Papers

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N\text{-}dim}(\Pi)/N})$. In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on $N$ and $\mathrm{N\text{-}dim}(\Pi)$.

We study PAC-Bayes derandomization for smooth loss functions. Our goal is to obtain generalization bounds that hold with high probability for deterministic predictors by exploiting smoothness properties of both the loss and the predictor class. We show that passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost, given by the generalization gap of the Jensen gap class. We control this class through its Rademacher complexity, leading to bounds for deterministic predictors that involve flatness quantities expressed in terms of parameter Jacobians and Hessians of the score map. The framework applies to both bounded and unbounded smooth loss functions, and we specialize the results to linear predictors and smooth neural networks. Finally, the Jacobian and Hessian quantities appearing in the theory motivate a practical regularizer. For BatchNorm networks, we compute this regularizer with respect to effective BatchNorm weights obtained by folding the BatchNorm transformation into the adjacent affine weights. Experiments on CIFAR-10 illustrate the behavior of this regularizer under different batch sizes.

Chronic disease management relies on regular patient-provider interactions to follow-up on disease progression and control. For Type 2 Diabetes (T2D), current guidelines prescribe fixed time intervals between subsequent primary care visits for all patients, overlooking heterogeneity in clinical trajectories and patient characteristics. This study introduces a Contextual Markov Decision Process (CMDP) model to optimize subpopulation-specific follow-up interval decisions using Electronic Health Record (EHR) data from 22,154 T2D patients across 10 primary care clinics. Contexts are identified by: i) dimensionality reduction of variables representing the individual health trajectories utilizing Principal Component Analysis, and ii) assigning patients to contexts via principal components and additional patient-level features using clustering. Two distinct contexts emerged, representing a lower- and a higher-risk subpopulation. CMDP-derived policies recommend: (i) follow-up within 1 month if lab value at current visit is unmeasured; (ii) up to 3 months for elevated lab values or recent hospitalizations; and (iii) 6 to 12 months for sustained glycemic control, with shorter follow-up intervals for patients in high-risk context. The optimal policies achieved lower expected cumulative cost than benchmarks (e.g., in the higher-comorbidity context, the CMDP policy reduced cost by about 34.8%, and in the lower-comorbidity context by about 6.4%, relative to an American Diabetes Association-like fixed interval follow-up policy. These findings demonstrate how context-aware approaches can inform adaptive follow-up strategies, and have the potential to advance chronic care management in primary care by synthesizing machine learning and probabilistic decision models.

Ethnic density is widely used in epidemiology and health geography as a contextual exposure, yet it is rarely examined as a measurement problem in its own right. Equivalent percentage values may represent different neighbourhood contexts across groups and places, particularly where migration, religion, language, household structure and socioeconomic conditions are spatially co-located. Using the harmonised Unified UK Census Data release, I analysed 239,023 small-area census data to examine ethnic density as an exploratory contextual co-occurrence construct. I estimated UK-wide mixed graphical models (MGM) for eight ethnic-density targets using 239,019 complete cases and 32 nodes per target-specific model. England-only spatial analyses then used k-nearest-neighbour Output Area centroids (k = 8) to estimate LISA and spatially adjusted residual networks. Ethnic density did not behave as a single contextual scalar. In the UK-wide MGM, the strongest retained target-neighbour edges differed across groups. Asian density was linked most strongly with Middle East/Asia-born share (0.59), Indian density with Hindu share (0.55), Pakistani density with Muslim share (0.47), Bangladeshi density with Muslim share (0.23), Black density with Africa-born share (0.42), and White density with Middle East/Asia-born share (0.35). England-only ethnic-density measures were strongly spatially autocorrelated, with Global Moran's I ranging from 0.57 for Mixed share to 0.90 for White share. After residualising against English region and local spatial lag, 64.3% to 96.4% of original target-node edges persisted across ethnic-density networks. Equivalent percentage values are not necessarily comparable across ethnic groups. This has implications for estimand definition, adjustment strategies, and the interpretation of ethnic density and other bundled contextual measures in urban health research.

