Papers

Transport MCMC trains a normalizing flow to precondition Metropolis–Hastings proposals, achieving high empirical efficiency on challenging posteriors; yet no prior work produces a numerically non-vacuous, rigorous spectral-gap bound for such samplers. We establish the first such bounds. For independence MH on the banana family we certify (\gamma^\ast = 0.828) at (D = 2) (covering in the original space) and (\gamma^\ast \ge 7.6\times 10^{-4}) at (D = 5) (covering in an analytically unwarped Gaussian space with a grid-certified gradient bound under the stated numerical Lipschitz certification), both rigorous at 95% confidence. The framework rests on three pillars: (i) spectral normalization with reduced scale clips constrains the flow Lipschitz constant from (10^{47}) to (10^4); (ii) a coverage-based empirical oscillation bound replaces the vacuous analytical bound with a data-dependent certificate; and (iii) oscillation-regularised training cuts the empirical oscillation by 60–90% at no cost to density fit, extending practical certificates through (D = 20) ((\gamma^\ast \ge 1.7\times 10^{-4})). Tests on four further targets (Gaussian mixture, shear-building, Neal's funnel, Bayesian logistic regression) identify three precise barriers: boundary curvature, target stiffness, and tail-coverage mismatch. An affine-vs-spline comparison shows that simpler architectures yield tighter certificates at identical NLL, inverting the usual expressiveness hierarchy.

Deploying an LLM judge panel spends human labels on fitting a calibrator, constructing candidate judge paths, and validating which candidate to deploy. We study when finite labels should support a low-dimensional stacker or reliability model, and when an unrestricted joint output table is worth its cell-count and unseen-pattern cost. We cast this as a finite-calibration regime map and instantiate it as Finite-Calibration Panel Selection (FCPS), a validation selector over judge path, deployed panel size, and aggregator family with support diagnostics. Across RewardBench, LLMBar, SummEval, and Arena100K with a seven-judge pool, scalar/reliability aggregation has lower MSE than unrestricted joint-table calibration in 16 of 20 real dataset–budget cells by point estimate, while paired 95% intervals exclude zero in 11 cells; richer backoff/shrinkage tables narrow some gaps while preserving the finite-support bottleneck. Controlled calibration-growth data show the opposite regime: when labels contain a six-way interaction, the selected table grows to the interaction-bearing prefix and its MSE falls from 0.224 to 0.061 once unseen mass vanishes. The practical deployment question is whether the next judge's information is estimable under the available human labels.

This paper studies conditional independence testing under the Gaussian additive noise model (GANM), where two variables are modeled as nonlinear functions of covariates with independent bivariate Gaussian regression errors. Under this framework, conditional independence can be characterized by the correlation coefficient of the regression errors, which motivates a test based on the Pearson correlation coefficient computed from the fitted residuals. Despite its simple form, the asymptotic behavior and statistical efficiency of the resulting test have not been well understood. In this paper, we develop the semiparametric efficiency theory under GANM and show, surprisingly, that the efficient estimator coincides exactly with the ordinary residual Pearson correlation estimator. We further establish the asymptotic properties of the proposed test and develop the corresponding inference procedure. Simulation studies demonstrate that the proposed method achieves near-oracle efficiency and competitive empirical power while maintaining valid Type I error control. We further apply the proposed test to conditional dependence analysis of U.S. stock returns.

Engression is a recently proposed and effective framework for conditional distribution learning. Its multi-step Reverse Markov extension further improves generative flexibility by decomposing complex conditional sampling into sequential reverse transitions. Despite their strong empirical performance, rigorous finite-sample statistical guarantees for these methods remain unavailable. In this paper, under deep neural network parameterizations, we establish nonasymptotic convergence bounds for Engression by directly controlling the Energy Distance between the learned and target conditional distributions. For the Reverse Markov framework, we further develop an Energy-Distance-based chain rule that enables a rigorous analysis of error propagation across reverse steps. Our analysis yields corresponding excess-risk bounds that are near-optimal up to logarithmic factors relative to the classical minimax rate over a general Hölder class.

