Covariate Shift

Peer-referral recruitment systems such as respondent-driven sampling are critical for studying and intervening on hidden populations affected by infectious diseases. To accelerate recruitment, public health agencies must adaptively allocate limited referral resources across multiple rounds, where current decisions shape both the number and the covariates of future recruits. Prior work makes this problem tractable by assuming that referrals are drawn i.i.d.\ from a homogeneous population, an assumption that ignores the homophily and shared context that drive real peer recruitment. We instead consider a more realistic model in which both referral capacity and the covariates of newly referred individuals are conditioned on the referrer, learned from data with a censored count model and a conditional generative model. The resulting planning problem is challenging because each candidate allocation induces a different distribution over future recruits. We propose \emph{Generative Frontier Planning} (GFP), a model-based planner that replaces per-step Monte-Carlo sampling with a deterministic backup over a latent covariate-coverage value surrogate. The surrogate is designed so that the expected value of the next frontier depends on the offspring generative model only through finite-dimensional summaries that are amortized offline, and so that the resulting per-round objective is monotone with diminishing returns. Together, these two properties make planning tractable: the deterministic backup eliminates Monte-Carlo sampling, and the diminishing-returns structure lets a marginal greedy allocation achieve a $(1-1/e)$-approximation for the per-round problem. On a simulation environment calibrated to a real respondent-driven sampling dataset, GFP outperforms random, reinforcement-learning, and i.i.d.\ dynamic-programming baselines across four discount factors.

We study off-policy evaluation (OPE) under strategic behavior where decision subjects (or agents) respond to a decision maker's policy by strategically modifying their covariates. Such behavior induces a policy-dependent covariate shift, breaking the standard assumption in existing methods that covariates are exogenous to the policy. Related work addresses this challenge by imposing strong assumptions such as repeated interactions or full knowledge of agents' response behavior, substantially limiting its applicability to OPE. In contrast, we consider a one-shot OPE setting where the decision maker has only partial knowledge of the agents' response behavior. Our key insight is that disclosing local information through post-hoc explanations reveals agents' pre-strategic covariates prior to adaptation, mitigating the information loss induced by strategic behavior. Leveraging this structure, we estimate a statistical model for the agents' responses and construct a doubly robust estimator for policy value. By assuming that the agents' cost sensitivity follows a conditional log-normal distribution, we establish consistency of the proposed estimator and validate our approach empirically. More broadly, our results highlight how interaction design can mitigate information asymmetry by revealing otherwise hidden structure in agents' strategic responses.

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

Foundation models mark a profound paradigm shift in time series modeling, with task-specific models being superseded by general-purpose zero-shot models. Yet, current approaches primarily focus on forecasting, while real-world time series are often irregularly and partially observed, requiring models that can jointly forecast, impute missing values, and handle degraded sampling conditions. To address these challenges, we introduce TS-ICL, a novel probabilistic In-Context Learning encoder--regressor Transformer that unifies forecasting and imputation. TS-ICL formulates time series tasks as timestamp-aligned regression and naturally incorporates covariates by training on synthetic dependency structures generated from a novel causal data prior. Empirically, TS-ICL achieves a new state-of-the-art in imputation, while remaining competitive with leading forecasting foundation models across both univariate and covariate-aware benchmarks. It shows particularly strong performance in forecasting with partially observed look-back windows.

We consider multi-environment prediction problems. We assume the environments change the distribution of a latent variable, while the mechanisms generating observed covariates and targets remain stable conditional on that variable. For example, hospitals or clinical cohorts may differ in the prevalence of latent patient states, even though the relationships between those states, physiological measurements, and outcomes remain unchanged. Given a dataset from multiple environments, we formulate a Bayesian model for such problems and derive the corresponding variational objective. We show that this objective decomposes into per-environment terms and an additional cross-environment balancing term induced by the model's structure. We use an empirical Bayes method to set the prior and incorporate it into the objective. Based on this objective, we develop an amortized variational algorithm for posterior approximation, and use the resulting learned latent variables to form predictions in new environments.We study our approach through simulations and real-world studies of astronomical source identification, microbiome-based disease detection, and ICU sepsis prediction. Across these settings, our method outperforms previous approaches for prediction in new environments.

A core goal of computational social science is to discover interpretable differences in how language varies across outcomes of interest, such as political affiliation or instructional quality. Recent LLM-based hypothesis generation methods describe such differences in natural language, but select for globally discriminative patterns without accounting for covariates that shape the data based on researchers' domain knowledge. When covariates are ignored, selected patterns can reflect confounds rather than differences of substantive interest. We introduce conditional hypothesis generation, a framework that incorporates researcher-specified covariates to steer hypothesis discovery toward differences that hold within relevant subgroups. Two challenges arise: the target subgroup may be underrepresented (stratum imbalance), and the direction of a difference may reverse across subgroups (sign reversal). We propose two econometrics-inspired methods: one introduces feature--covariate interactions to detect sign reversals, and the other applies within-stratum demeaning and inverse-frequency reweighting to equalize underrepresented strata. Synthetic experiments show each method outperforms global baselines in its targeted setting, and expert evaluation on two real-world datasets confirms that covariate-aware generation surfaces more useful hypotheses within relevant subgroups.

This paper proposes a method of creating synthetic data (SD) that will have two important advantages for the user compared to other methods currently available. The first is transparency; unlike other methods, the person in receipt of the SD will know which of the relationships between variables in the original data will be approximately maintained in the SD. The second is a guarantee that the SD is derived from information that has already been judged to be free of disclosure risk. This is achieved by first defining and calculating the margins where relationships between variables will be maintained in the SD. Each margin will then be subject to statistical disclosure control (SDC) to the standards defined by the data custodian, e.g. top-coding and bottom-coding, combination of small categories and/or modifying small counts. Further adjustment of the curated margins is advised by coarsening all counts in the table to multiples of the disclosure limit. These adjusted margins are used to create SD by the Iterative Proportional Fitting (IPF) algorithm. The practical steps involved in creating such SD are illustrated using data from the 1901 Census of Scotland.

In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing that fast labeled sample rates are recovered when proxy perturbation is controlled and unlabeled proxy covariates are sufficiently abundant. We also show that distribution regression is a direct special case, with analogous guarantees when the finite bag size is large enough. Experiments show consistent gains over supervised and semi-supervised baselines, especially in low label regimes.

We present a regression-adjustment framework designed for the estimation of longitudinal treatment effects in randomized experiments under static regimes. While regression-adjustment methods are useful for variance reduction in randomized experiments by using pre-treatment covariates, they usually focus only on average effects, from which we cannot obtain valuable insights into when the effects appear and how long they continue. To address this issue, we consider intermediate outcomes and evolving post-treatment covariates over time, and we represent such dynamic trajectories using transition kernels. Furthermore, we establish the asymptotic normality and the semiparametric efficiency bound for our estimator, enabling more powerful statistical inference. Simulation studies and empirical analysis using A/B test data from a streaming platform in Japan show the practical advantages of our method.