Risk and decision models often combine sparse marginal information, precisely specified probability distributions, and dependence assumptions that are only partly justified. Probability bound analysis (PBA) represents epistemic uncertainty through probability boxes, but many applications assume independence or require dependence structures to be fully specified. We develop a dependence-sensitive PBA framework for black-box risk and decision models in which both marginal information and dependence information may be incomplete. The framework combines p-box parameters, precise-CDF parameters, and fixed quantities; incorporates specified dependence through copulas; and propagates unknown dependence through Fréchet-style admissible coupling sets. We also extend the construction to cross-dependence between imprecisely specified and precisely specified inputs. In an illustrative risk decision model, dependence assumptions materially affected output bounds and tail-risk summaries; analyses that ignored or simplified dependence produced narrower characterizations of plausible outcomes. The framework supports transparent uncertainty propagation when evidence is insufficient to justify either precise marginal distributions or a single dependence model.

We provide a statistical theory explaining why empirical score matching can achieve minimax optimal performance for diffusion generative models when the data distribution is supported on a low-dimensional manifold. More precisely, we establish convergence rates for empirical risk minimization over suitably constrained Sobolev classes and show that, under appropriate regularity conditions, the resulting score estimators lead to minimax optimal Wasserstein-1 rates for the generated distribution, up to logarithmic factors. Our results provide sufficient conditions for score-based generative modeling to generalize from the data instead of overfitting, while the resulting statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension.

The Small BAseline Subset technique provides remote measurements of ground displacement with high spatial resolution, making it a key tool for monitoring geophysical processes in hazard-prone areas. An effective analysis of this type of data requires reliable estimation of their second-order structure, which is difficult to achieve because the measurements are systematically missing over relatively large portions of the investigated areas. We tackle the problem from a functional data analysis perspective and treat the observations as partially observed functional data with two-dimensional domain. To properly characterize the data, we introduce the fragmented regime of partial observation, where parts of the curves are systematically missing across replicates. For this regime, we propose a novel method for covariance estimation, formulating the task as a matrix completion problem with Laplacian regularization. The estimator is nonparametric and free from stationarity or isotropy assumptions. Extensive simulations show that our method achieves consistently low estimation error across a range of covariance structures. Application to ground displacement data relative to the Phlegraean Fields demonstrates its ability to recover meaningful spatial dependence patterns, highlighting its potential for environmental risk assessment and monitoring.

Large Language Models (LLMs) are increasingly used as judges for scalable evaluation, yet such LLM–as–a–Judge systems exhibit systematic biases that are decoupled from semantic quality, most notably verbosity bias. Meanwhile, human supervision is costly and typically selective, yielding reliable positive judgments but leaving most outputs unlabelled and potentially mixed in quality. We formulate LLM evaluation under selective human supervision as a positive–unlabelled learning problem and propose a geometric auditing framework based on Partial Optimal Transport. By aligning a small set of human–verified positives with a reliable subset of unlabelled outputs in a fixed embedding space, our method identifies human–consistent preferences and corrects biased judges without retraining. Experiments demonstrate improved alignment with human preferences, increased robustness to presentation biases, and interpretable confidence estimates, offering a scalable and statistically grounded alternative to existing LLM–as–a–judge pipelines.

