Papers

Model choice in backward Q-learning is recursive because a later-stage choice changes the response supplied to an earlier regression and can alter its model-comparison statistic. Separate stagewise criteria do not directly assess the target-stage prediction risk of a completed Q-learning fit. We address this mismatch by treating the entire backward-fitting rule as the unit of comparison and propose feedback-aware soft tuning for sequential multiple assignment randomised trials. Each backward fit uses its own generated responses and is assessed at a common prediction target. The risk criterion retains downstream effects on upstream comparisons, while a separate correction accounts for estimating the final exponential weights from the same observations. For a fixed finite library of smooth recursive maps, we establish an exact risk identity under a Gaussian shift model and an oracle inequality with an explicit adaptation remainder. Under coordinate-representation and moment conditions, these guarantees transfer to prediction risk at any prespecified stage, with the number of stages fixed as sample size increases. A two-stage construction supplies an explicit observable implementation. Numerical studies examine risk estimation and finite-sample performance, and a simulated attention-deficit/hyperactivity-disorder trial illustrates the relation between comparison feedback and treatment recommendations.

In this work, we provide a new perspective on semiparametric efficiency theory. In particular, we reformulate the questions of optimal efficiency and its attainment as a variational problem: minimize variance over estimating functions subject to robust unbiasedness constraints. We develop this theory for marginal-integral functionals without requiring pathwise differentiability. We study estimating functions whose expectations remain equal to the target when any one specified nuisance component is misspecified and the others are correct. We characterize the infimum of their variances through conditional variance minimization. For maxima of affine functions of treatment-specific conditional means, we obtain explicit optimal weights and construct cross-fitted estimators that attain the bound under conditions on nuisance estimation and the probability of near ties. For analogous maxima based on jointly observed quantities, the optimal weights use the full conditional covariance matrix. We also identify conditions under which the variance bound agrees with a classical convolution bound for parametric perturbations that preserve ties to first order. Examples include optimal policy values, $L^1$ calibration error, Balke–Pearl bounds, and mediation parameters. In an application to the National Longitudinal Survey of Young Men, covariance weighting reduces the median estimated variance of the cross-fitted estimating function relative to equal weighting by 12.9% for the lower Balke–Pearl endpoint and 16.5% for the upper, with improvements in all 20 repeated cross-fitting splits.

We estimate the scale of an exponential lifetime from observations censored randomly from both sides, under an informative model in which each censoring law is a power of the lifetime survival function – a two-sided generalization of the Koziol–Green proportional hazards model. Substituting the empirical distribution function into the likelihood equation yields a closed-form pseudo-maximum-likelihood estimator of the scale that is computed in one pass over the order statistics and needs neither iteration nor numerical optimization. A digamma identity shows the estimating equation to be exactly, not merely asymptotically, Fisher-consistent. Strong consistency and asymptotic normality are established with no restriction on the censoring depth; the key is an identity that rewrites the underlying $L$-statistic without its unbounded score function and so removes the condition that classical limit theorems would impose. The influence function and the asymptotic variance are explicit in polygamma functions, so confidence intervals require no numerical integration. Against the information bound of the observed-data model the efficiency exceeds $98.6\%$ in the designs considered and stays above $96.2\%$ over a wide sweep. Only the entry half of the model is needed: the estimator remains exactly Fisher-consistent and strongly consistent whatever the right-censoring law, and exponentiality is shown to be the precise price of that freedom. The construction extends verbatim to a proportional hazards class with known baseline. Three data sets illustrate the procedure, including a cohort in which left censoring is genuine.

