Papers

Survey responses on socially undesirable behaviors, such as self-reported spousal violence, are often subject to underreporting due to social stigma, fear of retaliation, and other reporting pressures. When such data are analyzed using standard econometric models that focus on conditional means, such as probit and logit models, the resulting estimates are likely to be biased and can obscure heterogeneity in covariate effects. To address these challenges, we propose a Bayesian binary quantile regression framework that accounts for misclassification and provides quantile-specific effects for the latent true response. The framework incorporates false-negative and false-positive probabilities to capture reporting errors and employs a novel partially collapsed Gibbs sampler for estimation. We also discuss the computation of covariate effects and marginal likelihood for Bayesian model comparison. Simulation studies under various settings (prior effective sample size, misclassification rates, and prior distribution) show that accounting for misclassification improves inference across quantiles relative to models that ignore reporting errors. We apply the framework to women's self-reported spousal violence and find that underreporting of spousal violence exceeds overreporting across quantiles, while model comparisons using marginal likelihood generally favor the quantile model with misclassification and yield different conclusions about the determinants of reported violence.

We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=\mu_\ast(\mathsf c_t)+\xi_t$, with an unknown utility map $\mu_\ast$ and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map $u\mapsto p^\ast(u)$ induced by the scalar index $u=\mu_\ast(\mathsf c)$ and the noise tail. Under the $\beta$-Hölder smoothness of the tail function for $\beta\geq 2$ and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself $(\beta-1)$-smooth. We exploit such structure through $\mathsf{ORBIT}$, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model $\mu_\ast(\mathsf c)=\mathsf c^\top\theta_\ast$, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret $\widetilde{O}\big(T^{\frac{2\beta-1}{4\beta-3}}+\sqrt{dT}\big)$. For fixed $d$, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Hölder utility.

We develop a model of choice over social norms that allows for complementarities along two dimensions: technological, analogous to complementarities between consumption goods, and social, capturing returns from conformity. Together, these determine whether two norms are complements, substitutes, or independent, as defined by how the equilibrium prevalence of one norm responds to a marginal shift in the utility of another. We estimate the model using repeated cross-sections from Sierra Leone and Nigeria, focusing on female genital cutting, polygyny, and child marriage. Social returns are significant across all specifications. For female genital cutting and child marriage, we find evidence of complementarities, especially strong in Sierra Leone. For polygyny and child marriage, we find evidence of social substitutability, particularly in Nigeria. We interpret these differences using insights from anthropology. Finally, we iterate the model forward to study policy counterfactuals, assessing the potential effects of legal reforms and social interventions.

Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $\phi$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $\phi$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.

Joint-embedding predictive architectures (JEPAs) propose that a model should learn more useful abstractions when trained to predict latent representations rather than observed outputs. For autoregressive language-model fine-tuning the principle entails a stricter requirement: the induced hidden-state geometry must reach the language-model head and improve the decoded task metric. We test that requirement under a fixed Llama-3.2-1B-Instruct LoRA harness on natural-language-to-regex generation, comparing twenty-two training-time auxiliaries across trajectory-shape regularisation, distributional constraints, predictor/target asymmetry, Fisher-metric Jacobi residuals, and a decoder-visible JEPA objective constructed to lie in cross-entropy's positive cone. The empirical answer is a structured null: several auxiliaries clear single-cell paired $\alpha = 0.10$ without correction (T3-Local at $\Delta = +2.53$~pp, $p = 0.003$ being the strongest), but none survives Bonferroni or Holm–Bonferroni at the relevant family-wise threshold, even though many change curvature, anisotropy, variance, and gradient direction. Decoder-visible JEPA yields the first positive auxiliary–cross-entropy gradient cosine in the study, yet exact match remains inside seed noise; a full-fine-tuning replication of the same auxiliary at $n = 5$ seeds reproduces the null on both benchmarks (TURK: $\Delta = +0.04$~pp, $p_{\text{paired}} = 0.96$; SYNTH: $\Delta = +0.52$~pp, $p_{\text{paired}} = 0.28$), so the null is robust across LoRA and full fine-tuning for the decoder-visible construction. Hidden-state representation work and decoded-task accuracy are therefore weakly coupled in this regime; we accordingly reframe LLM-domain JEPA evaluation as a coupling problem, in which the operative question is under which metrics useful hidden geometry becomes decoder-visible task signal.