An integrated and extendable approach for stress-testing loan portfolios is presented, which includes both a loan production component and a credit risk component. In this approach, we simulate a completed portfolio using realistic loan parameters and distributional assumptions. Thereafter, we generate the uncertain cash flow history of these loans within a multistate probabilistic framework. We illustrate our approach using a simulation-based study, though the approach can be fit to real-world data. Such a simulation-based approach is ideal for stress-testing since it allows for evaluating a range of conditions. From these completed loans, we compute portfolio-level credit risk metrics, e.g., default and loss rates. Stress scenarios are introduced by varying the loan parameters accordingly within a broader Monte Carlo setup, thereby resulting in a range of portfolios. A classical approach to stress-testing does not typically integrate loan production or embed the correlation structure amongst risk metrics. In our approach, we integrate the forecasting of risk metrics with receipt-generation. Given data, the loan parameters within our extendable approach can be dynamically modelled as functions of input variables using any applicable technique. Overall, our approach can render predictions that are more dynamic and flexibly tuned, which can enhance stress-testing practices within any bank.

Piecewise regression models are essential for identifying structural changes in longitudinal or spatial data across diverse scientific domains. While standard approaches often assume sharp, instantaneous transitions and single, non-hierarchical breakpoints, many real-world phenomena exhibit gradual, smoothed transitions that vary systematically across groups. We introduce smoothbp, an R package for fast, Bayesian hierarchical piecewise regression featuring logistic-smoothed transitions. By implementing a bespoke Metropolis-within-Gibbs sampler in Rust, smoothbp combines exact conjugate updates for linear terms with Hamiltonian Monte Carlo (HMC) transitions for non-linear location and sharpness parameters. smoothbp natively supports multiple change-points, random intercepts, random change-point timing, and structural covariates on all segment parameters. It also incorporates Kuo and Mallick (1998) spike-and-slab priors for automatic inference on the number of active breakpoints via the smoothbp_ss function. We document the sampler, validate parameter recovery and calibration through simulation-based calibration and interval-coverage studies, and contrast smoothbp against the existing software landscape across R, Python, Julia, and MATLAB, demonstrating its competitive efficiency against general-purpose probabilistic programming languages like brms and specialized packages like mcp.

Population-based biobanks, now established in many countries, offer opportunities for large-scale studies investigating the incidence of various diseases. Biobank data is typically collected from a study cohort recruited over a defined calendar period, with subjects entering the study at various ages falling between $R_L$ and $R_U$. This work focuses on biobank data that includes individuals in whom onset of the disease of interest occurred before recruitment, termed prevalent cases, along with individuals initially recruited as disease-free in whom disease onset occurred during the follow-up period. We propose a novel cumulative incidence function (CIF) estimator that goes beyond existing methods in that it incorporates all disease cases, both prevalent and incident, irrespective of their subsequent life course. In particular, the new method can handle situations involving diseases that can occur at young ages with long survival after disease onset. Asymptotic properties of the new method are established and a simulation study is presented examining the performance of the method. We illustrate the use of the method and highlight its advantages over existing methods with an application to cancer data from the UK biobank.

The Bayes space provides a Hilbert space structure for analysing probability density functions (PDFs), equipping them with a geometry that reflects their relative and constrained nature. A key tool in this framework is the centred logratio (clr) transformation, which establishes an isometric isomorphism between the Bayes space and (a subspace of) the classical $L^2$ space. This makes it possible to apply functional data analysis (FDA) techniques, particularly functional principal component analysis (FPCA), to both univariate and multivariate density data in the context of dimension reduction. For multivariate PDFs, embedding them in the Bayes space enables an orthogonal decomposition into independent and interactive components. Furthermore, the independent part can be decomposed into mutually orthogonal geometric marginals. This structure provides more profound insights into the sources of variation in multivariate densities. We show that this decomposition of the total variance is optimal in a PCA sense, impacting the interpretation of the eigenfunctions and scores resulting from FPCA. We demonstrate that applying FPCA directly to multivariate densities is equivalent in a certain sense to applying multivariate FPCA to their decomposed form, with the resulting eigenfunctions and scores decomposing accordingly. The unique decomposition based on these theoretical results is applied to housing and geological empirical data respectively, demonstrating the interpretability and practical value of this approach.

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X” paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.

Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable – e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.