We study linear contextual bandits under rare parameter updates: the learner may incorporate reward feedback into its parameter estimate only at a small number of update times, while still observing contexts online and selecting actions sequentially. This viewpoint clarifies a practical distinction that is often blurred in the literature: many "strictly batched" methods additionally restrict within-interval context adaptivity, meaning that the action rule inside an interval cannot depend on the sequence of realized contexts/actions in that interval (beyond the current round's context). For linear contextual bandits, we propose two practical algorithms with only $O(\log\log T)$ parameter updates. Our first algorithm BLCE-G attains minimax-optimal regret (up to polylogarithmic factors in $T$) simultaneously in both the small-$K$ and large-$K$ regimes under a static schedule. Our second algorithm BLCE removes the near G-optimal design step – a dominant computational bottleneck in prior strictly batched static-grid methods – yet preserves minimax-optimal regret and achieves the lowest known runtime complexity among optimal algorithms. We further extend these rare-update and computational principles to generalized linear contextual bandits. Overall, our results yield minimax-optimal algorithms for linear contextual bandits and a near-optimal generalized-linear extension under $O(\log\log T)$ parameter updates, while remaining computationally efficient in practice.

We study design-based causal inference for edge-level outcomes in directed networks under dyadic interference. In this setting, outcomes are defined on directed edges and depend on the joint treatment assignments of pairs of units, inducing a complex dependence structure that invalidates standard estimation and inference procedures developed for node-level data. We construct Horvitz–Thompson estimators for a general class of edge-level causal effects and establish their asymptotic normality under mild regularity conditions. To enable valid inference, we develop variance estimators that exploit identifiable components of network dependence, yielding substantially less conservative bounds than classical approaches. To improve efficiency, we incorporate auxiliary covariates through a sample splitting and cross-fitting procedure. A key technical challenge is that standard two-fold sample splitting fails in the presence of edge-level outcomes due to the dependence induced by shared units. To address this issue, we introduce a three-fold sample splitting and cross-fitting scheme that restores the conditional independence required for unbiased estimation. Under a stability condition, the resulting covariate-adjusted estimator is asymptotically normal and accommodates both linear adjustment and flexible machine learning methods. We further introduce a calibration step that guarantees no asymptotic efficiency loss relative to the unadjusted estimator. Simulation studies and a real-data application confirm the theoretical results and demonstrate substantial efficiency gains.

Network data are ubiquitous across the social sciences, biology, and information systems. Generating realistic synthetic network data has broad applications from network simulation to scientific discovery. However, many existing black-box approaches for network generation tend to overfit observed data while overlooking characteristic network structure, and incur substantial computational overhead at scale. These practical challenges call for synthetic network generation methods that are both efficient and capable of capturing structural properties of networks. In this paper, we introduce Synthetic Network Generation via Latent Embedding Reconstruction (SyNGLER), a general and efficient framework for synthetic network generation that builds on latent space network models. Given an observed network, SyNGLER first learns low-dimensional latent node embeddings via a latent space network model and then reconstructs the latent space by building a distribution-free generator over these embeddings. For generation, SyNGLER first samples (or resamples) node embeddings from the generator in the latent space and then produces synthetic networks using the latent space network model. Through the latent space framework, SyNGLER preserves unique characteristics in networks such as sparsity and node degree heterogeneity, while allowing for efficient training with lower computational cost than many existing deep architectures. We provide theoretical guarantees by developing consistency results on the distance between the true and synthetic edge distributions. Empirical studies further demonstrate the effectiveness of SyNGLER, which efficiently produces networks that better preserve key network characteristics such as network moments and degree distributions compared with existing approaches. Code is available at https://github.com/FeifanJiang/syngler.

Assessing structural performance under seismic hazard requires accounting for both damage accumulation and post-event recovery. In current performance-based earthquake engineering (PBEE), recovery is generally treated as a post-processing attribute, while structural performance is modeled using Poissonian exceedance assumptions that imply renewability and memorylessness. These assumptions hinder a unified treatment of reliability and resilience under repeated seismic loading. This study proposes a generalized PBEE framework in which damage and recovery are embedded directly into the system dynamics through a continuous-time Markov chain. A single generator matrix governs state-dependent transitions, providing a unified description of structural reliability and resilience while remaining compatible with standard PBEE metrics. Time-dependent failure probabilities and reliability indices are derived from the transient system dynamics, whereas resilience is quantified through the expected fraction of operational time before collapse. The framework exploits the spectral properties of the generator matrix to compute both metrics efficiently and transparently. The methodology is illustrated on a three-state example and applied to two structural archetypes: a braced frame and a base-isolated system. Results show that recovery dynamics can strongly affect long-term resilience even when conventional reliability measures exhibit limited sensitivity, emphasizing the need to explicitly account for recovery in life-cycle seismic performance assessment.