Detecting covariate shift is critical for building reliable vision systems. While most prior work focuses on improving robustness to shift, explicitly detecting covariate shift remains underexplored. Existing approaches typically rely on fully supervised training, requiring labeled examples from both original and shifted distributions, which is often impractical. In this paper, we show that covariate shift detection can be effectively addressed with weaker supervision using Positive Unlabeled (PU) learning. However, under covariate shift, in distribution and shifted data overlap significantly, making classical PU methods unstable and sensitive to noise. To overcome this challenge, we introduce Spectral PU Neighborhood Annotation (SPUNA), a geometry aware framework that progressively discovers shifted data by leveraging the local manifold structure of visual features. Extensive experiments show that SPUNA achieves state of the art performance in PU settings and remarkably matches the performances of fully supervised methods. Moreover, our approach transfers robustly across different types of shifts, demonstrating strong generalization capabilities.

Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining. However, most existing TSFMs remain univariate, and recent efforts to enable cross-variate modeling still operate directly within the raw variate space. This design introduces fundamental limitations in semantic alignment and relational expressivity. Specifically, raw-space group mixing lacks a dedicated mechanism to align heterogeneous physical quantities, while standard non-negative attention fails to capture the complex synergistic and antagonistic interactions ubiquitous in real-world systems. To address these challenges, we propose Falcon-X, decouples variates from the raw space and maps them into a unified latent prototype space. Falcon-X employs a Unified Prototype Diff-Attention mechanism that explicitly evaluates both positive and negative semantic affinities to explicitly align heterogeneous variates. Cross-variate interactions are then efficiently performed within this shared space via Latent Entity Attention, naturally facilitating zero-shot structural transfer. Finally, a Variate Reassembly Router robustly reconstructs variate-specific trajectories via a request-and-dispatch mechanism. Extensive evaluations on the GIFT-Eval and fev-bench benchmarks demonstrate that Falcon-X achieves excellent forecasting performance, offering a principled and scalable paradigm for complex multivariate environments. Falcon-X is publicly released to support future research.

Multicalibration extends classical calibration by requiring predictions to be unbiased over a rich collection of functions, encompassing both prediction slices and subpopulations. It has emerged as a powerful framework for fairness, robustness, and reliable prediction, yet the theoretical understanding of multicalibration boosting (MCBoost) remains fragmented and often relies on restrictive assumptions. In this work, we develop a unified and refined perspective on MCBoost that subsumes existing variants, including multiaccuracy, BatchGCP, and BatchMVP. We uncover several phenomena that provide new insights into its practical behavior: even highly accurate and flexible predictors can remain substantially miscalibrated; enforcing multicalibration introduces a calibration-risk trade-off; and early stopping plays a central role in controlling this trade-off. On the theoretical side, we establish a general framework for MCBoost under weaker and more realistic conditions. We show that the boosting iterates converge to a Bregman projection of the population-optimal predictor onto the cumulative span generated by the audit class, thereby explicitly characterizing the function space on which multicalibration is achieved. We further derive convergence rates under different smoothness assumptions, finite-sample guarantees, and principled stopping rules that ensure multicalibration at termination. Finally, we extend the theory of universal adaptability under covariate shift, providing more general transfer guarantees and clarifying when multicalibrated predictors generalize across domains. These results provide a more complete theoretical foundation and practical guidance for multicalibration boosting, positioning it as both a unifying framework and a reliable post-processing approach for modern predictive models.

Deploying clinical prediction models across healthcare systems often fails when key training covariates are unavailable at deployment and labeled outcomes are limited in the target domain. For example, high-performing models for out-of-hospital cardiac arrest (OHCA) rely on detailed prehospital measurements routinely collected in high-resource settings but unavailable in many international registries. Existing methods either discard missing covariates, sacrificing predictive information, or rely on untestable assumptions about their target distribution. We propose DRUM (\underline{D}istributionally \underline{R}obust \underline{U}nsupervised transfer learning with structurally \underline{M}issing covariates), a framework that transfers prediction models to target populations where certain covariates are structurally absent and outcome labels are unavailable. DRUM partitions covariates into shared components ($X$), observed across all settings, and missing components ($A$), observed only in the source. Rather than imputing missing covariates, DRUM optimizes worst-case predictive performance over the unknown target distribution of $A \mid X$ using a neural network generator, with a robustness parameter controlling allowable deviation from the source conditional. We further develop a bias correction procedure that reduces sensitivity to nuisance estimation error. Simulations show substantial improvements in both mean and worst-case prediction error under distribution shift. Applied to cross-national OHCA prediction, transferring models from a US registry to multiple Asian registries where prehospital variables are unrecorded, DRUM yields better-calibrated predictions and improved clinical classification performance across sites.

Topic modeling in applied psychology increasingly spans two methodological traditions: probabilistic bag-of-words models and newer embedding-based approaches. Yet many evaluations of these methods rely on longer and cleaner benchmark corpora, leaving less guidance for short, open-ended survey responses. This paper compares Structural Topic Models (STM), a probabilistic topic model, and BERTopic, an embedding-based model, for analyzing open-ended survey responses. We evaluated three STM conditions and five BERTopic conditions, varying typographical correction, stemming, embedding choice, and contextual augmentation, a strategy we introduced to provide additional semantic context for very short responses. Results indicate that BERTopic consistently produced higher topic coherence than STM, with contextual augmentation yielding the strongest performance gains. In contrast, higher-dimensional embeddings alone did not improve coherence and were associated with greater data loss. Qualitative evaluation showed that BERTopic generated more interpretable and stable topics, while STM topics were often broader and more mixed. However, STM provides stronger support for inferential covariate analysis, whereas BERTopic covariate comparisons are primarily descriptive. These findings suggest that STM and BERTopic offer complementary strengths. We conclude with practical guidance for selecting and combining topic modeling approaches in applied social science research.

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.

Multi-center survival prediction can improve robustness and generalizability, yet privacy regulations and institutional governance often prevent pooling patient-level clinical and genomic data across institutions. In practice, deployment is further complicated by feature-space heterogeneity, in which sites collect different covariates or use different sequencing panels, resulting in only partially overlapping feature sets. We present FederatedRSF, a Python package that implements federated random survival forests, aggregating locally trained survival trees and redistributing only feature-compatible trees to each site, enabling inference with partial overlap without sharing raw data. We evaluate FederatedRSF on the GBSG2 breast cancer cohort distributed with the scikit-survival package, simulating feature heterogeneity across clients by withholding subsets of features, and assessing discrimination using Harrell's concordance index (C-Index) under repeated cross-validation and site-splits. The results demonstrated that the federated model can achieve performance comparable to that of the centralized training setting.