Accurately estimating treatment effects in time series is essential for evaluating interventions in real-world applications, especially when treatment assignment is biased by unobserved factors. In many practical settings, interventions are adopted at different times across individuals, leading to staggered treatment exposure and heterogeneous pre-treatment histories. In such cases, aggregating outcome trajectories across treated units is ill-defined, making individual treatment effect (ITE) estimation a prerequisite for reliable causal inference. We therefore study the problem of estimating the average treatment effect for the treated (ATT) by first recovering individual-level counterfactuals. We introduce a neural framework that learns simultaneously low-dimensional latent representations of individual time series and propensity scores. These estimates are then used to approximate the individual treatment effects through a flexible matching procedure that avoids classical convexity constraints commonly used in synthetic control methods. By operating at the individual level, our approach naturally accommodates staggered interventions and improves counterfactual estimation under latent bias, without relying on explicit temporal modeling assumptions. We illustrate our approach on both real-world energy consumption data and clinical time series, including high-frequency electricity demand-response programs and semi-synthetic data for individuals in intensive care unit (ICU), where hidden confounding, staggered treatment adoption, and non-stationary dynamics are prevalent.

Predictive regression is a crucial tool for exploring return predictability. In this study, we introduce an efficient procedure for selecting and estimating active predictors and change points in structural break predictive regression. Our approach allows the number of change points to increase with the sample size and accommodates sparse active predictors that may be stationary or cointegrated. We begin by identifying the active predictors using a Sure Independence Canonical Screening (SICS) procedure. Next, we estimate the change points through a Ratio-Controlled Regression Screening (RCRS) method. Finally, we reduce redundancy by eliminating unnecessary breakpoints and predictors using information criteria (IC). This approach allows for consistent estimation and selection of true breakpoints and active predictors. Our simulations and empirical studies demonstrate that the proposed procedure performs effectively.

Response-adaptive randomization designs have attracted much attention in clinical trials. This paper proposes a new class of response-adaptive design which built on the efficient randomized-adaptive design (ERADE) proposed by Hu, Zhang, and He. The original ERADE uses a discrete allocation probability function and leverages the stopping time theory of stochastic processes to establish asymptotic results. It has been proven that the design can reach the Cramér-Rao lower bound for any target allocation proportion. This study further expands the original framework by replacing the traditional case-by-case sequential enrollment with group recruitment over fixed time intervals(weekly, biweekly, or monthly), and dynamically updates the allocation probabilities based on the cumulative response information within each group. Meanwhile, to better fit practical application scenarios, we further explicitly consider the situations of randomly missing data and response delay. Theoretical analysis shows that the new design retains all the main asymptotic properties of the original ERADE, and still performs well under the conditions of response delay and missing data. Finally, through simulation studies and the redesign of a real-world clinical trial, the effectiveness and practicality of the proposed method are verified.

Active feature acquisition (AFA) sequentially selects which features to observe to reach a classification or ranking decision. Its central limitation is reliance on large amount of labeled data to fit probabilistic models guiding acquisition. Large language models (LLMs) supply unsupervised domain knowledge, but are poor sequential planners. Asking one to both know and decide conflates capabilities best kept separate. Here, we develop a framework for zero-shot AFA through disciplined elicitation: asking the LLM only for what it can be trusted to return, the unary deviations and pairwise co-variations that are the sufficient statistics of a Markov random field (MRF). We apply our framework to two settings: binary classification and top-$k$ identification. In practice, the LLM reliably returns only discriminative statistics, what distinguishes the classes rather than each class in isolation, which precludes classical AFA. We apply a maximum-entropy closure that resolves this gauge ambiguity. We evaluate on a cohort of Inflammatory Bowel Disease (IBD) patients, an active clinical setting where diagnostic ambiguity and patient heterogeneity obstruct stable treatment strategies. Our framework outperforms the LLM both on real labels and on its own extracted beliefs. Where it matters most, on the hardest patients, our top-$k$ acquisition policy markedly outperforms all existing methods.