Real-world datasets across image and text domains are often characterized by skewed class distributions and noisy annotations, which jointly degrade model performance, particularly on minority classes. Among existing solutions, active learning offers an effective and efficient paradigm by selectively querying the most informative and balanced samples for annotation. We propose an innovative active learning framework that mitigates class imbalance and selects the most informative samples to annotate. Leveraging foundation model priors, our algorithm enables imbalance-aware co-decisions between foundation model and small model to tackle noisy and imbalanced labels across various domains. We introduce the first study to systematically explore active learning under the dual challenges of label noise and class imbalance across image and text domains. Extensive experiments on imbalanced datasets demonstrate that our method achieves substantial annotation savings-over 50% compared to the best active learning baseline-while preserving performance and robustness to label noise.

Accurate passenger queue forecasting in airport terminals is essential for efficient departure operations, as it enables proactive congestion management. However, time-varying passenger demand and heterogeneous facility usage across multiple departure facilities make forecasting challenging. In this work, we propose a passenger queue forecasting framework that learns historical passenger flow patterns from operational data. The proposed model employs a Transformer-based architecture to capture temporal dependencies and inter-facility correlations using past queue length and waiting time at departure gates and security checkpoints, together with passenger throughput at check-in islands. The learned representations are mapped to two facility-specific prediction heads to predict queue length and waiting time at departure gates and security checkpoints. Experimental results demonstrate accurate forecasts up to two hours ahead. The proposed approach offers practical real-time decision support for proactive queue management and staff reallocation in airport terminal operations.

Modern Machine Learning (ML) and Artificial Intelligence (AI) models, especially large language models (LLMs), are increasingly used to generate scientific hypotheses and mechanistic explanations from observational data. This position paper argues that in the high-dimensional proxy regimes where modern ML excels, mechanistic learning is generically underdetermined: many incompatible mechanisms induce essentially the same observational relationships on the support of the data, so predictive success and coherent explanations are insufficient evidence of mechanism discovery. This underdetermination becomes uniquely hazardous with large language models (LLMs), which tend to collapse large equivalence classes of explanations into a single fluent narrative. This paper proposes concrete standards for “mechanistic ML,” and argues these norms are necessary if LLM-centered workflows are to support science rather than merely simulate it.

Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge. After deploying bandits, a natural question is whether one can construct a confidence interval for its mean reward and assess whether it reliably outperforms a baseline policy. The total reward achieved in any single bandit deployment is random, and deploying a bandit twice on the same population typically yields different reward trajectories due to stochastic rewards. Standard statistical inference methods cannot be used because bandit algorithms introduce complex dependencies in the collected data, which violate the i.i.d. assumption underlying many classical approaches. Moreover, existing inference methods for adaptively collected data only apply to estimands that do not depend on the data-collection algorithm (such as the mean reward under a fixed action). We propose Bandit Simulation for Inference (BSI), a framework that fits a simulator of the bandit environment from observed data–either on-policy or off-policy–and uses it to estimate the mean reward under any evaluation policy, including adaptive blackbox algorithms. BSI formally propagates uncertainty in the estimated simulator parameters into the confidence interval construction. Furthermore, for BSI to be valid, it requires only weak exploration assumptions on the behavior policy and avoids importance weighting. We prove that BSI yields asymptotically valid confidence intervals, and demonstrate empirically that it maintains nominal coverage in settings where standard off-policy evaluation methods fail.

Randomized controlled trials (RCTs) and person-level observational studies feature prominently in debates over social media harms. I highlight some under-acknowledged limitations of such evidence. Most important is that published RCTs typically identify effects of a local, or small-scale, intervention: a person is assigned to quit social media, but her immediate peers continue using it in large numbers. Critics of social media, in contrast, focus on a global, or large-scale, intervention: the mass adoption of social media among U.S. teenagers. Such global interventions alter both the proximal social environment and the broader culture, potentially harming teenagers who abstain from social media entirely. This paper discusses the local–global distinction at length and offers other notes on the limits of learning about social media harms from existing RCTs and person-level observational studies. I suggest that triangulating different forms of imperfect evidence may provide the deepest insights about social media's aggregate effect on teen mental health.

