Papers

Preconditioning is a common method applied to modify Markov chain Monte Carlo algorithms with the goal of making them more efficient. In practice it is often extremely effective, even when the preconditioner is learned from the chain. We analyse and compare the finite-time computational costs of schemes which learn a preconditioner based on the target covariance or the expected Hessian of the target potential with that of a corresponding scheme that does not use preconditioning. We apply our results to various algorithms including the Unadjusted Langevin Algorithm (ULA) and the proximal sampler for an appropriately regular target, establishing non-asymptotic guarantees for versions of these algorithms that learn and use preconditioners. To do so, we establish non-asymptotic guarantees on the time taken to collect $N$ approximately independent samples from the target for schemes that learn their preconditioners under the assumption that the underlying Markov chain satisfies a contraction in the Wasserstein-2 distance. This approximate independence condition, that we formalize, allows us to bridge the non-asymptotic bounds of modern MCMC theory and classical heuristics of effective sample size and mixing time, and is needed to amortise the costs of learning a preconditioner across the samples it will help to produce.

Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on Gradient Descent (SGD), remain largely underexplored. In this work, we address this gap by analyzing the semi-dual formulation of Entropic UOT and demonstrating its suitability for adaptive gradient methods. While the semi-dual is a standard tool for large-scale balanced OT, its geometry in the unbalanced setting appears ill-conditioned under standard analysis. Specifically, worst-case bounds on the marginal penalties using $\chi^2$ divergence suggest a condition number scaling with $n/\varepsilon$, implying poor scalability. In contrast, we show that the local condition number actually scales as $\mathcal{O}(1/\varepsilon)$, effectively removing the ill-conditioned dependence on $n$. Exploiting this property, we prove that SGD methods adapt to this local curvature, achieving a convergence rate of $\mathcal{O}(n/\varepsilon T)$ in the stochastic and online regimes, making it suitable for large-scale and semi-discrete applications. Finally, for the full batch discrete setting, we derive a nearly tight upper bound on local smoothness depending solely on the gradient. Using it to adapt step sizes, we propose a modified Adaptive Nesterov Accelerated Gradient (ANAG) method on the semi-dual functional and prove that it achieves a local complexity of $\mathcal{O}(n^2\sqrt{1/\varepsilon}\ln(1/\delta))$.

Assortment optimization is a fundamental challenge in modern retail and recommendation systems, where the goal is to select a subset of products that maximizes expected revenue under complex customer choice behaviors. While recent advances in data-driven methods have leveraged historical data to learn and optimize assortments, these approaches typically rely on strong assumptions – namely, the stability of customer preferences and the correctness of the underlying choice models. However, such assumptions frequently break in real-world scenarios due to preference shifts and model misspecification, leading to poor generalization and revenue loss. Motivated by this limitation, we propose a robust framework for data-driven assortment optimization that accounts for potential distributional shifts in customer choice behavior. Our approach models potential preference shift from a nominal choice model that generates data and seeks to maximize worst-case expected revenue. We first establish the computational tractability of robust assortment planning when the nominal model is known, then advance to the data-driven setting, where we design statistically optimal algorithms that minimize the data requirements while maintaining robustness. Our theoretical analysis provides both upper bounds and matching lower bounds on the sample complexity, offering theoretical guarantees for robust generalization. Notably, we uncover and identify the notion of “robust item-wise coverage” as the minimal data requirement to enable sample-efficient robust assortment learning. Our work bridges the gap between robustness and statistical efficiency in assortment learning, contributing new insights and tools for reliable assortment optimization under uncertainty.

We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish Lojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.

Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible to covariance-based methods such as PCA. In practice, nonlinear neural networks often succeed in extracting such hidden structure in unsupervised and self-supervised learning. However, constructing a minimal high-dimensional model where this advantage can be rigorously analyzed has remained an open theoretical challenge. We introduce a tractable high-dimensional spiked model with two latent factors: one visible to covariance, and one statistically dependent yet uncorrelated, appearing only in higher-order moments. PCA and linear autoencoders fail to recover the latter, while a minimal nonlinear autoencoder provably extracts both. We analyze both the population risk, and empirical risk minimization. Our model also provides a tractable example where self-supervised test loss is poorly aligned with representation quality: nonlinear autoencoders recover latent structure that linear methods miss, even though their reconstruction loss is higher.