The average treatment effect can obscure important heterogeneity when individuals respond differently to a treatment. While the conditional average treatment effect (CATE) function captures such heterogeneity, it is difficult to communicate when it depends on many covariates. Sublevels sets of a multivariate CATE function are equally complicated objects, but the probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a univariate monotone curve appears which can be used to visualize the overall type and degree of heterogeneity in a population. We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model. To address this nonstandard estimation problem, we leverage recent advances in monotone function estimation and develop a Grenander-type estimator that incorporates machine learning. We also show that the best piecewise linear approximation to the curve of interest is a pathwise differentiable parameter, and we develop a debiased machine learning estimator of this approximation. We investigate our proposed estimators' finite sample performance in a sequence of numerical studies based on data synthesized from a randomized trial. The methods are illustrated in data from a randomized trial on diabetes medication.

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive importance sampling provides a natural localization tool: its evolving proposal distribution progressively identifies the failure-relevant region. Motivated by this observation, we propose a surrogate-assisted adaptive importance sampling framework that refines the surrogate locally along the evolving proposal, rather than over the entire input space. The surrogate combines an encoder with a neural network, providing a low-dimensional latent representation for both prediction and sample selection. At each adaptive iteration, candidates drawn from the current proposal are selected by a greedy latent-space rule balancing proximity to the estimated failure boundary and sample diversity. The selected samples are evaluated by the high-fidelity model and used to refine the surrogate, which then guides the subsequent cross-entropy-type adaptive proposal update. We establish one-step proposal stability bounds under local surrogate errors, together with surrogate-induced misclassification and finite-sample estimation error bounds. Numerical experiments on multimodal benchmarks and PDE-driven rare-event problems up to 100 dimensions show that the proposed method achieves accuracy comparable to true-model adaptive importance sampling while requiring substantially fewer high-fidelity evaluations.

Data augmentation is widely recognized for improving generalization in deep networks, yet its impact on the geometry of learned representations remains poorly understood. In this work, we characterize how different data augmentation strategies reshape internal representations in neural networks. Using tools from shape analysis, we embed network hidden representations into a metric space where distance is invariant to scaling, translation, rotation and reflection. We show that increasing augmentation strength leads to well-behaved trajectories in this space, and that different augmentation types steer representations in distinct directions. Moreover, we investigate how neural representation shapes are distorted along data augmentation trajectories, and show that insights from neural geometry can predict which representations provide the most improvement when ensembling models. Our results reveal shared geometric patterns across architectures and seeds, and suggest that analyzing shape-space trajectories offers a principled tool for understanding and comparing data augmentation methods.

Interval-censored data arise frequently in scientific studies, where the event of interest is known only to occur within a specific time interval. In such studies, functional covariates taking the form of continuous curves or spatial profiles are increasingly encountered, and it is of substantial scientific relevance to investigate how the trajectory of a functional covariate affects the event time. We formulate the effects of both scalar and functional covariates on the interval-censored event time through a functional Cox model. We consider penalized maximum likelihood estimation for this model and devise an EM algorithm to stably compute the parameter estimators. The resulting estimators for the regression parameters and linear functionals of the coefficient function are shown to be consistent and asymptotically normal, with limiting covariance matrices that attain the semiparametric efficiency bound and can be readily estimated through the profile likelihood method. Building upon these results, we construct a global test for the overall effect of the functional covariate. Finally, we assess the performance of the proposed methods through extensive simulation studies and present an application to data from the Alzheimer's Disease Neuroimaging Initiative.

Spatial domain identification requires jointly modeling molecular signatures and physical coordinates, yet current tools frequently over-smooth biological boundaries, require user-specified cluster numbers, and lack principled multimodal integration. We introduce BaySC, an integrative Bayesian spatial clustering framework for spatial domain identification. BaySC inherently learns the true number of spatial domains from the data by employing a Mixture of Finite Mixtures (MFM) prior. Tissue topology is modeled via a Markov Random Field (MRF) applied to discrete cellular assignments, a strategy that enforces local spatial coherence without distorting the underlying gene expression features. This enables BaySC to accurately map contiguous tissue layers as well as geographically scattered, transcriptionally identical cell populations. Furthermore, BaySC handles spatial multi-omics data through a weighted log-likelihood fusion mechanism executed via Gibbs sampling. This approach assigns interpretable weights to each modality, allowing users to quantify the biological relevance of different data layers to the final tissue map. Validated across ten single-modal spatial transcriptomics and two spatial multi-omics datasets, BaySC yields highly interpretable probabilistic outputs. It demonstrates competitive accuracy on standard clustering metrics and consistently outperforms existing tools in preserving spatial topography, as measured by spatially-aware Adjusted Rand Index (spARI).