Testing simple or composite hypothesis on a functional parameter has attracted considerable attention in time series analysis. To accommodate for the unknown temporal dependence, classical nonparametric approaches such as block bootstrapping and subsampling all involve a bandwidth parameter, the choice of which can substantially affect the finite sample performance. The self normalization (SN) method is tuning parameter free when applied to the inference of a finite-dimensional parameter but its applicability to a functional parameter is unknown. In this paper, we propose a sample splitting based approach to generalize the SN method to hypothesis testing of a functional parameter. Our SS-SN (sample splitting plus self-normalization) idea is broadly applicable to many testing problems for functional parameters, including testing for simple/composite hypothesis on marginal cumulative distribution function, testing for time-reversibility and testing for a change point on the spectral distribution of a multivariate time series. Specifically, we derive the pivotal limiting distributions of our SS-SN test statistics under the null for both simple and composite null hypothesis, and derive the limiting power function under the local alternatives. Numerical simulations show that our new tests tend to yield accurate size with competitive power performance as compared to many existing ones.

Confirmatory adaptive designs were introduced more than 30 years ago and enable for example sample size re-assessments and the selection of treatments, endpoints as well as subpopulations during the course of a clinical trial. Recently, sequential tests based on e-values for an anytime-valid inference have been developed, promising seemingly similar or even more flexibility and utility. In this note, we compare these two independently developed concepts, shedding light on their formal and methodological connections and differences. Specifically, we show that adaptive design tools like conditional error functions and combination tests are formally equivalent to e-value based, anytime-valid sequential tests. However, in spite of their common fundamental intention to bring flexibility into statistical inference, they have quite different emphases: While hypothesis testing with combination tests and conditional error function usually intent to exhaust type I error rates under the offered flexibility, e-value based testing aims on the additional flexibility with regard to optional continuation, the chosen level and, in recent extensions, in the loss functions to be controlled. We also indicate how recent e-value achievements could enrich clinical trial methodology and adaptive design methodology could inspire and improve e-value based testing.

Recent publications have suggested using the Shap- ley value for sensor anomaly/attack localization. We study the performance of such an approach by using mathematically de- fined optimum binary classifiers in the Shapley value calculation. To judge localization performance, we study the ability of the Shapley value of a given sensor observation to determine if that observation is anomalous. First, we prove that for cases with independent sensor observations, an optimized anomaly test using the Shapley value is equivalent to an optimized lower-complexity anomaly test using a single term in the Shapley value calculation, yielding the exact same probability of error. For some popular dependent observation cases involving two sensors, including correlated bivariate Gaussian/Laplacian probability density functions and constant/Gaussian at- tacks/anomalies, we prove that these two tests are fundamentally different, yielding different decision regions and error probabil- ities. Further, we prove that the Shapley value test is sometimes strictly inferior to the other (single term in Shapley calculation) test in certain statistically dependent bivariate Gaussian scenarios with large correlation magnitude and additive attacks/anomalies, while it is strictly superior in others, depending on the sign of the correlation. One can combine these two approaches to obtain a strictly better approach in these cases. These results, which provide the first theoretical statistical analysis of Shapley-based localization, seem very interesting based on the wide acceptance of the Shapley value by many researchers and should encourage further research on this topic. Numerical results are provided which illustrate our findings.

The bandwidth-free tests/inferences for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional HAC-based approaches, where consistent long run variance estimation was involved. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter and the magnitude of temporal dependence are moderate, making them unreliable to use in practice. In this paper, we propose a sample splitting based approach to reduce the dimension of the parameter to one for the subsequent bandwidth-free inference. Our SS-SN (sample splitting plus self-normalization) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, linear hypotheses testing in a time series regression model and testing for a change point in multivariate mean. Specifically, we propose $L_{\infty}$-type and $L_2$-type SS-SN test statistics and derive their limiting distributions under both the null and alternatives and show their effectiveness in alleviating size distortion via simulations. As an important theoretical contribution, we obtain the limiting distributions for both SS-SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge as sample size grows to infinity. In addition we show the asymptotic independence of $L_{\infty}$-type and $L_2$-type SS-SN test statistics under the null in the growing dimensional setting.