When algorithmic predictors inform resource allocation in high-stakes domains such as healthcare, these predictors must account for strategic manipulation of input features. The typical solution is to redesign the predictor itself to explicitly account for strategic interactions. In practice, however, decision makers are often constrained to adjusting coarser levers within existing prediction pipelines. For example, healthcare organizations often select which features to exclude based on perceived manipulability, while using standard regularization procedures to shrink the coefficients of retained features. In this work, we initiate a formal study of strategic classification through feature selection and its interaction with ridge regularization. Our main finding is that excluding individual features based on their manipulability alone is generally suboptimal. We provide a fine-grained characterization of the performance of a feature subset under optimal regularization, yielding new insights for policy design. Motivated by this characterization, we develop a practical algorithm for jointly choosing the feature set and the level of ridge regularization. Through a real-world case study on a healthcare payments benchmark, we illustrate how our algorithm can guide the design of coarse policy levers in practice. Our results provide a principled, practical framework for mitigating the effects of strategic behavior in algorithmic decision-making systems.

A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and feature-importance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. The present paper studies that object. KPP indexes the feature map by the nodes of the forest, weighted by a path metric that turns each coordinate into a component of a squared-Euclidean path-isometric embedding. KPP unifies four pillars under a single node-indexed representation whose Gram is non-diagonal and carries a metric: prediction, exact additive attribution, deterministic Lipschitz robust radius in the KPP metric, and uniform Rademacher risk bounds for regression and classification under fixed, honest, or cross-fit conditioning. All probabilistic guarantees are conditional on the representation and are stated under three explicit conditioning regimes; the robust-radius guarantee is deterministic in the KPP metric rather than in a norm on the raw input. Conjectured fast-rate refinements for both regression and classification are stated as open problems and are not claimed as theorems.

Mixed models are popular for the prediction of subject-specific repeated outcomes or center performance among many centers. When the goal is to identify extreme or poor outcomes, standard random effects predictions may, however, suffer from regression to the mean and underestimate values in the tail of their distribution. Optimally weighted random effect estimators have recently been proposed to mitigate this. Motivated by clinical settings where repeated outcomes may end in death, we extend that method to predict poor outcome defined as 'death or substandard repeated measures'. We start from joint models with shared random effects for the longitudinal and survival outcome and estimate their random effects by minimizing squared weighted prediction errors given available data on survival and repeated measures. As for mixed models, weights are chosen to more heavily penalize errors in the tails. We call the results WRaPs: Weighted Random effect Predictors. For basic models and a select set of weights analytical closed form solutions are derived from the usual joint model parameters. For the more complex setting, computational solutions are developed in rjags using MCMC methods within the Bayesian paradigm. We illustrate finite sample properties of the proposed method in Type I simulations with random intercept and slope; and apply the new approach to predict individual future outcomes and survival in a randomized study with glioblastoma patients.

Post-marketing pharmacovigilance relies on statistical signal detection methods to identify potential adverse drug reactions. The Weibull shape parameter (WSP) test concept exploits temporal information (electronic health records) to assess the hazard of an adverse event over time after drug initiation. A statistically significant deviation from constancy results in a signal. The WSP framework comprises a family of tests that differ with respect to the estimation approach (frequentist or Bayesian), the chosen time-to-event distribution (Weibull, double Weibull, power generalized Weibull) for hazard modeling, and test specification parameters. To facilitate practical application and encourage consideration of the WSP signal detection test in future research, we developed the R package WSPsignal. The package consolidates all functionalities required for WSP testing into a unified, open-source interface. It enables practitioners and researchers to apply default test specifications or perform simulation-based tuning to identify the optimal test for a given data scenario. We illustrate the package functionalities in two examples to follow along. In a large-sample setting (ca. 20 000 observations), a frequentist WSP test is considered. In a small-sample setting (ca. 1 000 observations), a Bayesian WSP test is chosen. The additional test specifications are optimized through simulation-based tuning.