Abundance data are used in ecology for species monitoring and conservation. These count data often display several specific characteristics like numerous missing data, high variance, and a high proportion of zeros, particularly when monitoring rare species. We present a model that aims to impute missing data and estimate the effect of covariates on species presence and abundance. It is based on the log-normal Poisson model, which offers more flexibility in the variance of counts than a Poisson model. A latent variable is added for the overrepresentation of zeros in the data. The imputation of missing data is made possible by assuming that the latent variance matrix has low rank and the inclusion of covariates. \\ We demonstrate the identifiability in the presence of missing data. Since maximum likelihood inference is intractable, we use a variational expectation-maximization algorithm to infer the parameters. We provide an estimate of the asymptotic variance of the estimators and derive prediction intervals for the imputations, an estimate of the temporal trend, and a procedure for detecting a potential change in this trend. \\ We evaluate our imputations and associated prediction intervals using artificially degraded monitoring data set. We conclude with an illustration on a monitoring waterbirds data set.

In this article we develop a new method for summarizing a ranking distribution, i.e. a probability distribution on the symmetric group $\mathfrak{S}_n$, beyond the classical theory of consensus and Kemeny medians. Based on the notion of local ranking median, we introduce the concept of consensus ranking distribution ($\crd$), a sparse mixture model of Dirac masses on $\mathfrak{S}_n$, in order to approximate a ranking distribution with small distortion from a mass transportation perspective. We prove that by choosing the popular Kendall $\tau$ distance as the cost function, the optimal distortion can be expressed as a function of pairwise probabilities, paving the way for the development of efficient learning methods that do not suffer from the lack of vector space structure on $\mathfrak{S}_n$. In particular, we propose a top-down tree-structured statistical algorithm that allows for the progressive refinement of a CRD based on ranking data, from the Dirac mass at a Kemeny median at the root of the tree to the empirical ranking data distribution itself at the end of the tree's exhaustive growth. In addition to the theoretical arguments developed, the relevance of the algorithm is empirically supported by various numerical experiments.

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack a reweighting procedure required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a framework for reduced-order generative modeling with importance sampling in coarse-grained coordinate space. CG-BGs generate samples using a flow-based model and reweight them using a learned potential of mean force (PMF). We show that the PMF can be learned from rapidly converged trajectories via enhanced sampling force matching. Experiments demonstrate that CG-BGs capture solvent-mediated interactions in highly reduced representations while substantially reducing computational cost relative to atomistic BGs, providing a practical route toward equilibrium sampling of larger molecular systems.

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions due to the large design matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a related ridge-regularized analogue. Building on both procedures, we introduce the Principal Component Highly Adaptive Lasso (PCHAL) and Principal Component Highly Adaptive Ridge (PCHAR). These estimators use an outcome-blind principal-component reduction of the HAL basis, offering substantial computational gains over HAL while achieving empirical performance comparable to HAL and HAR. We also describe an early-stopped gradient descent variant, which provides a convenient form of smooth spectral regularization without explicitly selecting a hard principal-component cutoff. Finally, we uncover that under special circumstances, the HAL kernel is identical to the covariance function of Brownian motion.

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be leveraged to regularize the learning process. In practice, however, PINNs are frequently trained using experimental or numerical data that are not fully consistent with the governing equations due to measurement noise, discretization errors, or modeling assumptions. The implications of such data-to-PDE inconsistencies on the accuracy and convergence of PINNs remain insufficiently understood. In this work, we systematically analyze how data inconsistency fundamentally limits the attainable accuracy of PINNs. We introduce the concept of a consistency barrier, defined as an intrinsic lower bound on the error that arises from mismatches between the fidelity of the data and the exact enforcement of the PDE residual. To isolate and quantify this effect, we consider the 1D viscous Burgers equation with a manufactured analytical solution, which enables full control over data fidelity and residual errors. PINNs are trained using datasets of progressively increasing numerical accuracy, as well as perfectly consistent analytical data. Results show that while the inclusion of the PDE residual allows PINNs to partially mitigate low-fidelity data and recover the dominant physical structure, the training process ultimately saturates at an error level dictated by the data inconsistency. When high-fidelity numerical data are employed, PINN solutions become indistinguishable from those trained on analytical data, indicating that the consistency barrier is effectively removed. These findings clarify the interplay between data quality and physics enforcement in PINNs providing practical guidance for the construction and interpretation of physics-informed surrogate models.