This article is concerned with change point detection for object-valued data that reside in a metric space, which has attracted some recent interests in statistics and econometrics literature. The existing methods either focus on independent data or can only detect change in the Fréchet mean or variance. In this paper, we propose a self-normalization (SN, hereafter) based statistic for detecting a shift in the marginal distribution of object-valued time series. Our test is universally applicable to a wide range of object-valued data, such as distributional and network data, and can accommodate weak serial dependence. In addition the proposed test statistic is almost tuning parameter free, has pivotal limiting null distribution and only uses the pairwise distances. When combined with the Wild Binary Segmentation algorithm (WBS, hereafter), our statistic can be used to estimate the number and locations of multiple change points. Asymptotic results for our SN based statistic are derived under both null and local alternatives in the single change point setting. For the first time, the WBS estimation consistency is shown for a broad class of object-valued time series and in a nonparametric setting, which requires new non-standard theoretical arguments. Extensive numerical experiments and real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method.

Partial identification provides informative causal guarantees when point identification is impossible, but existing approaches based on optimal transport (OT) become computationally and statistically intractable in high-dimensional settings. This limitation is particularly severe when both potential outcomes and confounders are high-dimensional, where classical OT-based bounds suffer from the curse of dimensionality and unfavorable convergence rates. To address this challenge, we propose a novel estimator that decomposes the transport problem into a low-dimensional signal subspace and a high-dimensional residual subspace. Unlike existing projection-based methods that discard residual information, we recover the residual transport energy using the Sliced Wasserstein distance, which is computationally efficient and robust to high dimensions. We establish interpretable conditions controlling the approximation gap based on residual structure and provide a data-driven rule for signal dimension selection. Empirical results show that our estimator consistently outperforms projection-only baselines by recovering lost transport energy, yielding more informative causal bounds while remaining computationally tractable in high dimensions.

In this work, we study the problem of testing the marginal distributions of multiple independent, sequentially observed data streams, where for each stream there are multiple candidate hypotheses to select from, in the presence of prior information on the unknown hypothesis configuration. The goal is to understand the benefit of such information and to design a sequential testing procedure that effectively leverages it. We start with arbitrary prior information and specialize to concrete examples, including known number or known lower bound on the number of streams following each hypothesis, and the presence of exclusive hypotheses. The designed procedure is three-fold: (i) reliable, i.e., controlling all types of familywise error probabilities below arbitrary user-specified levels, (ii) computationally efficient, i.e., focusing on minimal sets of alternative hypothesis configurations in making decisions, and (iii) asymptotically optimal, i.e., achieving the minimum expected sample size among all reliable procedures asymptotically as the error levels go to zero. Numerical studies are presented for illustration.

Accurate malaria forecasting remains a major challenge in sub-Saharan Africa, where strong seasonality, reporting uncertainty, and non-stationary transmission dynamics reduce the reliability of conventional models. In Ghana, district-level malaria surveillance requires forecasting frameworks that are probabilistically rigorous and robust under limited data. This study proposes a hybrid framework integrating Gaussian Process Regression (GPR) with Holt-Winters exponential smoothing for modelling monthly under-five malaria admissions. GPR captures non-linear behaviour and predictive uncertainty, while Holt-Winters stabilises long-horizon forecasts and preserves seasonal structure. Using ten years of district-level data (2014-2023), performance was evaluated via rolling-origin expanding-window validation. The hybrid model achieved $R^2 = 0.9906$ versus $0.8213$ for Holt-Winters alone, with $94.2\%$ of residuals within $\pm 2\sigma$ bounds. Forecasts for 2024-2028 project average monthly admissions from approximately 8{,}000 to 12{,}200 cases. Spatio-temporal analysis revealed pronounced ecological heterogeneity: northern high-burden districts exhibited stable relative patterns despite large absolute fluctuations. The framework provides a scalable probabilistic approach for malaria early warning and operational planning in endemic settings, supporting Ghana's national malaria control strategy.

Population-level heterogeneity is ubiquitous in biomedical data, where differences across demographic or clinical subgroups can substantially alter risk patterns. For example, in intensive care unit (ICU) studies, the mortality risk associated with specific admission diagnoses can vary across ethnic groups. Existing approaches for detecting risk heterogeneity are often sensitive to baseline model misspecification and regularization bias, both of which commonly arise in practice. In this paper, we propose a robust framework for inferring risk heterogeneity between two populations using Neyman orthogonality, which yields estimators that are locally insensitive to nuisance parameter estimation error. The proposed estimator is consistent and asymptotically normal, and simulation studies demonstrate that in finite samples our method substantially reduces bias and improves inferential stability compared with standard likelihood-based approaches. In an application to the eICU Collaborative Research Database, our method reveals clinically meaningful ethnicity-specific heterogeneity in admission diagnoses for in-hospital mortality that standard likelihood-based methods fail to detect.