We establish the stochastic-gradient query complexity of sampling smooth strongly log-concave distributions in every fixed dimension $d\geq1$. For $\mu$-strongly convex, $L$-smooth potentials with unknown minimizers $x_f^\star$ in the ball $\mathbb{B}(0,\mu^{-1/2})$, and unbiased gradient oracles with variance at most $\sigma^2$, the minimax worst-case expected query complexity is $\Theta\left(\log(1+\kappa)+\frac{\sigma^2}{\mu\varepsilon}\right)$, jointly optimal for the condition number $\kappa:=L/\mu$, variance $\sigma^2\ge 0$, and TV accuracy $0<\varepsilon\leq 1/10$. In the noiseless setting $\sigma=0$, this tight complexity $\Theta\left(\log(1+\kappa)\right)$ is independent of $\varepsilon$. Moreover, a gradient-only sampler generates an exact sample with ${O}(\log(1+\kappa))$ worst-case expected queries. Without previous ball $\mathbb{B}(0,\mu^{-1/2})$, exact sampling from any initial point $x_0$ can be implemented with expected cost ${O}\left(\log(1+\kappa)+\log(1+\sqrt{\mu}\|x_0-x_f^\star\|)\right)$, without knowing the initial distance. We also show that dependence on initial distance is generally unavoidable.

This note presents new findings on the distribution of the volume and surface area of both the Poisson polyhedron and the Crofton polyhedron. It also considers the distribution of the area of the Poisson polygon and the Crofton polygon in the plane. This note motivates the modeling of the distributions of these convex body functionals as mixture distributions and the essential inclusion of the generalized gamma distribution therein as mixture components. Finally, model parameters are estimated and models are selected based on extensive stochastic simulations of these random polytopes. This includes that for the first time, this note gives very accurate estimates of the side number probabilities for both the Poisson polyhedron and the Crofton polyhedron, as these are used as mixing weights in the distribution models.

In many settings involving stochastic differential equations, including in diffusion based generative AI, our aim is to accurately generate samples from a terminal distribution. Typically, this is done by generating i.i.d. samples of diffusion paths. Given a fixed simulation budget, a reasonable way to gain efficiency may be to instead generate a tree of paths through appropriately split partial paths. This suggests improved performance, but one worries about the injected dependence. In this paper, we study this issue comprehensively. With Kolmogorov-Smirnov distance as a measure of accuracy, we identify the limiting errors of the associated empirical distributions as the simulation budget increases to infinity. We characterize a splitting strategy motivated by a corresponding asymptotic optimization problem. The theoretical results bring out the elegant underlying structure in the problem. Practical implementation involves two phases, an initial estimation phase and a final inference phase. Overall, we observe a 10-25% improvement in mean error over i.i.d. samples in many settings. In an exploratory CIFAR-10 study, our method reduces the maximum mean discrepancy by 8-13%.

When reconstructing the hidden state of a partial differential equation (PDE) system from partial observations, aggregate prediction error measures performance on a given data distribution but does not reveal how strongly the observations constrain each predicted direction. We introduce UniPDE-Bench, a direction-wise evaluation protocol that incorporates local observation geometry into state-estimation assessment, providing a reference for prediction recovery and confidence-based selection that is independent of the estimator. The protocol whitens the joint observation Jacobian by the noise covariance and normalizes it by a state metric. Its complete right singular basis represents joint variations of the state, which a relative sensitivity threshold partitions into retained and below-threshold directions. In this common basis, the protocol evaluates recovery and the agreement between prediction claims and the geometric partition, while recovery and abstention curves describe confidence-based selection at different claim coverages. In the simulated tasks and observation configurations studied here, confidence rules whose overall ranking exceeds chance can still exhibit below-random abstention on below-threshold directions at some high claim coverages. By separating empirical recovery from direction-selection quality, the protocol relates prediction performance to local observation sensitivity and provides an evaluation of partially observed state estimators beyond aggregate error.