Operator-valued concentration inequalities are foundational to the analysis of modern high-dimensional statistics and randomized algorithms. However, standard oracle bounds are frequently limited in practice: they require explicit a priori knowledge of the true variance, and often explicitly scale with the ambient dimension, rendering them vacuous for infinite-dimensional or heavily structured operators. Motivated by these challenges, we establish the first empirical Bennett and Bernstein inequalities for sums of independent, bounded, self-adjoint Hilbert-Schmidt operators. Our fully data-driven bounds replace the unknown variance with an empirical estimate and rely strictly on the intrinsic dimension rather than the ambient dimension. This structural shift yields computable, dimension-free guarantees with a sharper first-order asymptotic radius for non-isotropic random matrices and seamlessly extends to infinite-dimensional Hilbert spaces. We demonstrate that our empirical bounds achieve asymptotic sharpness with the best known oracle rates. Finally, as an independent byproduct, we derive novel empirical concentration guarantees for the intrinsic dimension itself.

This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in kernel methods and the estimation of eigenvectors and eigenvalues of matrices, offering a more intuitive understanding compared to prior work with minimal assumptions. We also show that, since the prediction task in KRR is essentially the weighted sum of eigenvectors/singular vectors, by analyzing how much error can be caused by perturbations to the kernel matrix, we can then derive a bound on this generalization error using the estimation stability of matrix eigenvalues and eigenvectors. Compared with previous work, our analysis concentrates on finite-sample settings and on the generalization error arising from having a suboptimal finite training set. Our findings reveal that in kernel methods, as long as the kernel is of high rank, the near-zero reconstruction error can be trivially obtained, implying that the reconstruction error will have limited predictive power for generalization. Additionally, we establish a generalization bound from an eigenvalues/eigenvectors estimation perspective, showing that strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between consecutive eigenvalues. Finally, we also demonstrate empirically our simplified risk estimator is able to track testing errors in trailing eigendirections more closely than the existing literature.

Clinical language models increasingly operate over electronic health records (EHRs), yet patient records are not stored as temporally grounded trajectories. Clinical notes describe symptoms, assessments, and disease progression, but often compress or narratively reorder events. Structured EHR rows provide timestamps for labs, medications, vitals, and procedures, but capture only part of the clinical story. We formulate clinical timeline reconstruction as retrieval-augmented temporal grounding: constructing a patient trajectory by using narrative text for event semantics and structured rows as partial temporal evidence. We introduce a scaffolded workflow that extracts central narrative events, builds an initial temporal scaffold, attaches non-central events, and calibrates timestamps using retrieved structured EHR rows. We evaluate on 40 discharge summaries, including 15 i2b2-derived and 25 MIMIC-IV summaries, each with manual gold-standard timelines and aligned structured EHR data. Across models, multimodal calibration left event match rates largely unchanged and generally improved temporal performance: mean paired case-level multimodal-unimodal differences were positive in 7 of 12 model-metric comparisons across concordance and AULTC, with none negative. However, uncertainty was substantial given the 40-case sample; paired case-level bootstrap intervals excluded zero only for the DeepSeek V3.2 AULTC improvement. A gap analysis shows that 35.1% of text-derived events have no structured counterpart. These findings support treating structured EHR data as partial temporal evidence for narrative-derived patient trajectories.

The U.S. social safety net delivers essential services at mass scale, but access burdens persist, as congested contact or call centers serve as a primary mode of application completion and assistance. In Holmes v. Knodell, Missouri's SNAP call centers were so congested that nearly half of all application denials were procedural, caused by applicants' inability to complete required interviews, rather than underlying ineligibility. The judge ruled these system failures led to a violation of procedural due process. We propose a performance evaluation framework based on queueing models from operations research and management to assess and improve access in such systems. Operational access failures of call centers are distinct from prior automation failures in benefits provision. Emergent arbitrariness arises from interactions between system dynamics and access demand, rather than from an explicit algorithmic rule, making diagnosis and repair inherently system-level. We develop a queueing model that incorporates phenomena that distinguish social services from standard service domains, redials and abandonment, through which backlogs generate endogenous congestion. Standard queueing guidance from Erlang-A that does not address endogenous congestion fundamentally understaffs, which could lead to persistent shortfalls in practice. Using a fluid approximation, we derive steady-state performance metrics to analytically characterize the impacts of bundled staffing and service delivery changes. We fit model parameters to call-center data disclosed in court documents. Our queueing model can support ex-ante evaluation and design of access systems, inform policy levers for improving access, and provide evidence about whether applicants are afforded a meaningful opportunity to be served at scale.