Reliable quantification of malaria dynamics in sub-Saharan Africa is hindered by short, noisy, and spatially heterogeneous surveillance records. In Ghana, health-facility data from 2014 to 2023 reveal non-linear and age-specific fluctuations in hospital admissions, yet existing approaches struggle to capture stochastic variability or provide credible uncertainty bounds. This study develops a Bayesian nonlinear inference framework that integrates a cubic baseline with a damped oscillatory kernel, estimated via an affine-invariant ensemble Markov Chain Monte Carlo sampler. The framework accommodates limited data, models parameter uncertainty, and generates probabilistic forecasts for children under five years and individuals aged five years or more. Results show strong empirical adequacy ($R^2 = 0.9958$ for $<5$ years; $R^2 = 0.9956$ for $\geq 5$ years) with residual errors below $2\%$ and well-mixed posteriors confirming convergence. District-level analysis reveals pronounced spatial heterogeneity, with coefficients of variation ranging from $<0.07$ in urban centres such as Kumasi to $>3.3$ in peripheral districts such as Mpohor and Bia East. Forecasts for 2024-2026 indicate a gradual resurgence: from 137,000 to 149,000 cases among children under five years and from 348,000 to 375,000 cases among older individuals, with uncertainty widening over time. By producing probabilistic forecasts, this Bayesian framework provides a principled tool for anticipating malaria fluctuations and strengthening data-driven decision-making in Ghana's national malaria control strategy.

Accurate decomposition of methanol maser spectra is essential for understanding high-mass star-forming regions, especially in complex blended spectra where small differences alter physical interpretation. Conventional Gaussian fitting often fails to capture non-Gaussian structure and lacks uncertainty quantification. We develop a Bayesian spectral decomposition framework using Gaussian, Lorentzian, and Voigt profiles with Markov Chain Monte Carlo sampling, enabling model comparison and uncertainty estimation. Applied to the 6.7\,GHz methanol maser G339.884$-$1.259 observed with the Ghana Radio Astronomy Observatory, our method reveals seven velocity-coherent components. The Voigt model is statistically preferred, yielding the lowest AIC and BIC ($\approx 1.98 \times 10^{4}$ and $1.99 \times 10^{4}$), the smallest RMSE ($\approx 11.1$ Jy), and the highest $R^{2}$ (0.985). Purely Gaussian or Lorentzian models leave systematic residuals. Elevated reduced $\chi^{2}_{\nu}$ values indicate unresolved substructure and non-ideal noise. Bayesian inference provides a robust framework for maser spectral analysis, extendable to other molecular lines and combinable with high-resolution interferometry.

Resting-state fMRI (rs-fMRI) is widely used to investigate brain functional connectivity, but the reliability of these measurements remains a key concern for ensuring reproducibility. The distance-based intraclass correlation coefficient (dbICC) generalizes classical ICC to more general data types, making it well-suited for assessing the reliability of measures of functional connectivity. In this study, we applied dbICC to assess the reliability of rs-fMRI data from the Midnight Scanning Club (MSC) dataset, which consists of 10 subjects, each undergoing 10 sessions of 30-minute rs-fMRI scans. The functional connectivity was estimated using Pearson's correlation coefficients between all pairs of brain regions, resulting in a correlation matrix for each session. We compared two distance metrics-the widely used Frobenius metric and the Affine Invariant Riemannian Metric (AIRM) selected to respect the geometry of the space of covariance matrices-to evaluate how the choice of metric affects the reliability of estimating correlation. In addition, we investigated the impact of scan length and time interval between sessions on reliability. Results based on each metric agreed in some respects but disagreed in others, illustrating the impact of choice of metric. We also found that longer scan lengths significantly improve reliability, while the time interval between sessions has less impact.

In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.