Confidence calibration for classification models is vital in safety-critical decision-making scenarios and has received extensive attention. General confidence calibration methods assume training and test data are independent and identically distributed, limiting their effectiveness under covariate shifts. Previous calibration methods under covariate shift struggle with class-wise or canonical calibrations and often rely on unstable importance weighting when density ratios are large or unbounded. Given the above limitations, this paper rethinks confidence calibration under covariate shifts. First, we derive a necessary and sufficient condition for confidence calibration under covariate shifts, named Expectation consistency condition, which reveals covariate shifts do not necessarily lead to uncalibrated confidence and provides a weaker condition for confidence calibration than global covariate distribution alignment. Then, utilizing Expectation consistency condition, this paper proposes an unsupervised domain adaptation loss to calibrate confidence of the target domain, named Expectation consistency loss (ECL), which is compatible with canonical calibration, class-wise calibration, and top-label calibration. Third, we prove that computing ECL loss has the same sample complexity as Expected Calibration Error (ECE) and provide a theoretically grounded mini-batch trainable scheme for ECL loss. Finally, we validate the effectiveness of our method on both simulated and real-world covariate shift datasets.

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency - where observed variables share no latent confounders - or the pretreatment assumption, which limits covariates to those unaffected by the treatment or outcome. These requirements are often unrealistic in practice, and global learning becomes computationally prohibitive in high-dimensional settings.To address these challenges, we propose a novel local learning method for covariate selection in nonparametric causal effect estimation that avoids both the pretreatment and causal sufficiency assumptions. We first characterize a local boundary that contains at least one valid adjustment set whenever one exists for identifying the causal effect, and then develop local identification procedures to efficiently search within this boundary.We prove that the proposed method is sound and complete. Experiments on multiple synthetic datasets and two real-world datasets show that our approach achieves accurate causal effect estimation while substantially improving computational efficiency.

Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this work, we prove that all parametric models exhibit similar gradient bias for various imputation procedures and characterize exactly the dependence on the missingness ratio vector $p$, with $O(\|p\|)$ as the leading term. We exploit this analysis to propose a simple debiasing procedure for stochastic gradient descent (SGD) with missing values based on Richardson extrapolation, which leverages the exact expression of the gradient bias. The key idea is to \emph{deliberately add missingness}: from an already incomplete observation, we generate a further-thinned version at a higher, controlled missingness level, and combine the two resulting stochastic gradients to cancel the leading bias term. We prove that one Richardson step reduces the gradient bias from $O(\|p\|)$ to $O(\|p\|^2)$ under several missingness scenarios. Our proposed method is computationally efficient, model-agnostic and applies to any parametric loss whose stochastic gradient can be computed after imputation. Furthermore, when missing indicators are independent, the population gradient bias is a multilinear polynomial in $p$ and depends only on population gradient errors induced by declaring a single coordinate missing. In this case, our method generalizes to a multi-step Richardson procedure which recursively cancels higher-order terms. Empirically, Richardson debiasing improves optimization and estimation across several generalized linear models and combines positively with widely used imputation procedures such as MICE. These results suggest that, somewhat counter-intuitively, adding controlled missingness on top of existing missing data can make stochastic learning from incomplete data more accurate.

A unified framework for learning under covariate shift is presented, in which a constrained density-ratio network approximates the Radon-Nikodym derivative $r^\star = dP/dQ$ and feeds an anytime PAC-Bayes generalization certificate. A change-of-measure identity decomposes the gap between target risk and importance-weighted source risk into a ratio-bias term governed by $\|r_θ- r^\star\|_{L^2(Q)}$ and a generalization-gap term governed by the variability of the weighted loss. Normalization and moment-matching identities are enforced as hard integral constraints through an augmented-Lagrangian scheme, with a second-moment penalty controlling the effective sample size. PAC-Bayes is instantiated on the weighted risk in a fixed-time regime that yields Bernoulli-KL bounds, identifies the network-weighted Gibbs posterior as the unique KL-regularized minimizer, and quantifies stability under $L^2(Q)$ perturbations of the learned ratio, and is then strengthened by geometric peeling to an anytime certificate uniform in $t \geq t_{\min}$. A pre-registered two-campaign protocol combining a patch test against analytic ground truth with a real-data deployment validates the framework: the network produces calibrated ratios, reduces target $0/1$ loss against unweighted ERM and classical direct ratio-estimation baselines, and attains the anytime certificate. A single fixed-time coverage failure is recorded, with per-split coverage aligning one-to-one with the magnitude of the label shift, confirming that the covariate-only assumption is operationally tight rather than a defect of the certificate.

Large-scale pretraining on Earth observation imagery has yielded powerful representations of the natural and built environment. However, most existing geospatial foundation models do not directly model the structured socioeconomic covariates typically stored in tabular form. This modality gap limits their ability to capture the complete total environment, which is critical for reasoning about complex environmental, social, and health-related outcomes. In this work, we propose GeoViSTA (Geospatial Vision-Tabular Transformer), a vision-tabular architecture that learns unified geospatial embeddings from co-registered gridded imagery and tabular data. GeoViSTA utilizes bilateral cross-attention to exchange spatial and semantic information across modalities, guided by a geography-aware attention mechanism that aligns continuous image patches with irregular census-tract tokens. We train GeoViSTA with a self-supervised joint masked-autoencoding objective, forcing it to recover missing image patches and tabular rows using local spatial context and cross-modal cues. Empirically, GeoViSTA's unified embeddings improve linear probing performance on high-impact downstream tasks, outperforming baselines in predicting disease-specific mortality and fire hazard frequency across held-out regions. These results demonstrate that jointly modeling the physical environment alongside structured socioeconomic context yields highly transferable representations for holistic geospatial inference.

We introduce and analyze Target-Induced Loss Tilting (TILT) for unsupervised domain adaptation under covariate shift. It is based on a novel objective function that decomposes the source predictor as $f+b$, fits $f+b$ on labeled source data while simultaneously penalizing the auxiliary component $b$ on unlabeled target inputs. The resulting fit $f$ is deployed as the final target predictor. At the population level, we show that this target-side penalty implicitly induces relative importance weighting at the population level, but in terms of an estimand $b^*_f$ that is self-localized to the current error, and remains uniformly bounded for any source-target pair (even those with disjoint supports). We prove a general finite-sample oracle inequality on the excess risk, and use it to give an end-to-end guarantee for training with sparse ReLU networks. Experiments on controlled regression problems and shifted CIFAR-100 distillation show that TILT improves target-domain performance over source-only training, exact importance weighting, and relative density-ratio baselines, with a stable dependence on the regularization parameter.

Time Series Foundation Models (TSFMs) have recently achieved state-of-the-art performance, often outperforming supervised models in zero-shot settings. Recent TSFM architectures, such as Chronos-2 and TabPFN-TS, aim to integrate covariates. In this paper, we design controlled experiments based on simple target-covariate relationships to assess this integration capability. Our results show that TabPFN-TS captures these relationships more effectively than Chronos-2, especially for short horizons, suggesting that the strong benchmark performance of Chronos-2 does not automatically translate into optimal modeling of simple covariate-target dependencies.

In causal inference, confounders are variables that influence both treatment decisions and outcomes. However, unlike as in randomized clinical trials, the treatment assignment mechanism in observational studies is not known, and it is thus unclear which covariates act as confounders. Here, we aim to generate insight for causal inference and answer: which of the observed covariates act as confounders? We introduce ConfoundingSHAP, a Shapley-based method for attributing confounding strength to individual covariates. Our contributions are twofold. First, we propose a Shapley game targeted to infer the confounding strength of the covariates. Our resulting Shapley values differ from the standard applications of SHAP explanations on causal targets, such as understanding treatment effect heterogeneity, which are ill-suited for our task. Second, as our task requires evaluating the value function over many adjustment sets, we provide a scalable TabPFN-based estimation that avoids exhaustive refitting. We demonstrate the practical value across various datasets, where ConfoundingSHAP provides informative explanations of which observed covariates drive confounding and thereby helps to provide more insight for causal inference in practice.