Feature attribution analysis is critical for interpreting machine learning models and supporting reliable data-driven decisions. However, feature attribution measures often exhibit stochastic variation: different train–test splits, random seeds, or model-fitting procedures can produce substantially different attribution values and feature rankings. This paper proposes a framework for incorporating stochastic nature of feature attribution and a robust attribution metric, RoSHAP, for stable feature ranking based on the SHAP metric. The proposed framework models the distribution of feature attribution scores and estimates it through bootstrap resampling and kernel density estimation. We show that, under mild regularity conditions, the aggregated feature attribution score is asymptotically Gaussian, which greatly reduces the computational cost of distribution estimation. The RoSHAP summarizes the distribution of SHAP into a robust feature-ranking criterion that simultaneously rewards features that are active, strong, and stable. Through simulations and real-data experiments, the proposed framework and RoSHAP outperform standard single-run attribution measures in identifying signal features. In addition, models built using RoSHAP-selected features achieve predictive performance comparable to full-feature models while using substantially fewer predictors. The proposed RoSHAP approach improves the stability and interpretability of machine learning models, enabling reliable and consistent insights for analysis.

Component network meta-analysis (CNMA) is a statistical methodology that enables estimation of relative effects for multi-component treatments, such as combinations of antidepressants, and individual components, such as single antidepressants, by synthesizing data from multiple studies. A commonly desired output of a systematic review and meta-analysis is a hierarchy of the treatments in terms of a certain performance metric. Methods have been established for standard network meta-analysis (NMA), but have not yet been extended to CNMA. In particular, CNMA presents unique challenges because the set of relative effects that can be uniquely estimated is more complex to determine compared to standard NMA, and a hierarchy involving relative effects that are not uniquely estimable is misleading. We present a step-by-step workflow for answering treatment hierarchy questions in both frequentist and Bayesian CNMA, including explicitly identifying the uniquely estimable relative effects. We illustrate the workflow by posing multiple treatment hierarchy questions in two distinct networks, one concerning primary care of depression and one disconnected network investigating treatment for chronic lymphocytic leukemia.

Instrumental variables (IV) methods are central to applied microeconomics. While classical approaches assume linear models with constant effects, recent literature has shifted toward the local average treatment effect (LATE) framework to accommodate heterogeneous treatment effects. This paper provides a practical guide to aligning empirical practice with recent theory. We first examine how different specifications with covariates lead to distinct weighted averages of covariate-specific LATEs. We then discuss how parametric misspecification can undermine the causal interpretation of these estimands and suggest flexible specifications as essential robustness checks. Finally, we review formal tests for LATE assumptions and methods robust to monotonicity violations. We provide a guide to software implementations to help researchers apply the methods in practice.

Off-policy evaluation (OPE) estimates the value of a target treatment policy (e.g., a recommender system) using data collected by a different logging policy. It enables high-stakes experimentation without live deployment, yet in practice accuracy depends heavily on the logging policy used to collect data for computing the estimate. We study how to design logging policies that minimize OPE error for given target policies. We characterize a fundamental reward-coverage tradeoff: concentrating probability mass on high-reward actions reduces variance but risks missing signal on actions the target policy may take. We propose a unifying framework for logging policy design and derive optimal policies in canonical informational regimes where the target policy and reward distribution are (i) known, (ii) unknown, and (iii) partially known through priors or noisy estimates at logging time. Our results provide actionable guidance for firms choosing among multiple candidate recommendation systems. We demonstrate the importance of treatment selection when gathering data for OPE, and describe theoretically optimal approaches when this is a firm's primary objective. We also distill practical design principles for selecting logging policies when operational constraints prevent implementing the theoretical optimum.

Nowadays refinery optimization utilizes sheer amounts of data, which can be handled with modern Linear Programming (LP) software, but the interpreting and applying the results remains challenging. Large petrochemical companies use massive models, with hundreds of thousands of input matrix elements. The LP solution is mathematically correct, but simplifications are made in the model, and data supply errors may occur. Therefore, further insight is needed to trust the results. The LP solver does not have a memory, so additional understanding could be gained by analyzing historical data and comparing it to the current plan. As such, machine learning approaches were suggested to support decision making based on the LP solution. Among these, Anomaly Detection tools are proposed to be used in tandem with the LP output. A transformed version of the popular ECOD methodology is applied. New methods are proposed to handle high-dimensional data: choosing the most informative pairs. Then, this is used alongside two 2D Anomaly Detection algorithms, revealing several business opportunities and data supply errors in the MOL refinery scheduling and planning architecture.