We study the full density ratio between a specified intervention regime $P_a$ and an observational regime $P_0$, $\rho_a=dP_a/dP_0$, under the prerequisite $P_a\ll P_0$. We call the regime-indexed ratio a causal density function when $P_a$ is an identified or directly observed interventional law. The underlying Radon-Nikodym derivative and the identity $ \mathbb{E}_{a}[f(Z)] = \mathbb{E}_{0}\!\left[f(Z)\rho_a(Z)\right] $ are classical importance weighting, not new identification results. Our narrower question is whether retaining the entire pointwise ratio is useful as a reusable diagnostic across several downstream functionals. We evaluate a two-density plug-in baseline through held-out moment transport and overlap stress tests on synthetic and perturbation data. We also report a pairwise graph-scoring heuristic as a negative result: its F1 is \(0.10\) on a synthetic DAG, \(0.12\) on Sachs, and \(0.33\) on a multi-regime chain. These experiments do not establish an estimation advantage over direct density-ratio, inverse-probability, Riesz, or doubly robust methods; they instead delimit what the pointwise ratio target and the present plug-in estimator do and do not provide.

Transistor scaling is approaching a quantum-mechanical limit, as thin gate oxides induce electron leakage through quantum tunneling. Unlike conventional digital systems, AI inference can tolerate such errors provided their structure is modeled correctly. In this paper, we introduce quantum tunneling-aware machine learning (QTAML). We derive the deployment-time weight-error distribution from first principles using the Wentzel-Kramers-Brillouin (WKB) approximation and show that it has structure that generic Gaussian noise models miss: an exact affine mean drift, a per-bit variance hierarchy dominated by the most-significant bit, and a per-layer dependence on $\|W_\ell\|_\infty$ and the trained-network Jacobian. We package these three structural properties into a single deployment-time algorithm, Tunneling-Aware Compensation (TAC), that combines closed-form mean correction with an optimal layer-adaptive bit-budget allocation derived from the WKB variance decomposition. Across four convolutional architectures at $p_\mathrm{flip}$=0.10 and a transformer encoder at $p_\mathrm{flip}$=0.05, TAC reaches $95\%$ of clean accuracy with 3.4$\times$ to 33.6$\times$ less ECC overhead than Uniform-MSP, the natural baseline derived from the same physics. The closed-form saturation ratio $\rho^*$ predicts these gains in advance, and on heterogeneous architectures WKB-derived scoring outperforms magnitude-based allocation by up to 24 percentage points at small budgets. The algorithm requires no retraining, no labels, and no inference-time overhead. We also verify the WKB-derived distributional theorems to Monte Carlo precision. These results connect WKB tunneling physics with noise-aware deep learning and suggest a principled path toward hardware–software co-design beyond conventional scaling limits.

Uncertainty quantification is essential in high-stakes machine learning tasks. However, one of the principled solutions, conformal prediction, faces challenges under limited local calibration data, privacy constraints, and data heterogeneity. In multi-agent settings, existing works do not simultaneously and satisfactorily address these challenges with guarantees either limited to averages across agents or losing validity in heterogeneous settings. Hence, we propose personalized federated weighted conformal prediction (PFWCP), a framework that combines local density ratio weighting with weighted quantile aggregation to correct for heterogeneity while preserving privacy. The method yields asymptotically valid marginal and calibration-conditional coverage guarantees for each participating agent and supports protocols with one-shot communication. Theoretical analysis presents an adjustment to the coverage variance, governed by an effective sample size expression, which is necessary in the context of weighted conformal prediction, and experiments on synthetic and real datasets show improved calibration quality over state-of-the-art federated conformal baselines.

We study boundary detection for unlabeled noisy images from a statistical perspective. The aim is to recover an unknown object region from raw intensity observations without pixel-wise annotating labels or a parametric model for the intensity distributions. Motivated by robust Gibbs posterior approaches based on thresholded misclassification losses, we propose a continuous hinge-type surrogate loss for boundary detection. The proposed loss is amenable to gradient-based optimization and can be combined with deep neural networks to represent complex object boundaries. We prove that the proposed loss function is Fisher consistent under a mild separation assumption and obtain a calibration inequality linking excess surrogate risk to the symmetric difference error of the estimated region. Under a piecewise smooth boundary model, we prove that the resulting deep neural network estimator achieves the minimax-optimal boundary recovery rate, up to logarithmic factors. The piecewise smooth formulation accommodates boundaries with corners and kinks, thereby extending beyond globally smooth boundary models. Numerical experiments demonstrate that the proposed method accurately and stably recovers object boundaries across a range of noise levels and shape configurations, and compares favorably with existing unsupervised boundary detection methods.