Learning parity functions, more general modular addition, is a challenging machine learning task due to its input sensitivity. A recent study substantially scaled modular addition learning in both the number of summands and the modulus. Its key idea is to increase zeros in training sequences, reducing the effective number of summands and thus controlling training difficulty; however, this induces covariate shift between training and test input distributions. This study theoretically and empirically analyzes this side effect and proposes a covariate-shift-free method for modular addition. Specifically, we introduce an auxiliary modulus $Kq$ during training, which reduces wrap-around frequency and problem difficulty while preserving the same input distribution across training and testing. Experiments show strong scalability and sample efficiency: even for large input length $N$, large modulus $q$, and small datasets -- where the sparse method fails to learn -- our method achieves equal or better match accuracy and relaxed $τ$-accuracy. For example, at $N=64$ and $q=974269$, our method trained on 100K samples achieves $97.0\%$ $τ$-accuracy at $τ=0.05$, while the sparse method achieves only $9.5\%$ with the same data size and $93.9\%$ even when extended to 1M samples.

Randomized controlled trials typically assume that prognostic covariates are known and available at no cost. In practice, obtaining high-dimensional pretreatment data is costly, forcing a trade-off between covariate-adaptive precision and a measurement budget. We introduce Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS), which treats covariate acquisition as a sequential optimization problem embedded within a design-based causal inference task. A budgeted combinatorial Thompson sampler learns which covariates are most prognostic across successive batches; selected covariates then drive rerandomization and regression adjustment to reduce batch-level average treatment effect variance. Our primary theoretical contribution is a decoupling result: adaptive covariate selection based on past batches preserves batch-level randomization validity, and the cumulative inverse-variance weighted estimator achieves at least nominal asymptotic coverage. We further derive a Bayes risk bound for the acquisition layer that matches the minimax lower bound up to logarithmic factors. Empirically, DARTS systematically concentrates the budget on informative features, significantly closing the efficiency gap to oracle designs while maintaining strict inferential validity.

This position paper argues that, in debiased machine learning, balancing functions should be derived from the Neyman orthogonal score, not chosen only as functions of covariates. Covariate balancing is effective when the regression error entering the score can be represented by functions of covariates alone, and it is the natural finite-dimensional approximation for targets such as ATT counterfactual means. For ATE estimation under treatment effect heterogeneity, however, the score error generally contains treatment-specific components because the outcome regression is a function of the full regressor $X=(D,Z)$. In that case, balancing common functions of $Z$ can leave the treatment-specific component unbalanced. We therefore advocate regressor balancing, implemented by Riesz regression with basis functions of $X$, as the general balancing principle for DML. The position is not that covariate balancing is invalid, but that covariate balancing should be understood as the special case that is appropriate when the score-relevant regression error is a function of covariates alone.

Estimating causal effects from observational data requires identifying valid adjustment sets. This task is especially challenging in realistic settings where latent confounding and feedback loops are present. Existing approaches typically assume acyclicity or rely on global causal structure learning, limiting applicability and computational efficiency. In this work, we study a local, data-driven method for covariate selection based on conditional independence information. While this method is known to be sound and complete in acyclic causal models, its validity in the presence of cycles has remained unclear. Our main contribution is to show that these guarantees extend to cyclic causal models. In particular, our result relies on the invariance of conditional independence assertions under $σ$-acyclification. These findings establish a unified, cycle-agnostic perspective on covariate selection and causal effect estimation, showing that the method applies across cyclic and acyclic settings without modification. Empirically, we validate this on extensive synthetic data, showing reliable performance in cyclic causal models.

Conformal prediction is a framework that provides valid uncertainty quantification for general models with exchangeable data. However, in the online learning and time-series settings, exchangeability is not satisfied. Existing online conformal methods, such as adaptive conformal inference (ACI), can achieve long-run validity, yet they remain inefficient under covariate heterogeneity because they rely on global calibration. We propose \emph{Online Localized Conformal Prediction (OLCP)}, which combines online adaptation with covariate-dependent localization to better reflect heterogeneity. To reduce sensitivity to the localization bandwidth, we further develop \emph{OLCP-Hedge}, which performs bandwidth selection as an online expert aggregation problem using a constrained online convex optimization framework. Importantly, we provide coverage guarantees for both algorithms and demonstrate through simulations and real-data experiments that the proposed methods attain valid long-run coverage with narrower prediction sets than existing baselines.

We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincare inequality first reduces temporal risk volatility to derivative energy. A Jacobian-velocity theorem then supplies the corresponding pathwise control. Given explicit regularity and domination assumptions, the theorem identifies directional tangent energy along the deployment path as the governing quantity. Under low-rank drift, that quantity reduces to directional Jacobian energy in the drift subspace, motivating drift-aligned tangent regularization (DTR) and a matched monitoring proxy. Rather than smoothing the network isotropically, DTR penalizes sensitivity only along estimated drift directions. We validate the theorem-to-method pipeline in four experiments: a synthetic benchmark for the time-domain inequality, a controlled synthetic comparison against isotropic Jacobian regularization, and two frozen-deployment studies on the UCI Air Quality and Tetouan power-consumption datasets. DTR reduces risk volatility and directional gain in the controlled low-rank regime and beats isotropic smoothing there. It also gives validation-selected deployment gains on both real datasets, with the Air Quality subspace estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit.

Doubly Robust (DR) estimation of treatment effect relies on an untestable assumption that is the absence of unobserved confounding. This assumption is par- ticularly problematic in the context of healthcare research, where variables like pre- scription refill rates serve as proxies for unobserved behaviors such as medication adherence. These proxy variables are often endogenous, exhibiting correlation with the regression error term due to unmeasured confounding or measurement error. We propose a copula-corrected doubly robust estimator that addresses endogeneity in both the treatment and outcome models without requiring instrumental variables. Gaussian copulas model the joint distribution of endogenous covariates and the error term, enabling consistent estimation while preserving the doubly robust property that requires correct specification of either the treatment or outcome model, not both. Monte Carlo simulations demonstrate that naive DR estimation exhibits substantial bias under endogeneity, whereas our corrected estimator recovers unbiased treatment effects across different data-generating processes. We apply our method to examine the effect of nutritional counseling on blood pressure using the National Health and Nutrition Examination Survey (NHANES) data. Naive DR estimation suggests counseling is associated with increased blood pressure. After copula correction, this effect becomes statistically insignificant, consistent with literature showing modest effects of nutri- Counseling in reducing blood pressure. Our methodology provides researchers with a practical tool for obtaining treatment effects in the presence of endogeneity.