Generalized Poisson matrix factorization (GPMF) is a matrix factorization method for count data with overdispersion based on the generalized Poisson distribution. While GPMF provides point estimates of the model parameters through maximum likelihood estimation, it does not quantify estimation uncertainty. In this paper, we propose a Bayesian extension of GPMF, referred to as Bayesian GPMF, and develop a Gibbs sampler for posterior inference. The proposed method is based on a compound Poisson representation of the generalized Poisson distribution, which introduces latent variables and yields closed-form full conditional posterior distributions for all model parameters. To efficiently sample the overdispersion parameter, we derive an infinite mixture representation of the exponentially tilted beta (EBeta) distribution and develop a finite approximation based on this representation. Simulation studies demonstrate that the proposed Bayesian GPMF achieves smaller mean squared errors than the conventional GPMF while providing credible intervals with empirical coverage probabilities close to the nominal level. Furthermore, the proposed finite approximation attains estimation accuracy comparable to Sampling/Importance Resampling (SIR) while requiring less computation. An application to football event data further illustrates the usefulness of Bayesian GPMF for extracting interpretable latent structures and quantifying estimation uncertainty. These results demonstrate that the proposed framework provides an effective Bayesian approach to generalized Poisson matrix factorization.

We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schrödinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller–still a linear state feedback–can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.

Community detection in bipartite networks is a fundamental problem in modern data analysis, with applications in recommendation systems, biological networks, and social network analysis. Unlike conventional unipartite graphs, bipartite networks consist of two distinct types of nodes with edges only connecting across types, so recovering latent communities requires estimating labels on the two node types. The stochastic co-blockmodel is a classical probabilistic framework for such networks, yet theoretical guarantees for exact community recovery in this setting remain limited, especially when the number of communities grows, the community sizes are unbalanced, or the degrees are heterogeneous. In this work, we prove that a simple spectral clustering algorithm based on the diagonal-deleted Gram matrix achieves exact recovery with high probability under mild conditions on sparsity, community balance, and the number of clusters. We further extend the result to the degree-corrected stochastic co-blockmodel, where each node carries its own degree heterogeneity parameter, and show that a row-normalized version of the same algorithm maintains the exact recovery guarantee. Extensive experiments validate our theoretical findings.

Even with a fixed dataset and research question, data analysis involves many defensible decisions. Understanding how these choices influence the results is scientifically important but remains challenging. Crowdsourcing and agentic AI can generate hundreds of end-to-end analyses, but scaling generation alone can create a processing bottleneck and an analytic “black hole.” A common workaround is to impose a shared fixed decision taxonomy, which can limit insight and understate uncertainty. We present ForkSCOPE, a human-AI collaboration framework that induces structure bottom-up from the code corpus of end-to-end analyses, without a taxonomy fixed before or after generation, so the organization and evaluation of the garden can scale with the corpus. ForkSCOPE surfaces the charted garden of forking paths through a human-AI collaboration pipeline and an evidence-linked interactive viewer for steering and verification: it spotlights organically identified forks and structures and produces a derived taxonomy and decision map compatible with existing multiverse tools.

We study an online sketched Newton method that approximates the Newton direction at each step via a state-of-the-art sketching solver, called the generalized accelerated sketch-and-project solver (GAS), thereby mitigating the computational bottleneck of classical second-order methods. The GAS solver improves upon vanilla, unaccelerated sketch-and-project solvers by achieving accelerated convergence through Nesterov momentum updates, and accommodates a flexible projection metric whose proper choice further reduces computational cost. Building on this design, we establish asymptotic normality of the averaged sketched Newton iterates and characterize their limiting covariance matrix. The resulting covariance recovers that of the unaccelerated sketched Newton method under a specific choice of acceleration parameters, converges more rapidly (in the number of sketching steps) to the minimax-optimal covariance in general, and is smaller than that of the last iterate produced by the accelerated method. Finally, we strengthen these results by establishing a functional central limit theorem for the Newton iterates, which allows us to bypass explicit covariance estimation and develop an online inference procedure based on random scaling. Specifically, we construct a pivotal test statistic by appropriately rescaling the averaged iterates, so that its limiting distribution is free of any unknown parameters, enabling asymptotically valid online inference. Numerical experiments demonstrate superior performance of the proposed inference procedure.

