generated according to a finite mixture of latent component distributions, where each component is endowed with a Bayesian nonparametric prior such as the Dirichlet process mixture. We present conditions under which the individual mixture component's distribution can be identified, and establish posterior contraction behavior for the data population's density, as well as densities of the latent mixture components. We develop an efficient MCMC algorithm for posterior inference and demonstrate via simulation studies and real-world data illustrations that it is possible to efficiently learn complex forms of probability distribution for the latent subpopulations. In theory, the posterior contraction rate of the component densities is nearly polynomial, which is a significant improvement over the logarithmic convergence rates of estimating mixing measures via deconvolution.

While joint pruning–quantization is theoretically superior to sequential application, current joint methods rely on auxiliary procedures outside the training loop for finding compression parameters. This reliance adds engineering complexity and hyperparameter tuning, while also lacking a direct data-driven gradient signal, which might result in sub-optimal compression. In this paper, we introduce CoDeQ, a simple, fully differentiable method for joint pruning–quantization. Our approach builds on a key observation: the dead-zone of a scalar quantizer is equivalent to magnitude pruning, and can be used to induce sparsity directly within the quantization operator. Concretely, we parameterize the dead-zone width and learn it via backpropagation, alongside the quantization parameters. This design provides explicit control of sparsity, regularized by a single global hyperparameter, while decoupling sparsity selection from bit-width selection. The result is a method for Compression with Dead-zone Quantizer (CoDeQ) that supports both fixed-precision and mixed-precision quantization (controlled by an optional second hyperparameter). It simultaneously determines the sparsity pattern and quantization parameters in a single end-to-end optimization. Consequently, CoDeQ does not require any auxiliary procedures, making the method architecture-agnostic and straightforward to implement. On ImageNet with ResNet-18, CoDeQ reduces bit operations to ~5% while maintaining close to full precision accuracy in both fixed and mixed-precision regimes.