Conformal prediction (CP) provides powerful, distribution-free prediction sets, but its guarantees rely on the exchangeability of training and test data, which is often violated in practice due to covariate shifts. While weighted conformal prediction (WCP) is designed to handle such shifts, it can suffer from significant undercoverage when the density ratio between the distributions is unbounded and/or must be learned. This is because of both overfitting in learning the density ratio, and high variance in estimating the nonconformity score threshold. To address this, we introduce clipped least-squares importance fitting (CLISF) as a reduced-variance method for density ratio estimation. Specifically, we show that density ratios learned using CLISF, when plugged into WCP, have bounded expected undercoverage. Furthermore, we show that the undercoverage can be corrected by running WCP with a slightly inflated coverage target; crucially, we are able to estimate the required level of inflation from the data. We provide the first theoretical guarantees for weight clipping in conformal inference, achieving dataset-conditional coverage with a sample complexity that does not blow up with the higher moments of the true density ratio -- a key limitation of prior work. We verify our results on real-world benchmarks and synthetic data.

We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However, incorporating covariates potentially breaks the exchangeability assumption under the null, which further complicates a calibration procedure. To address these issues, we propose a semi-supervised method that produces a test statistic with asymptotic normality, while effectively integrating additional information from covariates. Our test is straightforward to calibrate due to the asymptotic normality under the null and achieves asymptotic power that is often much higher than existing kernel tests without covariates. Furthermore, we formally show that the proposed method is consistent in power against fixed and local alternatives. Simulations confirm the practical and theoretical strengths of our approach.

Reliable subnational population estimates are essential for applications, yet remain difficult where censuses are sparse, outdated or spatially coarse. Existing population-mapping workflows rely on hand-built geospatial covariates, such as settlement extent, night-time lights, and environmental conditions, which must be assembled and harmonised across scales and geographies. Geospatial foundation models offer an alternative by learning reusable representations of place from more multifaceted and heterogeneous data sources. Here, we benchmark Population Dynamics Foundation Model (PDFM) embeddings against the harmonised geospatial covariates for subnational population estimation in Brazil, Nigeria and the United States. Under geographically structured validation, PDFM increased predictive fit by a median of 20.1% (IQR: 10.0-33.2%, across country-model comparisons) reduction in unexplained variance, and reduced Kullback-Leibler divergence by 23.2% (9.2-26.2%). However, these gains were uneven. PDFM was most advantageous where the geospatial covariates weakly characterised settlement context, such as larger and less-developed subnational areas. Moreover, PDFM performance was scale-coupled with embeddings providing less flexible transfer across spatial aggregations than geospatial covariates. These findings showed that geospatial foundation-model representations of place can improve population estimation in data poor settings, but their benefits break down predictably under spatial scale mismatch, revealing a fundamental limitation of current geospatial AI.

Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet existing vector and scalar results typically rely on bounded covariates and an explicit regularization matrix, producing bounds that are \emph{not scale-invariant}: although the self-normalized quantity is scale-invariant by definition, its standard upper bounds are not. We characterize when scale-invariant upper bounds on self-normalized martingales are possible. Without further assumptions, we prove that nontrivial scale-invariant bounds exist only in dimension $d=1$; moreover, in $d=1$ we obtain $O(\log T)$ scale-invariant self-normalized bounds without any assumptions on the covariates. In contrast, for $d>1$ we show that no nontrivial scale-invariant bound can hold in full generality. We then connect this dichotomy to \emph{doubly-uniform} regret in online linear regression (i.e., regret bounds that are simultaneously independent of the covariate scale and the comparator norm) and use it to resolve the open question of Gaillard, Gerchinovitz, Huard, and Stoltz, \emph{``Uniform regret bounds over $\mathbb{R}^d$ for the sequential linear regression problem with the square loss''} (ALT 2019): in $d=1$ we give an explicit algorithm with $O(\log T)$ doubly-uniform regret, whereas for $d>1$ sublinear doubly-uniform regret is impossible. Finally, under a natural \emph{smoothness} condition (bounded Radon--Nikodym derivatives of the conditional covariate laws with respect to a fixed base measure), we recover sublinear regret for $d>1$ without bounded covariates and derive a self-normalized concentration inequality free of the usual regularization penalties, yielding arguably a first natural scale-invariant bound for adaptive, non-i.i.d. vector martingales.

We study high-dimensional LASSO under differential privacy via objective perturbation with heterogeneous covariate scales. In practical scenarios, covariates often exhibit diverse scales; however, standard preprocessing is problematic under privacy constraints, as it consumes additional privacy budget. This heterogeneity induces effective anisotropy in the objective perturbation via the inverse Gram matrix of covariates, which can degrade the stability and accuracy of algorithms. To address this, we propose a Gram-based anisotropic objective perturbation, a ``pre-distortion" strategy that counteracts the distortion from the covariate structure to restore isotropy in the estimation process. Using an Approximate Message Passing (AMP) framework and state evolution analysis, we demonstrate that our proposed perturbation significantly stabilizes convergence and improves both statistical efficiency and privacy performance compared to standard uniform noise injection. Our results provide theoretical insights into designing stable and efficient private estimators without relying on data-dependent preprocessing.

We study the problem of understanding where two populations differ within a feature space, which we formalize in the concept of a differential subgroup: a subset of individuals from both populations who, despite sharing similar characteristics, exhibit exceptional differences in a target outcome. Differential subgroups reveal the regions of the feature space where population-level gaps are most pronounced and can help practitioners identify the covariate combinations that are structurally responsible for these differences, e.g.~in clinical analysis, model diagnostics, or treatment-effect studies. We introduce a general optimization objective for discovering differential subgroups and establish conditions under which the resulting subgroups admit a causal interpretation of population differences. We propose DiffSub, a gradient-based approach that discovers interpretable differential subgroups in tabular data. Across synthetic benchmarks, medical case studies, model-error analyses, and treatment-effect settings, DiffSub identifies informative subgroups that reveal where population differences arise and why.

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static method does not account for changes in spatial correlation induced by covariates, limiting its ability to predict nonstationary GPs under new covariate conditions. To enable predictive modeling of the deformation method, we propose to model the spatial deformation as a function of covariates. The spaces of diffeomorphic deformations and Euclidean covariate vectors are connected by characterizing deformations as generated by velocity fields living in a Lie algebra. To overcome the estimation instability caused by high-order interactions between multiple covariates in a general Lie algebra, we prove that those interactions can be truncated with a moderate physical assumption. Based on the theoretical results, a concise functional form of deformations driven by multiple covariates can be established, and an efficient estimation-inference algorithm is developed for out-of-sample nonstationary GP prediction with limited covariate-deformation sample pairs. The effectiveness and generalizability of the method are demonstrated on a simulation study and two case studies, in the fields of manufacturing and geostatistics, respectively.