Dementia is a major and growing global health burden, with Alzheimer's disease (AD) accounting for most cases. Timely and accurate diagnosis is central to managing this burden and increasingly depends on integrating complementary clinical and imaging information. Multimodal deep learning can combine these modalities for AD diagnosis, but how its explanations behave across modalities, fusion strategies, and cohorts remains unclear. We developed an explainable multimodal framework pairing a 3D CNN encoder for T1-weighted MRI with a feedforward network for harmonized clinical and demographic data, comparing varied model setups on three-way and pairwise diagnostic tasks using 6,479 internal records from the ADNI and 1,703 independent records from the OASIS-3. On ADNI, the tabular-only model achieved the highest three-class AUC-ROC of 0.879 and best discriminated cognitively normal (CN) versus mild cognitive impairment (MCI; 0.903), while cross-attention performed best for MCI versus AD (0.861); CN versus AD was highly discriminative overall. On OASIS-3, the vision-only model performed best (three-class AUC-ROC 0.910); CN versus MCI remained difficult, and no fusion strategy consistently outperformed single modalities across tasks and cohorts. SHAP and Integrated Gradients identified the MMSE as the dominant tabular feature in both cohorts, with global feature rankings agreeing strongly in ADNI ($\rho=0.94$) and OASIS-3 ($\rho=0.96$); CAM-based explanations, however, changed with model configuration and cohort. These findings show that multimodal performance and explanations are task, modality, fusion, and cohort-dependent: a dominant cognitive signal persisted across cohorts, but feature contributions and CAM explanations did not, underscoring the need to evaluate explainability under cohort shift rather than as a stable, intrinsic property.

ReaxFF is a molecular dynamics method that can be considered a good approximation to quantum methods for investigating reactive molecular systems consisting of ten thousand to one hundred thousand atoms. While ReaxFF is usually a much faster alternative to quantum methods, the force field consists of nearly 100 parameters per element, which makes the force field development a high dimensional optimization problem. In addition to the high-dimensionality, non-convexity and non-continuity make it a hard problem to optimize. We use random optimization along with coordinate search strategies to optimize efficiently and sample new parameter points that yield good molecular properties close to predefined `reference values' obtained from quantum mechanical methods for the $\mathrm{Mo-S}$ system. We also provide empirical error guaranties starting from any random sample of inputs. We discover new points for the $\mathrm{Mo-S}$ system at adjusted error levels of $13{,}000$ as compared to Sengul et al. (2022) at $70{,}000$ levels under the same loss function, registering over $80\%$ improvement. We also extend our algorithm to an out-of-sample system, $\mathrm{W-S}$, with no training data to record over $70\%$ improvement over Sengul et al. (2021).

Masked Diffusion Models (MDMs) have emerged as a compelling paradigm for language modeling, offering the capability for efficient parallel text generation. However, existing parallel sampling methods typically update multiple masked tokens independently and ignore the complex mutual dependencies among the masked tokens. This independent updating mechanism lacks global coordination and might lead to incoherent outputs. To address this limitation, we propose Representation-based Masked Diffusion Model (RMDM), a framework that leverages the text representation to explicitly encode global semantics and help to parallel update tokens more precisely. Specifically, we first encode text into a continuous semantic space using a pretrained encoder and learn an invertible transformation that normalizes the representation distribution to a Gaussian prior, facilitating efficient sampling during generation. Conditioned on this latent semantic representation, we train a masked diffusion model to learn the conditional text distribution, where the representation serves as global semantic guidance to coordinate parallel token updates and faithfully approximate the target distribution. Empirical results demonstrate that RMDM significantly improves generation quality, particularly in aggressive few-step sampling regimes.