We study a prototypical situation when a learned predictor can discover useful low-dimensional structure in data, while using fewer samples than are needed for accurate prediction. Specifically, we consider the problem of recovering a multi-index polynomial $f^*(x)=h(Ux)$, with $U\in\mathbb{R}^{r\times d}$ and $r\ll d$, from finitely many data/label pairs. Importantly, the target function depends on input $x$ only through the projection onto an unknown $r$-dimensional central subspace. The algorithm we analyze is appealingly simple: fit kernel ridge regression (KRR) to the data and compute the Average Gradient Outer Product (AGOP) from the fitted predictor. Our main results show that under reasonable assumptions the top $r$-dimensional eigenspace of AGOP provably recovers the central subspace, even in regimes when the prediction error remains large. Specifically, if the target function $f^*$ has degree $p^*$, it is known that $n\asymp d^{p^*}$ samples are necessary for KRR to achieve accurate prediction. In contrast, we show that if a low degree $p$ component of $f^*$ already carries all relevant directions for prediction, subspace recovery occurs in the much lower sample regime $n\asymp d^{p+\delta}$ for any $\delta\in(0,1)$. Our results thus demonstrate a separation between prediction and representation, and provide an explanation for why iterative kernel methods such as Recursive Feature Machines (RFM) can be sample-efficient in practice.

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under alternative specifications of the transition probability matrix. We extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model of Bazzi et al. (2017) to the general $K$-regime case with regime-specific means and variances, and develop an open-source R package, multiregimeTVTP, for simulation and estimation of such models. A Monte Carlo study shows that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. The GAS score coefficient appears to be statistically non-identifiable, owing to a ridge in the likelihood surface linking it to the regime variance. The filtered regime probabilities are accurately recovered under correct specification, whereas the one-step-ahead conditional mean is insensitive to misspecification of the transition dynamics. An empirical application to U.S. Treasury zero-coupon yield changes (1961-2024) at four maturities shows that a specification driven by the lagged yield level provides the best fit, attaining the lowest AIC at all four maturities and the lowest BIC at the short end of the yield curve, and that the estimated regimes align with documented episodes of U.S. monetary history.

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples – including those with low likelihood under the base model – which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens – those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

Randomized controlled trials often enroll participants whose characteristics differ from those of a target population, which can limit the generalizability of the estimated treatment effects when effect modifiers differ across populations. While existing generalizability methods primarily focus on estimating the average treatment effect (ATE) in the target population, such summaries may obscure important heterogeneity that is relevant for clinical and policy decision-making. In this work, we illustrate an approach for estimating the conditional average treatment effect (CATE) in a target population of trial-eligible individuals as a function of prespecified effect modifiers within a nested trial setting. Our approach combines semiparametric theory with flexible estimation: we first estimate nuisance functions using data-adaptive methods and construct pseudo-outcomes from conditional influence functions, then estimate the CATE function via local linear (kernel) regression. Sample splitting and cross-fitting are used to reduce overfitting bias and ensure asymptotic valid inference. Finite-sample performance is assessed via simulations and illustrated in the Coronary Artery Surgery Study (CASS).

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key limitation of such estimators: their inability to provide meaningful marginal properties, such as shadow prices or elasticities. We propose a novel piece-wise linear smoothing framework that recovers meaningful marginal estimates even in non-convex settings. Building on the concept of conditional convexity originally developed in deterministic frontier analysis, we formulate the smoothing process as a bilevel optimization problem that fits a continuous, monotonic, piece-wise linear function to the initial isotonic regression predictions. Monte Carlo simulations demonstrate that the proposed approach can significantly improve estimation accuracy in both convex and non-convex settings for univariate and multivariate data. We apply this approach to analyze agglomeration economies in Finnish municipalities, illustrating its practical value.

Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors, directed acyclic graphs, or transport plans. When employed as a transformation of random variables, projection is especially useful, since its contraction property not only preserves probability concentration, but also often preserves differentiability for gradient-based posterior computation. On the other hand, unless the projection can be obtained by some non-iterative algorithm, posterior computation can be expensive because it requires nesting an iterative optimization routine within each Markov chain Monte Carlo iteration. In this article, inspired by the success of continuous shrinkage models as replacements for discrete spike-and-slab priors, we propose a continuous relaxation of projected priors. The key idea is to quantify the duality gap between the primal projection loss and the dual objective, and impose a probabilistic prior that shrinks this gap toward zero. The resulting gap-shrinkage prior has a tractable form, does not require running an optimization subroutine inside each posterior update, and puts probability mass near the exact projection. We demonstrate useful properties of gap-shrinkage priors, including connections to global-local shrinkage priors, broad applicability to generalized projection functions, and competitive performance in posterior contraction. We apply the gap-shrinkage model to a marketing data analysis aimed at identifying important predictor effects on multivariate grocery-shopping decisions.

Active learning for continuous regression has lacked an acquisition function that targets epistemic uncertainty when the predictive distribution is multimodal: variance misses modal disagreement, and information-theoretic targets like BALD are designed for discrete outputs. We introduce a Two-Index framework that makes this separation explicit: one stochastic index selects among competing model hypotheses (epistemic source), while a second governs within-hypothesis randomness (aleatoric source). An entropy decomposition within the framework identifies the mutual information between the output and the epistemic index as a principled acquisition objective, and we prove this quantity vanishes as the model is trained on growing datasets, confirming that it captures exactly the uncertainty data can resolve. Because this mutual information is intractable for continuous outputs, we derive the Mutual Information Lower Bound (MI-LB) acquisition function, a closed-form approximation for Mixture Density Network ensembles. On benchmarks featuring multimodal systems, MI-LB matches or beats every baseline evaluated and is the only method to do so consistently – geometric and Fisher-based baselines compete only when the input space already encodes the multimodality, and collapse otherwise.

We study inventory control with decision-dependent censoring, focusing on the censored or repeated newsvendor (R-NV), where each order quantity determines whether demand is fully observed or censored by sales. Existing approaches based on parametric Thompson sampling (TS) can be brittle under prior mismatch, while offline imputation methods need not transfer to online learning. Motivated by the predictive view of decision making, we combine these ideas by taking oracle actions on learned completions of latent demand. We propose in-context generative posterior sampling (ICGPS), which uses modern generative models that are meta-trained offline and deployed online by in-context autoregressive generation. Theoretically, we show that the Bayesian regret of ICGPS with a learned completion kernel is bounded by the Bayesian regret of a TS benchmark with the ideal completion kernel plus a deployment penalty scaling as $\sqrt{T}$ times the square root of the completion mismatch. This yields a plug-in template for operational problems with known TS regret bounds. For R-NV, we derive sublinear Bayesian regret by reducing censored feedback to bandit convex optimization feedback. We also show that, under reasonable coverage and stability assumptions, the online completion mismatch is controlled by the offline censored predictive mismatch, so offline predictive quality transfers to online performance. Practically, we instantiate ICGPS with ChronosFlow, which combines a frozen time-series transformer backbone with a trainable conditional normalizing-flow head for fast censoring-consistent sampling. In benchmark experiments, ChronosFlow-ICGPS matches correctly specified TS, outperforms myopic and UCB-style baselines, and is robust to prior mismatch and distribution shift. ChronosFlow-ICGPS also performs well for the real-world SuperStore dataset, especially under heavy censoring.

Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.

Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference). To overcome these drawbacks, the novel class of combined INAR (CINAR) models is proposed, which both exhibits the classical autoregressive dependence structure and allows to specify the marginal distribution within the wide class of discrete self-decomposable distributions. In particular, CINAR random fields can be equipped with a Poisson or negative-binomial marginal distribution. The CINAR's key stochastic properties are derived (including a simple expression for conditional probabilities), and special cases as well as possible extensions are discussed. Approaches for parameter estimation are developed and investigated, and the practical relevance of the novel CINAR family is demonstrated by an agricultural data application.

We propose a novel and systematic differentially private (DP) inference framework for non-Euclidean data. First, we design two types of DP mechanisms for the Fréchet mean and variance for i.i.d. Riemannian manifold-valued data, tailored to different geometric structures and accompanied by analytic privacy budgets calibrated to the geometry of the underlying manifold. Second, we establish the consistency and central limit theorems (CLTs) of the proposed DP estimators, enabling a suite of statistical inference procedures under privacy constraints. Furthermore, we provide comprehensive implementation guidelines and feasible procedures, including consistent DP estimators of the asymptotic variance in the CLTs. Extensive numerical experiments support the proposed methodologies. Finally, we demonstrate the effectiveness of our approach on real-world medical image and sociological datasets supported on two representative manifolds.