Malaria, childhood acute respiratory infection, and child undernutrition together account for over two million deaths annually in children under five, with the burden concentrated in low and middle-income countries where climate variability modulates transmission, exposure, and nutritional outcomes. Routine health surveillance in these settings remains sparse and reactive. Satellite-derived representations of the Earth's surface offer a scalable, low-cost complement to traditional covariates, yet their utility as predictors of population health outcomes is poorly characterised. We summarise findings from three studies evaluating AlphaEarth Foundations 64-dimensional satellite embeddings as predictors of population health outcomes, focusing on vulnerable populations. The studies span infectious disease (malaria, respiratory infection) and stunting. In each study, embeddings provide predictive value at sufficient spatial granularity: (i) malaria prediction across Nigeria shows consistent per-region R^2 gains; (ii) childhood acute respiratory infection prediction across 11 DHS countries increases pooled R^2 from 0.157 to 0.206 across three tree-based estimators; (iii) stunting prediction across 35 countries is neutral at country level due to collinearity with fixed effects. The stunting case is currently limited by lack of DHS cluster-level coordinates, which is the next key experiment.

Federated learning (FL) trains a shared model from updates contributed by distributed clients, often implicitly assuming that contributing clients are representative of the target population. In practice, this representativeness assumption can fail at two distinct stages, inducing selection bias. First, eligibility rules such as device constraints, software requirements, or user consent determine which clients are ever enrolled and reachable for training, inducing \emph{enrollment bias}. Second, among enrolled clients, user and system factors such as battery state, network status, and local time determine which clients participate in each communication round, inducing \emph{participation bias}. Although existing work has largely addressed round-level participation bias, it has paid far less attention to population-level enrollment bias, which can induce a persistent mismatch between the training objective and the target-population objective. We formalize FL under a two-stage selection model and derive \textsc{FedIPW}, an inverse-probability-weighted aggregation scheme that recovers the target-population mean update under standard ignorability and positivity assumptions. Because client-level covariates are often unavailable for non-enrolled clients, we also introduce a limited-information aggregate-calibration extension that uses known target-population summaries to reweight the enrolled sample, partially correcting enrollment bias. We further provide an algorithm-agnostic optimization analysis under residual weighting error and show that incomplete selection correction can induce a non-vanishing bias floor. Finally, experiments on synthetic federated logistic regression validate the predicted objective mismatch and show that enrollment correction reduces target-population error under two-stage selection.

Synthetic tabular data are often evaluated by distributional similarity, privacy distance, or train-on-synthetic-test-on-real predictive performance, but these criteria do not ensure validity for causal inference. We show that fully generative tabular synthesizers, including GAN- and LLM-based models, can preserve predictive utility while distorting average treatment effect (ATE) estimates. The failure is structural: ATE preservation requires both a realistic covariate law and an accurate treatment-effect contrast, whereas prediction loss penalizes treatment-effect error only through an overlap-weighted term. Thus, under imbalance or limited overlap, a generator may reproduce dominant observed outcomes while underlearning intervention-relevant contrasts. We formalize this mismatch through sensitivity and loss-decomposition results. Motivated by this causal analysis and intuition, we propose a hybrid synthetic-data framework for causal inference that generates covariates while modeling treatment and outcome mechanisms separately. We evaluate the framework in three settings: ATE preservation under fully generative versus hybrid synthesis, augmentation for practical positivity problems, and diagnostic simulation engines for comparing OR, IPW, AIPW, and TMLE before real-data analysis. We also stress-test the hybrid construction across settings that vary overlap, covariate dimension, seed sample size, and treatment-effect complexity, including a logistic outcome-model misspecification check. Across controlled simulation experiments, hybrid synthesis improves causal fidelity relative to fully generative baselines; the ACTG application shows improved predictive fidelity and potential for finite-sample estimator benchmarking. LLM-based hybrid synthesis is often more faithful than CTGAN in settings where causal fidelity can be assessed.

Predicting customers' long-term revenue from sparse and irregular transaction data is central to marketing resource allocation in non-contractual settings, yet existing approaches face a trade-off. Traditional probabilistic customer base models deliver robust long-horizon forecasts by imposing strong structural assumptions, while flexible machine-learning models often require substantial training data and careful tuning. We propose a variational-autoencoder-based model that preserves the process-based likelihood of established attrition-transaction-spend models conditional on customer heterogeneity, but replaces the restrictive parametric mixing distribution with a flexible latent representation learned by encoder-decoder networks. The resulting approach (i) provides a single model for customer attrition, transactions and spending, (ii) remains reliable when contextual covariates are unavailable, and (iii) flexibly incorporates rich covariates and nonlinear effects when they are available. This design balances structural stability with the flexibility needed to capture complex purchase dynamics. Across multiple real-world datasets and prediction horizons, the proposed model improves upon the latest benchmarks. Businesses benefit directly, as a better assessment of customers' future revenues improves the efficiency of campaign targeting. For research, this work provides guidance on how to embed domain-specific models into the variational autoencoder framework, enabling flexible representation learning while retaining an econometrically meaningful process structure.

Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications -- estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM -- demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.

Causal inference from electronic health records (EHR) is fundamentally limited by unmeasured confounding: critical clinical states such as frailty, goals of care, and mental status are documented in free-text notes but absent from structured data. Large language models can extract these latent confounders as interpretable, structured covariates, yet how to effectively integrate them into causal estimation pipelines has not been systematically studied. Using the MIMIC-IV database with 21,859 sepsis patients, we compare seven covariate-integration strategies for estimating the effect of early vasopressor initiation on 28-day mortality, spanning tabular-only baselines, traditional NLP representations, and three LLM-augmented approaches. A central finding is that not all integration strategies are equally effective: directly augmenting the propensity score model with LLM covariates achieves the best performance, while dual-caliper matching on text-derived categorical distances restricts the donor pool and degrades estimation. In semi-synthetic experiments with known ground-truth effects, LLM-augmented propensity scores reduce estimation bias from 0.0143 to 0.0003 relative to tabular-only methods, and this advantage persists under substantial simulated extraction error. On real data, incorporating LLM-extracted covariates reduces the estimated treatment effect from 0.055 to 0.027, directionally consistent with the CLOVERS randomized trial, and a doubly robust estimator yielding 0.019 confirms the robustness of this finding. Our results offer practical guidance on when and how text-derived covariates improve causal estimation in critical care.

External validation is widely regarded as the gold standard for prognostic model evaluation. In this study, we challenge the assumption that successful external calibration guarantees model generalizability and propose two complementary strategies to improve transportability of prognostic models across cohorts. Using six real-world surgical cohorts from tertiary academic centers, we tested whether successful external calibration depends largely on similarity in covariates and outcomes between training and validation cohorts, quantified using Kullback-Leibler (KL) divergence, with calibration assessed by the Integrated Calibration Index (ICI). From the model-developer's perspective, we trained the "best-on-average" prognostic model by tuning toward a meta-analysis-derived covariate and outcome distribution as an approximation of the broader target population. From the end-user perspective, we proposed a simple measure for cohort outcome similarity to identify, among published models, the one most suitable for a given target cohort in terms of both calibration and clinical utility. External calibration worsened as distributional mismatch increased. Higher KL divergence was associated with higher ICI in both surgery-alone (Spearman $ρ=0.614$, $p=0.004$) and surgery + adjuvant chemotherapy cohorts (Spearman $ρ=0.738$, $p<0.001$). Meta-analysis-informed weighting improved calibration in most settings without materially affecting discrimination, with the clearest benefit when evaluated on the aggregated external population ($p=0.037$). Models developed in more similar cohorts achieved lower ICI in surgery-alone (Spearman $ρ=0.803$, $p<0.001$) and surgery + adjuvant chemotherapy cohorts (Spearman $ρ=0.737$, $p<0.001$), and provided greater clinical utility on DCA.

Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose CALM (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source's features into a common representation space. OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate CALM in two forms: a closed-form linear version, CALM-Lin, and a neural representation-learning version, CALM-NN. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while CALM-NN wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies CALM-NN delivers the largest gains over the trial-only baseline.

Out-of-distribution (OOD) detection remains a critical challenge in open-world learning, where models must adapt to evolving data distributions. While recent vision-language models (VLMS) like CLIP enable multimodal OOD detection through Dual-Pattern Matching (DPM), existing methods typically suffer from two major shortcomings: (1) They rely on fixed fusion rules and assume static environments, failing under temporal drift; and (2) they lack robustness against covariate shifted inputs. In this paper, we propose a novel two-step framework to enhance OOD detection and covariate distribution shift robustness in dynamic settings. We extend the dual-pattern regime into Temporal Quadruple-Pattern Matching (T-QPM). First, by pairing OOD images with text descriptions, we introduce cross-modal consistency patterns between ID and OOD signals, refining the decision boundary through joint image-text reasoning. Second, we address temporal distribution shifts by learning lightweight fusion weights to optimally combine semantic matching and visual typicality. To ensure stability, we enforce explicit regularization based on Average Thresholded Confidence (ATC), preventing performance degradation as distributions evolve. Experiments on temporally partitioned benchmarks demonstrate that our approach significantly outperforms static baselines, offering a robust, temporally-consistent framework for multimodal OOD detection in non-stationary environments.

Cost-per-click (CPC) in paid search is an auction-generated outcome shaped by a competitive landscape that is only partially observable from any single advertiser's history. From 1.66 billion Google Ads log records for a concentrated car-rental market (2021-2023), we construct a weekly panel of 1,811 keyword series over 127 weeks (218,924 keyword-week observations) and build competition-aware proxies from keyword text, CPC trajectories, and geographic market structure. The design combines (i) semantic neighborhoods and a semantic keyword graph from pretrained transformer-based keyword representations, (ii) behavioral neighborhoods from Dynamic Time Warping (DTW) alignment of CPC trajectories, and (iii) geographic-intent covariates capturing localized demand and marketplace heterogeneity. We evaluate these signals both as exogenous covariates and as relational priors in spatiotemporal graph forecasters, benchmarking them against statistical, neural, and time-series foundation-model baselines. The results reveal a clear horizon crossover. At one week, graph-based models achieve the lowest error, reducing sMAPE by 15.1% relative to the strongest classical/ML baseline; at the six- and twelve-week horizons, covariate-augmented foundation models dominate, reducing sMAPE by 22.5% and 27.6%, respectively. The gains concentrate in the high-CPC, high-volatility keywords where forecasting errors are most costly. A falsification battery supports the competition interpretation at the planning horizon: the semantic competition graph outperforms a confounder-matched non-competitive graph by 4.05 sMAPE points, and matched-neighbour and time-shuffled controls show the six-week gains are competition-specific rather than generic smoothing. Together, the findings establish a horizon-dependent competition-aware forecasting design for auction-driven advertising markets under partial observability.

We revisit transductive learning where predictions are made with the set of all covariates known in advance. In the leave-one-out (LOO) setting, the prediction is made with labels of the remaining sample points and evaluated by the average error. In particular, we study multiplicative oracle inequalities for agnostic transductive LOO prediction for a variety of tasks, including classification with 0-1 loss, squared loss regression, density estimation, and logistic regression. Specifically, we introduce \emph{Median of Level-Set Aggregation} (MLSA), an aggregation procedure built on near-ERM level sets (i.e., empirical-risk level sets around the ERM). We prove a general multiplicative oracle inequality for the LOO error of the form $$LOO_S(MLSA) \;\le\; C \left( \frac{1}{n} \min_{h\in H} L_S(h) \;+\; \frac{\log |H|}{n}\right), \qquad C>1,$$ where $H$ is the hypothesis/function class. This inequality holds for hypothesis classes under a local level-set growth condition together with losses satisfying a mild monotonicity assumption. For classification with VC classes under the $0$--$1$ loss, the $\log |H|$ factor can be improved to be $d\log n$, where $d$ is the VC dimension, recovering Long (1998) up to a $\log n$ factor. For logistic regression with bounded covariates and parameters, the $\log |H|$ factor can be improved to be $d\log n$ up to problem-dependent factors, where $d$ is the ambient dimension.

Factorizable joint shift (FJS) represents a type of distribution shift (or dataset shift) that comprises both covariate and label shift. Recently, it has been observed that FJS actually arises from consecutive label and covariate (or vice versa) shifts. Research into FJS so far has been confined mostly to the case of categorical labels. We propose a framework for analysing distribution shift in the case of a general label space, thus covering both classification and regression models. Based on the framework, we generalise existing results on FJS to general label spaces and present and analyse a related extension to label distribution estimation of the expectation maximisation (EM) algorithm for class prior probabilities. We also take a fresh look at generalized label shift (GLS) in the case of a general label space.

Effective HFMD surveillance requires forecasts capturing both time-series patterns and contextual drivers such as school calendars, weather, and policy or surveillance reports. In clinical settings, forecasts must be trusted and actionable; thus, beyond point accuracy, decision-makers require concise, auditable explanations of why risk is expected to rise or fall. Classical models (e.g., ARIMA and Prophet) and foundation models (e.g., Chronos, Moirai, and TimesFM) treat external covariates as numerical inputs, lacking semantic reasoning to reflect epidemiological mechanisms or resolve conflicting signals. We propose a two-agent neuro-symbolic framework that decouples contextual interpretation from probabilistic forecasting. An LLM-based Event Interpreter ingests heterogeneous signals -- school schedules, weather summaries, government reports, and clinical guidelines -- and outputs a scalar transmission-impact signal. A Forecast Generator combines this signal with historical case counts to produce point forecasts that are mapped to probabilistic predictions through Poisson/negative-binomial moment matching. We focus on one-week-ahead rolling forecasts, aligning with weekly hospital-capacity planning and the rapid, context-driven inflections typical of HFMD. We evaluate on two datasets: Hong Kong surveillance (90 target weeks in 2023--2024) and Lishui hospital visits (33 target weeks in 2024). Against traditional and foundation-model baselines, our approach achieves competitive point accuracy while providing robust 90% intervals (coverage approximately 0.85--1.00) and concise rationales. This demonstrates that integrating domain knowledge through LLM-based agents can match strong numerical forecasters while yielding interpretable, context-aware forecasts aligned with public-health decision-making.