History-based risk factors, such as known family history, recorded personal history, and documented regional history, are often treated as covariates. Because these variables depend on testing, diagnosis, and recording, their observed values are influenced by detection. However, monitoring data are often unavailable, making it difficult to distinguish true history effects from detection-driven associations. We study the feedback loop that arises when observed history affects future monitoring and future monitoring affects which histories become observed. Prostate cancer screening serves as a case in point: knowing a family history may raise awareness and increase testing compared with having no known history. We develop Markov models for true and observed history states and show that differential detection can distort both observed risk ratios and the distribution of the observed history variable, and can create an apparent history effect even when true event risk does not depend on history. With history-dependent true risk, the observed history process is generally not Markovian, although the joint true-observed process is. Uniform incomplete detection can attenuate true history effects by shifting individuals with missed events into less recent observed-history states. We also develop an inverse sensitivity-analysis framework that combines a published observed association, a baseline event probability, and plausible detection probabilities to obtain the implied true risk contrast. Numerical analyses illustrate the distortions, and a prostate cancer family-history example demonstrates the sensitivity calculation using external calibration values. The framework is intended for registry, electronic health record, and surveillance studies that use documented history as a risk factor.

Membership inference attacks (MIAs) are the standard tool for auditing the privacy risks of machine learning models. Given a query point, an MIA aims to determine whether that point was used to train the target model. In practice, such inference must rely on the statistical signals exposed by the model's outputs, such as confidence scores, logits, and intermediate feature representations. However, existing methods often fail to efficiently summarize and combine these statistical signals. To address this limitation, we propose Pairwise Likelihood MIA (PL-MIA), a unified method that combines a Gaussian likelihood-ratio (GLR) statistic with population calibration and the Cauchy combination test. We characterize theoretically how the GLR retains variance-contraction signals and establish conditions under which population calibration and Cauchy combination improve attack power. We obtain $p$-values from pairwise comparisons between the query point and reference points not used for training, and aggregate these continuous signals using the Cauchy combination test. This preserves the evidence strength that is discarded when each pairwise comparison is reduced to a binary vote. Extensive experiments demonstrate that PL-MIA outperforms strong baselines, improving the true positive rate (TPR) by over 25% in the critical low-false-positive regime, corroborating our theoretical findings. These results demonstrate how statistical principles can turn noisy model outputs into more powerful, calibrated, and reproducible evidence for membership privacy auditing.

We study the problem of estimating unknown parameters in PDE-constrained inverse problems from noisy observations, where the PDE solution is approximated using Physics-Informed Neural Networks (PINNs). While PINNs have demonstrated remarkable empirical success, existing estimators often inherit the slow nonparametric convergence rate of the neural-network solution, leading to biased and statistically inefficient inference for the finite-dimensional parameters of interest. To address this, we propose a two-step debiased estimation procedure that combines neural-network-based nonparametric estimation with an influence-function-based bias correction. By eliminating the first-order sensitivity of the estimator to errors in the nuisance function, our procedure yields a $\sqrt{n}$-consistent and asymptotically normal estimator without requiring undersmoothing of the neural network component. We further extend this framework to Bayesian inference by replacing the original likelihood with a debiased quasi-likelihood and establish a Bernstein-von Mises theorem showing that the resulting posterior contracts at the $\sqrt{n}$-rate with an asymptotic covariance matching that of the frequentist estimator. As a by-product of our analysis, we establish near-minimax optimal convergence rates for estimating a nonparametric regression function and its derivatives in Sobolev spaces using neural networks. Extensive numerical experiments corroborate our theoretical findings and demonstrate the necessity of the proposed debiasing procedure for valid statistical inference in PDE-constrained inverse problems.

Sampling error affects the finite-sample values of residual-based fit indices. We show that the unweighted comparative fit index ($CFI_u$) rests on a quadratic-kernel maximum mean discrepancy and that a Gaussian-kernel comparative fit index (KCFI) converges to $CFI_u$ as bandwidth increases. Because kernel discrepancies lack an analytic sampling correction, we extend expected-discrepancy bootstrap methods to a fitted-correlation reference state: the sample is transformed to reproduce the fitted correlation matrix, then resampled and refitted to estimate the exact-fit sampling component. Across 18 confirmatory factor analysis conditions, this correction reduced the root mean square error (RMSE) of both indices by 62%-87%. Under normality it matched an analytic residual-covariance estimator of $CFI_u$ within .0001, and in small samples it outperformed ordinary bootstrap correction in accuracy and availability. Corrected KCFI had lower RMSE than identically corrected $CFI_u$ in all 29 nonnormal conditions, even against a common target, but in six heavy-tailed small-sample conditions the analytic estimator was more accurate than both. The results validate the reference-state correction where it is needed and delimit where the analytic estimator is preferable.