Whether global warming is accelerating remains contested because internal variability and spatial heterogeneity can obscure changes in warming rates. Here we use a Bayesian hierarchical spatio-temporal model with structured spatial dependence to estimate local warming trajectories and acceleration, and apply the model to progressively truncated observations to infer when acceleration becomes detectable. We find that detectable acceleration emerges unevenly across the climate system, with the earliest high-confidence signals concentrated in selected high-latitude regions. Across retained grid cells, the proportion exceeding a 90% posterior probability of positive acceleration increases from 13.6% for 1970-1990 to 39.7% for 1970-2026, while the proportion exceeding a 50% threshold increases from 46.4% to 70.3%. These results show that spatial aggregation can delay detection by averaging regions where acceleration has already emerged with regions where it remains weak or uncertain. The framework provides a probabilistic diagnostic for identifying where warming is intensifying and when acceleration becomes statistically detectable.

Online learning in non-stationary streams is often formulated as tracking a point estimate, but many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and adversarial corruption. Our approach represents each candidate law through a latent cluster geometry: a variable-size configuration of centers that organizes probability mass and induces a predictive distribution. A Gibbs quasi-posterior over these configurations yields an online predictor by posterior averaging, and the resulting variable-dimensional posterior can be sampled with reversible-jump MCMC. The method therefore avoids specifying a parametric streaming law while retaining a structured latent space for uncertainty, regularization, and comparison. We evaluate performance by cumulative Wasserstein-1 regret against the time-varying true law. The analysis separates two effects: corruption perturbs the loss-based posterior update, whereas drift makes long-horizon posterior memory stale. We address the latter with a restarted variant that temporally localizes the same quasi-Bayesian update. The resulting high-probability bounds decompose into a PAC-Bayesian complexity term, a corruption-sensitive posterior perturbation term, and a dynamic optimal-transport term driven by \(A_T^{\mathrm{OT}}=\sum_{t=2}^T W_2^2(p_{t-1}^*,p_t^*)\). Under bounded support, stable latent geometry, predictive-map regularity, oracle realizability, localized restart windows, sublinear transport action, and sublinear corruption budget, the restarted predictor achieves sublinear cumulative Wasserstein regret. These guarantees require no parametric model for the stream, drift mechanism, or corruption process.

A/B testing has become the gold standard for data-driven decision-making in large-scale online experimentation, providing critical guidance for feature launch, pricing optimization, and user experience enhancement. To maximize statistical sensitivity, many technology companies routinely employ Controlled-experiment Using Pre-Experiment Data (CUPED), a technique that achieves substantial variance reduction while preserving the unbiasedness of estimating the average treatment effect. Despite its widespread adoption, several critical methodological and practical nuances of CUPED remain underexplored. This paper systematically addresses five frequently encountered yet overlooked questions regarding the application of CUPED. First, we provide a comparative analysis of various post-CUPED estimators to identify the optimal adjustment specification. Second, we evaluate the validity of regression-based adjustments and delineate robust variance estimation methods tailored for such frameworks. Finally, we extend our investigation to complex but common scenarios, including multi-arm experiments and two-stage sampling designs. Our findings reveal that in these settings, naive reliance on standard variance estimators can lead to severely misleading inferences. By offering rigorous theoretical insights and extensive experimental validation, this work deepens the conceptual understanding of CUPED. Notably, the recommended methodologies have been successfully deployed and integrated into ByteDance's experimentation platform.

Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

We study estimation and prediction in the Gamma model $\mathrm{Ga}(\alpha,\beta)$, where the shape parameter $\alpha$ is known and the scale parameter $\beta$ is unknown, under the Kullback–Leibler loss. For $\alpha\le1$, all scale-invariant estimators of $\beta$ have infinite risk, indicating a qualitative change in the estimation problem at the boundary $\alpha=1$. Our main result is that the Bayesian predictive density based on the Jeffreys prior is admissible for all $\alpha>0$. This resolves the admissibility problem for Bayesian predictive densities in Gamma models. As a related result, we also establish the admissibility of the corresponding Bayesian estimator for $\alpha>1$. To prove the predictive admissibility result, we develop an infinitesimal prediction framework based on Gamma processes. This framework naturally leads to a Kullback–Leibler loss for Lévy densities and establishes a connection between predictive distributions and Lévy measures. Under the resulting loss, the Bayesian predictive Lévy density is shown to be the posterior mean Lévy density. Unlike the normal and Poisson models, infinitesimal prediction in the Gamma model does not reduce to parameter estimation. Instead, it reduces to the estimation of a Lévy density. We relate this phenomenon to mean mixture curvature and discuss it from an information-geometric viewpoint.

We propose a parameter-efficient speech enhancement framework, Quaternion Conformer GAN (QC-GAN), which combines a Quaternion Conformer generator with MetricGAN-based training. The Hamilton product encodes the magnitude and phase via structured weight sharing, reducing the number of layer parameters while preserving their interdependencies. A metric-learning discriminator was employed to maximize perceptual quality by optimizing the approximate perceptual evaluation scores. On the VoiceBank+DEMAND dataset, QC-GAN achieved a Perceptual Evaluation of Speech Quality (PESQ) score of 3.48 with only 0.89M parameters, delivering a performance comparable to state-of-the-art models at less than half their size. A 35K-parameter variant achieved a PESQ score of 3.23, surpassing conventional methods with significantly fewer parameters. Evaluation on the DNS-Challenge 3 dataset further confirmed generalization to real-world conditions.

This paper presents a methodology-centered transfer learning framework for fragility adaptation under domain shift, class imbalance, and scarce target labels while preserving engineering interpretability and supporting decision-making under uncertainty. Four transfer learning strategies (instance-based, parameter-based, hierarchical Bayesian, and multi-source) are demonstrated through three complementary case studies: (i) instance-based transfer learning via importance weighting, demonstrated on coastal bridge fragility using Hurricane Katrina observations; (ii) parameter-based transfer learning together with hierarchical Bayesian transfer learning, enabling partial pooling across strata and posterior uncertainty quantification, demonstrated on residential building fragility using Hurricane Ian observations; and (iii) multi-source transfer learning that fuses multiple analytical fragility models with learned source weights and regularized target-domain adaptation, demonstrated on seismic bridge fragility using observations from the 2001 Nisqually earthquake. Across these case studies, direct transfer of source models (i.e. using existing state-of-the-art models) fails under domain shift and severe class imbalance, while targeted adaptation substantially improves failure detection and predictive stability in low-data regimes. These findings highlight the need for systematic guidance on diagnostics, strategy selection, and uncertainty reporting when developing and adapting fragility models.

Depression treatment often requires switching medications due to inadequate response or adverse effects. Estimating individualized treatment effects in this setting is challenging because treatment assignment is confounded by patient characteristics, switching induces time-varying selection, and counterfactual outcomes are not observed in follow-up data. Using a proprietary longitudinal major depressive disorder (MDD) clinical trial dataset, we formulate a next-visit counterfactual prediction task to estimate Hamilton Depression Rating Scale (HAMD-17) total scores under alternative treatments. We benchmark 8 estimators, including meta-learners, residual-based methods, and tree-based approaches. Causal Forest (CF) demonstrates the most favorable and consistent performance across all criteria. Our analysis shows that symptom benefits concentrate in specific switch directions, with dose intensification being generally beneficial. Notably, we identify a counterintuitive exception where a lower-intensity regimen outperforms a higher-intensity alternative for specific patient subsets. While crude observational comparisons substantially overstate gains, confounding-adjusted estimates yield modest, actionable magnitudes. These findings provide prospectively testable candidates for clinical decision support in depression care.