We introduce Gradient Boosted Mixed Models (GBMixed), a framework which extends boosting to clustered data by jointly modeling the mean and variance components in a linear mixed model via likelihood-based gradients. GBMixed estimates a nonparametric fixed effects function characterizing the overall mean of the response, while also allowing the random effects covariance matrix along with the residual variance to depend on covariates in a flexible manner. We demonstrate how GBMixed facilitates covariate-dependent random effect predictions, and subsequently point predictions and prediction intervals for individual treatment effects, that can adapt between population-level and cluster-level information. Simulations and applications to two real-world datasets demonstrate that GBMixed can accurately recover complex nonlinear fixed effect functions and covariate-dependent covariances in a linear mixed model, while also improving point and probabilistic predictive performance compared with several existing approaches such as parametric linear mixed models, Natural Gradient Boosting, and Gaussian Process Boosting.

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset and delete entries in up to an $η$-fraction of samples per coordinate; a strong form of the Missing Not At Random model. In the corrupted data setting, the adversary instead replaces values arbitrarily, and the corruption locations are unknown to the learner. Despite substantial work on missing data, linear regression under such adversarial missingness remains poorly understood, even information-theoretically. Unlike the clean setting, where estimation error vanishes with more samples, here the optimal error remains a positive function of the problem parameters. Our main contribution is to characterize this error up to constant factors across essentially the entire parameter range. Specifically, we establish novel information-theoretic lower bounds on the achievable error that match the error of (computationally efficient) algorithms. A key implication is that, perhaps surprisingly, the optimal error in the missing data setting matches that in the corruption setting-so knowing the corruption locations offers no general advantage.

Regression problems with bounded continuous outcomes frequently arise in statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting the response at a new covariate value. Most of the existing literature has focused either on point prediction or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes within the framework of transformation regression models, encompassing widely used models such as beta regression and logit-normal regression. We construct non-conformity scores based on model-aligned residuals and identify a quantile-residual score that is particularly well suited to bounded outcomes, bridging normalized conformal prediction and distributional conformal prediction. This score accounts for both the heteroscedasticity inherent in such data and the asymmetry that emerges near the boundaries of the response space. We establish marginal validity and asymptotic conditional validity for both full and split conformal prediction, holding under model misspecification. A comprehensive simulation study confirms that both methods empirically attain valid finite-sample coverage, including cases under model misspecification. A real-data application demonstrates their practical performance against bootstrap-based alternatives.

We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed basis expansions, which limit flexibility and degrade performance under irregular sampling. PSLR leverages the well-established properties of path signatures - basis-free representation, cross-channel dependency capture, and robustness to sampling irregularity - as an enabling tool. The key novelty, however, lies in two distinctive contributions: (i) a semi-parametric additive structure that preserves interpretable linear effects for scalar covariates, and (ii) a fully data-driven procedure for adaptively selecting the signature truncation order via a penalized empirical risk criterion. This selection mechanism is supported by rigorous non-asymptotic guarantees, including the existence of an optimal truncation order, its consistent estimation from finite samples, convergence rates for the classifier risk, a finite computable search bound, and an error propagation framework that formally quantifies PSLR's robustness under irregular sampling. Experiments on synthetic and real-world datasets demonstrate that PSLR with adaptive order selection consistently outperforms traditional functional classifiers and fixed-order signature baselines in accuracy, robustness, and interpretability. Our results highlight the practical and theoretical value of integrating rough path theory with adaptive model complexity control.

Disentangled representations separate factors that are shared across conditions from those that are condition-specific. Such separation is needed for generalization to new domains, treatments, patients, or species. A dominant line of work pursues this goal through variational formulations. While these approaches achieve partial disentanglement, they often exhibit three common limitations: they either do not remove all condition-specific information from the condition-specific representation, allow the condition-specific representation to become uninformative, or impose independence assumptions that do not reflect the underlying generative process. In this work, we introduce DisCoVR, a variational framework that addresses these limitations. Its objective is aligned with the probabilistic structure of the data-generating process, and includes an adversarial term that prevents condition-specific information from being encoded in the condition-specific representation.DisCoVR reconstructs the data from both shared and condition-specific representations, ensuring that each remains informative, and uses a structured prior that further reinforces the informativeness of both representations. We show that across synthetic, image, and single-cell RNA-sequencing datasets, DisCoVR achieves stronger disentanglement compared to previous approaches.

In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural network trained on the imputed data, PENNs pass the vectors of observation indicators through a second neural network to provide a compact representation. The outputs are then combined in a third neural network to produce final predictions. Our main theoretical result exploits an assumption that the observation patterns can be partitioned into cells on which the Bayes regression function behaves similarly, and belongs to a compositional Hölder class. It provides a finite-sample excess risk bound that holds for an arbitrary missingness mechanism, and in combination with a complementary minimax lower bound, demonstrates that our PENN estimator attains in typical cases the minimax rate of convergence as if the cells of the partition were known in advance, up to a poly-logarithmic factor in the sample size. Numerical experiments on simulated, semi-synthetic and real data confirm that the PENN estimator consistently improves, often dramatically, on standard neural networks without pattern embedding. Code to reproduce our experiments, as well as a tutorial on how to apply our method, is publicly available.

Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting (IPCW). Unfortunately, IPCW is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to IPCW. Source code is available at https://github.com/thecml/DependentEVAL.

We propose the use of latent space generative world models to address the covariate shift problem in autonomous driving. A world model is a neural network capable of predicting an agent's next state given past states and actions. By leveraging a world model during training, the driving policy effectively mitigates covariate shift without requiring an excessive amount of training data. During end-to-end training, our policy learns how to recover from errors by aligning with states observed in human demonstrations, so that at runtime it can recover from perturbations outside the training distribution. Additionally, we introduce a novel transformer-based perception encoder that employs multi-view cross-attention and a learned scene query. We present qualitative and quantitative results, demonstrating significant improvements upon prior state of the art in closed-loop testing in the CARLA simulator, as well as showing the ability to handle perturbations in both CARLA and NVIDIA's DRIVE Sim.

This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available. Min-norm interpolators arise naturally as implicit regularized limits of modern machine learning algorithms. Prior work has characterized their out-of-distribution risk when samples from the test distribution are unavailable during training. In many applications, however, limited test samples may be available at training time, yet properties of min-norm interpolation in this regime remain poorly understood. We address this gap by characterizing the bias and variance of pooled min-$\ell_2$-norm interpolation under both covariate shift and model shift. Our results yield several important implications. In certain cases under model shift, we show that adding data always hurts when the signal-to-noise ratio (SNR) is low. At higher SNR levels, transfer learning is beneficial provided the shift-to-signal ratio falls below a threshold that we characterize explicitly. Under covariate shift, we find that when the source sample size is small relative to the dimension, greater heterogeneity between domains reduces risk, and vice versa. While our model shift results are initially established for Gaussian designs, we extend them to more general designs through a universality argument. To illustrate the broader applicability of our technical tools beyond interpolation learning, we characterize the risk of a bias-corrected estimator that uses the pooled interpolator as an initialization and corrects the resulting bias with target data. On the technical side, we develop a novel anisotropic local law and a Lindeberg-swapping argument, yielding tools that may be of independent interest in random matrix theory and universality analysis. Finally, we supplement our theory with simulations demonstrating the finite-sample efficacy of our results.