We study estimation of a linear functional in random-design linear models when $\gamma=p/n \in (1, \infty)$ under the dense regime where the design covariance is unknown, and neither the regression vector nor the precision matrix is assumed sparse. Suppose the spectrum of the design covariance belongs to $[\ell,L]$, we establish the minimax mean squared rate for the linear functional has the order $n^{-\alpha(\kappa,\gamma)}$, where the exponent $\alpha(\kappa,\gamma)$ has an explicit elliptic-integral representation and $\alpha(\kappa,\gamma) < 1$ when both $\kappa > 1$ and $\gamma > 1$. We propose the Bocca estimator, which combines empirically calibrated resolvents through a complex contour integral to attain the optimal rate.

This paper develops a theorem-level pipeline in symmetry-quotient settings: quotient linear stability implies quotient flatness, quotient flatness implies input smoothness, and input smoothness yields generalization under local covering assumptions. Flatness is often associated with generalization, and Stochastic Gradient Descent (SGD) is frequently viewed as implicitly biased toward flat solutions. However, standard flatness measures are typically defined in the raw parameter space and are therefore not invariant under function-preserving symmetries such as positive rescaling. We develop a symmetry-aware theory of quotient flatness, quotient linear stability, input smoothness, and generalization on quotient spaces of neural-network parameters. For square loss and models equipped with function-preserving group actions, we define quotient flatness as the trace of the Hessian of the empirical loss on the regular quotient manifold. We show that quotient flatness controls input smoothness through a quotient-space analogue of the flatness-to-smoothness argument. We also prove that one-step mean-square quotient linear stability of the linearized SGD dynamics implies an explicit quotient-flatness bound in terms of the batch size and learning rate, and extend this analysis to higher-order tensor moments. Finally, under local covering and boundedness assumptions, we derive population generalization bounds in terms of quotient flatness and, consequently, in terms of quotient linear stability.

Large language models (LLMs) are proposed as synthetic respondents for pilot testing, but their usefulness depends on whether they supply the evidence assessment development requires. We calibrated rating scale models on 14 digital-use skill items from 6,245 adults and used the human item parameters to evaluate responses generated for 1,300 demographically matched personas. LLM responses had high internal consistency ($\alpha \approx .94$) but used the lowest category in 0.2-0.3% of responses versus 13.7-21.5% for humans, and no persona chose it on every item. These gaps changed the response-category judgment on both subscales and the PC targeting judgment; on the human-calibrated scales, 12 of 14 items had infit below 0.70, indicating responses more predictable than the Rasch model expects. Preregistered changes to the prompt, category order, and persona information did not restore the human lower range. High internal consistency is insufficient evidence that LLM responses can replace human pilot data.

Understanding how the brain's cortical regions respond to stimuli like fingertip tapping is a significant challenge in neuroscience, especially with high-resolution functional magnetic resonance imaging data. To address this, we propose a new statistical method for evaluating how a factor's influence locally varies across a complex graph, such as the brain's cortex. Our approach is designed to handle the complexities of large graph sizes and computational demands. Our method uses a novel Bayesian hidden Markov random field to partition the factor's influence into collapsed states with similar effects on the outcome at each node. This unique model promotes sparsity in the partitions and penalizes large variations across adjacent nodes. The result is a highly detailed local influence map that captures subtle changes in the patterns and magnitudes of a factor's influence across the graph. To ensure efficient analysis of large datasets, we developed a specialized Markov chain Monte Carlo algorithm. Our simulation experiments demonstrate significant improvements over existing techniques in both accuracy and scalability. Ultimately, our method provides a powerful new framework for exploring the intricate relationship between stimuli and brain activity, offering a clearer picture of the cortical mapping of fingertips.

One method of generalizing a distribution is to add new parameter to the baseline distribution. In this paper the author discusses this methodology to create a new six parameters generalized Weibull-Kumaraswamy-{Lomax) Distribution. The author utilizes the approach of the T-X{Y} family to add new parameters the baseline distribution Kumaraswamy distribution defined on the unit interval with two shape parameters a & b>0. The author used the Lomax distribution with two parameters {\alpha} & {\lambda}>0 , scale and shape parameters respectively, to link the baseline distribution with the generator distribution. The generator distribution is the Weibull distribution with the two parameters, c & {\gamma}>0 , shape and scale parameters respectively as will be explained in the paper. The result is a new distribution with six parameters. The author derived the PDF, CDF, and quantile functions. The author used a new technique to expand the pdf in a linear series expansion that is simple and does not require special function. This makes the computational statistics for the raw moments easier and simpler. The author discusses the Shannon entropy and the paper contains figures for the PDF, CDF and the quantile functions.

Medical image classification is frequently complicated by transitional categories whose feature distributions overlap those of adjacent classes, producing ambiguous decision boundaries. Conformal prediction returns uncertainty-aware prediction sets, but these are not directly actionable in clinical screening, where a single decision is required. This work proposes adaptive conformal redistribution (AdaConRed), a label-free post-conformal decision rule that converts ambiguous prediction sets into refined class assignments. A five-stage pipeline is developed. Vision-language generative augmentation addresses minority-class scarcity; a frozen DermFoundation encoder provides embeddings; a lightweight multi-layer perceptron performs classification; an entropy-modulated, margin-aware nonconformity score constructs adaptive prediction sets; samples predicted as transitional with multi-label sets are reassigned to the most probable alternative class within the set, using only model outputs at inference. Evaluation uses the OSCC oral lesion and ISIC skin lesion benchmarks at a miscoverage level of 0.2. On the 3-class OSCC benchmark, overall accuracy improves from 73.54% to 77.38%, with oral cancer accuracy rising from 64.29% to 82.14% and benign accuracy from 56.57% to 70.20%. Reassignment of transitional samples reduces OPMD accuracy from 84.78% to 80.16%, consistent with the asymmetric cost of missed malignancy. On ISIC, overall accuracy improves from 85.83% to 87.19%, melanoma accuracy rising from 66.04% to 68.34%. AdaConRed outperforms LAC, APS and RAPS under an identical backbone and redistribution rule. Conformal prediction can be extended beyond uncertainty quantification toward actionable decision support where transitional disease categories are present, with gains concentrated in the clinically critical malignant categories. Code repository: https://github.com/saibal436ghosh/AdaConRed.

Identification in vector autoregressions involves two distinct choices: how extensively to orthogonalize shocks and whether orthogonality is imposed sequentially or simultaneously. Generalized identification imposes no orthogonality; Sims (1980} imposes full orthogonality sequentially; Francis et al. (2026) impose full orthogonality simultaneously; and Buchwalter et al. (2026a) provide clustered partial orthogonalization sequentially. We fill the remaining case by developing simultaneous clustered orthogonalization (SCO). SCO preserves contemporaneous dependence within economically meaningful clusters while imposing orthogonality across clusters jointly, thereby eliminating dependence on cluster ordering. We formulate the associated correlation-maximizing identification problem and show that, in correlation space, it reduces to a quadratic matrix equation. This yields a closed-form solution, and we prove that the associated identification matrix is the unique global maximizer. SCO is order- and scale-invariant and nests generalized identification and full simultaneous orthogonalization as special cases, yielding a flexible family of structural decompositions indexed by the number and composition of clusters.

We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the data. Second, the log-determinant objective carries an additive ridge regularization: it removes the endpoint boundary layers, so no trimming of the candidate set is required, and tuning the ridge weakens the consistency condition. As an application of the main theorem, we establish consistency of QML breakpoint estimation in pervasive factor models whose dimension diverges with the sample size, for completely general error terms – not necessarily independent, idiosyncratic, or even random.

Inference-time power sampling via Sequential Monte Carlo (SMC) can substantially improve large language model (LLM) reasoning without requiring post-training. However, many existing SMC approaches rely on equal-weight resampling, which can aggressively prune low-weight trajectories, discarding potentially correct reasoning paths and degrading the genealogical diversity of the search space. To address this, we introduce Chopthin-Consensus Power Sampling (CCPS). Our method applies the Chopthin resampler to LLM decoding: rather than equalizing weights and forcing unnecessary particle duplication, it enforces an upper bound on the ratio between the largest and smallest weights and carries the unequal weights forward. This targeted intervention preserves a richer set of distinct reasoning paths, keeps the weighted SMC approximation unchanged in conditional expectation, and guarantees a lower bound on the post-resampling effective sample size (ESS). To fully exploit this enriched population, we employ a semantic-majority selection mechanism that merges token-identical final trajectories, clusters semantically equivalent answers, and returns the answer supported by the largest number of distinct trajectories. Evaluating across three open-weight models and five reasoning benchmarks, we show that Chopthin increases oracle coverage in 13 of 15 settings. Combined with semantic-majority selection, CCPS matches or exceeds the final-answer accuracy of the Power-SMC baseline in 14 of 15 settings, delivering absolute gains of up to 10.6 percentage points. These findings demonstrate that diversity-preserving resampling and diversity-aware selection are complementary mechanisms for training-free LLM reasoning. Code is available at github.com/MinooAhmadii/chopthin-consensus-power-sampling.

In this work we consider numerical models with random input parameters, where the model output is a spatially distributed random field. We carry out a statistical sensitivity analysis of spatial sets which arise for instance when the model output exceeds a critical threshold. We consider two approaches: (i) a kernel-based sensitivity analysis working with the Hilbert–Schmidt Independence Criterion, and (ii) a function-valued sensitivity analysis working with generalized Sobol' indices, where the model output is the indicator function of the spatial set of interest. We develop efficient estimators for the sensitivity indices, especially for finite-element-based numerical models, where we approximate volume integrals in the sensitivity measures by finite element quadrature, thereby avoiding Monte Carlo sampling over the spatial domain. This improves the state-of-the-art for the kernel-based indices and makes these methods practically accessible for expensive numerical models. For the generalized Sobol' indices we utilize the same finite element quadrature for efficient computation. We present numerical experiments for a hydrogen combustion process, modeled by a coupled system of convection-diffusion-reaction equations in a two-dimensional spatial domain, and ask whether the temperature remains below a critical value in selected regions of the combustion domain. Our results show that in this example the kernel-based and the generalized Sobol' indices give qualitatively similar input importance rankings. Moreover, the ranking depends on the chosen observation window and can flip between different windows. The algorithms for implementing the proposed methods are provided in the supplementary materials and in an open source code repository.

The Lehmer transform of a positive signal is the ratio of its power sums at consecutive orders, read as a function of the order, and it is a strictly increasing analytic curve from the smallest observation to the largest. Composing this curve with a map whose inverse is the Lambert function turns it into a probability law on the real line, the Lehmer-Lambert distribution, which we introduce and study. Its distribution, density and quantile functions are closed-form, its random variates are exact, and the law is invariant under changes of gain and of power-law calibration of the signal. Its modes lie at orders at which the signal changes scale, and for a sample its tails are exponential with rates equal to the two extreme logarithmic gaps of the sample. We derive moments, generating functions and limit theorems, and we investigate applications of the Lehmer-Lambert distribution in the analysis of electroencephalograms of patients with major depressive disorder.