Policy inference plays an essential role in the contextual bandit problem. In this paper, we use empirical likelihood to develop a Bayesian inference method for the joint analysis of multiple contextual bandit policies in finite sample regimes. The proposed inference method is robust to small sample sizes and is able to provide accurate uncertainty measurements for policy value evaluation. In addition, it allows for flexible inferences on policy comparison with full uncertainty quantification. We demonstrate the effectiveness of the proposed inference method using Monte Carlo simulations and its application to an adolescent body mass index data set.

When a source-trained model $Q$ is replaced by a model $\tilde{Q}$ trained on shifted data, its performance on the source domain can change unpredictably. To address this, we study the two-model risk change, $\Delta R := R_P(\tilde{Q}) - R_P(Q)$, under covariate shift. We introduce TRACE (Theoretical Risk Attribution under Covariate-shift Effects), a framework that decomposes $|\Delta R|$ into an interpretable upper bound. This decomposition disentangles the risk change into four actionable factors: two generalization gaps, a model change penalty, and a covariate shift penalty, transforming the bound into a powerful diagnostic tool for understanding why performance has changed. To make TRACE a fully computable diagnostic, we instantiate each term. The covariate shift penalty is estimated via a model sensitivity factor (from high-quantile input gradients) and a data-shift measure; we use feature-space Optimal Transport (OT) by default and provide a robust alternative using Maximum Mean Discrepancy (MMD). The model change penalty is controlled by the average output distance between the two models on the target sample. Generalization gaps are estimated on held-out data. We validate our framework in an idealized linear regression setting, showing the TRACE bound correctly captures the scaling of the true risk difference with the magnitude of the shift. Across synthetic and vision benchmarks, TRACE diagnostics are valid and maintain a strong monotonic relationship with the true performance degradation. Crucially, we derive a deployment gate score that correlates strongly with $|\Delta R|$ and achieves high AUROC/AUPRC for gating decisions, enabling safe, label-efficient model replacement.

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given the covariates. This model is then used to generate bootstrap samples by pairing the original covariates with newly synthesized responses. We reformulate nonparametric regression as conditional sample mean estimation, which is implemented directly via the learned conditional diffusion model. Unlike traditional bootstrap methods that decouple the estimation of the conditional distribution, sampling, and nonparametric regression, our approach integrates these components into a unified generative framework. With the expressive capacity of diffusion models, our method facilitates both efficient sampling from high-dimensional or multimodal distributions and accurate nonparametric estimation. We establish rigorous theoretical guarantees for the proposed method. In particular, we derive optimal end-to-end convergence rates in the Wasserstein distance between the learned and target conditional distributions. Building on this foundation, we further establish the convergence guarantees of the resulting bootstrap procedure. Numerical studies demonstrate the effectiveness and scalability of our approach for complex regression tasks.

Spectral clustering and node rankings are commonly reported from one observed network without a finite-sample statement of what the observation supports. We develop a certification protocol that either returns a coverage-guaranteed set or explicitly returns “no nontrivial certificate.” For an inhomogeneous Bernoulli graph, a matrix-Bernstein quantile with all numerical constants and its ambient-dimension factor retained is combined with a one-sided spectral-gap certificate. The resulting Grassmann ball is valid at finite \(n\), but is reported as informative only when its radius is below the diameter of the Grassmannian. We propagate the ball through a certificate-bearing approximate \(k\)-means map under declared population separation and minimum-cluster envelopes, derive simultaneous bands and an observed-gap certificate for degree centrality, and give a corrected normalized-Katz extension. A \(12\)-cell simulation study with \(1{,}000\) graphs per cell maps the difference between coverage and usefulness. The submitted \(n=200\) block-model example is shown to be necessarily vacuous after the dimension factor is restored; in the benchmark \(p=0.30,q=0.10\), the subspace radius first falls below one at \(n=\ExactRadiusThreshold\), whereas the mean-square clustering certificate remains unavailable until \(n=\HammingThreshold\). An unequal-block example produces a genuine centrality certificate, while an analysis of the Zachary karate-club network correctly declines to certify despite \(97.1\%\) agreement with the observed factions. These results separate algorithmic success, coverage validity and inferential informativeness.

Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored model upscaling: initializing larger models from trained smaller ones to accelerate convergence. However, this method can be sensitive to hyperparameters that need to be tuned at the target upscaled model size, which is prohibitively costly to do directly. It remains unclear whether tuning hyperparameters on smaller models and extrapolating via scaling laws is sound in this setting. We address this with principled approaches to width-based upscaling and efficient hyperparameter tuning in this setting. Motivated by $\mu$P and any-dimensional architectures, we introduce a general upscaling method that, like Net2Net, copies and perturbs weights, but uses theoretically grounded, width-dependent scalings for the perturbation noise and optimizer hyperparameters. First, we prove that under zero perturbation, the upscaled model is functionally equivalent to the base model throughout training. Second, we extend the $\mu$P theory to enable infinite-width limit analysis and establish hyperparameter transfer for upscaled models, greatly reducing the tuning cost. We empirically demonstrate that this method is effective on realistic datasets and architectures.

Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We study this question through statistical provability: the probability of reaching a verified proof within a budget on a specified stream of theorem instances. We model formal proof search as a finite-horizon reachability MDP with deterministic verifier dynamics, and show that under a faithful state abstraction the optimal success probability coincides with ordinary syntactic provability. We then analyze a simple but practically important pipeline: depth-wise offline action-value regression followed by greedy test-time proving. Our main theorem bounds the provability gap between the learned prover and the optimal prover by an occupancy-weighted sum of uniform action-value errors; in the common uniform-error reading, the leading complexity multiplier is the learned prover's average truncated proof length. The error decomposes into approximation error, geometric coverage of the training distribution, and Monte Carlo label noise, and improves to a fast rate under an action-gap margin condition. The result gives a component-sensitive account of why verifier feedback, retrieval, representation geometry, and proof-shortening mechanisms help on biased theorem workloads, without contradicting classical worst-case hardness.

The SHAP (short for Shapley additive explanation) framework has become an essential tool for attributing importance to variables in predictive tasks. In model-agnostic settings, SHAP uses the concept of Shapley values from cooperative game theory to fairly allocate credit to the features in a vector $X$ based on their contribution to an outcome $Y$. While the explanations offered by SHAP are local by nature, learners often need global measures of feature importance in order to improve model explainability and perform feature selection. The most common approach for converting these local explanations into global ones is to compute either the mean absolute SHAP or mean squared SHAP. However, despite their ubiquity, there do not exist approaches for performing statistical inference on these quantities. In this paper, we take a semi-parametric approach for calibrating confidence in estimates of the $p$th powers of Shapley additive explanations. We show that, by treating the SHAP curve as a nuisance function that must be estimated from data, one can reliably construct asymptotically normal estimates of the $p$th powers of SHAP. When $p \geq 2$, we show a de-biased estimator that combines U-statistics with Neyman orthogonal scores for functionals of nested regressions is asymptotically normal. When $1 \leq p < 2$ (and the hence target parameter is not twice differentiable), we construct de-biased U-statistics for a smoothed alternative. In particular, we show how to carefully tune the temperature parameter of the smoothing function in order to obtain inference for the true, unsmoothed $p$th power. We complement these results by presenting a Neyman orthogonal loss that can be used to learn the SHAP curve via empirical risk minimization and discussing excess risk guarantees for commonly used function classes.

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.

Multiview datasets are common in scientific and engineering applications, yet existing fusion methods offer limited theoretical guarantees, particularly in the presence of heterogeneous and high-dimensional noise. We propose Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM), a new kernel-based diffusion geometry framework for integrating multiple noisy data sources. The key innovation of GRAB-MDM is a {view}-dependent bandwidth selection strategy that adapts to the geometry and noise level of each view, enabling a stable and principled construction of multiview diffusion operators. Under a common-manifold model, we establish asymptotic convergence results and show that the adaptive bandwidths lead to provably robust recovery of the shared intrinsic structure, even when noise levels and sensor dimensions differ across views. Numerical experiments demonstrate that GRAB-MDM significantly improves robustness and embedding quality compared with fixed-bandwidth and equal-bandwidth baselines, and usually outperform existing algorithms. The proposed framework offers a practical and theoretically grounded solution for multiview sensor fusion in high-dimensional noisy environments.

Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study a variant in which the goal is to minimize a quantile of the cost, rather than the mean. For the semidiscrete setting, where one distribution is continuous and the other is discrete, we derive a complete characterization of the optimal transport plan and develop simulation-based methods to efficiently compute it. One particularly novel aspect of our approach is the efficient computation of a tie-breaking rule that preserves marginal distributions. In the context of geographical partitioning problems, the optimal plan is shown to produce a novel geometric structure.

Agentic theorem provers often introduce intermediate lemmas, proof sketches, or subgoal decompositions before returning to tactic-level search. This can look like an expensive detour: if proving lemmas is itself hard, why should a learned prover spend effort there? We give a statistical learning answer. Instead of worst-case proof complexity over all formulas, we study the biased data distribution produced by a teacher prover: initial theorem states together with successful verified proof traces. We model proof search as a deterministic finite-horizon MDP and analyze offline imitation learning from those traces. The success bounds depend on the average length of teacher proofs, how predictable the teacher's next action is, and how accurately the student learns that local prediction problem. A flat student learns from fully inlined traces, so repeated subproofs appear many times in its training and test-time certificate. A hierarchical student instead predicts a reusable proof DAG and solves each shared block once. When flattening duplicates the same hard local argument exponentially many times, the sufficient-sample certificate produced by our bounds can be exponentially smaller for the hierarchical learner. This gives a concrete statistical mechanism by which reusable proof structure helps verifier-based theorem proving.

Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this work, we develop a semi-parametric methodology to estimate CoVaR for asymptotically independent pairs within the framework of bivariate extreme value theory. We use parametric modelling of the bivariate extremal structure to address data sparsity in the joint tail regions and prove consistency and asymptotic normality of the proposed estimator. The robust performance of the estimator is illustrated via simulation studies. Its application to the US stock returns data produces insightful dynamic CoVaR forecasts.

Recent advances in artificial intelligence have enabled the generation of large-scale, low-cost predictions with increasingly high fidelity. As a result, the primary challenge in statistical inference has shifted from data scarcity to data reliability. Prediction-powered inference methods seek to exploit such predictions to improve efficiency when labeled data are limited. However, existing approaches implicitly adopt a use-all philosophy, under which incorporating more predictions is presumed to improve inference. When prediction quality is heterogeneous, this assumption can fail, and indiscriminate use of unlabeled data may dilute informative signals and degrade inferential accuracy. In this paper, we propose Filtered Prediction-Powered Inference (FPPI), a framework that selectively incorporates predictions by identifying a data-adaptive filtered region in which predictions are informative for inference. We show that this region can be consistently estimated under a margin condition, achieving fast rates of convergence. By restricting the prediction-powered correction to the estimated filtered region, FPPI adaptively mitigates the impact of biased or noisy predictions. We establish that FPPI attains strictly improved asymptotic efficiency compared with existing prediction-powered inference methods. Numerical studies and a real-data application to large language model evaluation demonstrate that FPPI substantially reduces reliance on expensive labels by selectively leveraging reliable predictions, yielding accurate inference even in the presence of heterogeneous prediction quality.

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems remains largely unexplored. We address this by incorporating the periodicity inherent to these systems into continuous normalizing flows using Riemannian flow matching. The high computational cost of exact density estimation intrinsic to continuous normalizing flows is mitigated by using Hutchinson's trace estimator, utilizing a crucial bias-correction step based on cumulant expansion to render the stochastic estimates suitable for rigorous thermodynamic reweighting. Our approach is validated on monatomic ice, demonstrating the ability to train on systems of unprecedented size and obtain highly accurate free energy estimates without the need for traditional multistage estimators.

Instrumental variable (IV) methods mitigate bias from unobserved confounding in observational causal inference but rely on the availability of a valid instrument, which can often be difficult or infeasible to identify in practice. In this paper, we propose a representation learning approach that constructs instrumental representations from observed covariates, which could enable IV-based estimation even in the absence of an explicit instrument. Our model (ZNet) achieves this through an architecture that mirrors the structural causal model of IVs; it decomposes the ambient feature space into confounding and instrumental components, and is trained by enforcing it empirical conditions corresponding to the defining properties of valid instruments (i.e., relevance and exclusion restriction). ZNet is compatible with a wide range of downstream two-stage IV estimators of causal effects. Our experiments demonstrate that ZNet (i) can recover ground-truth instruments when they already exist in the ambient feature space and (ii) constructs candidate latent instruments in the embedding space when no explicit IVs are available. However, instrument representations have inherent challenges which warrant caution and further research. This work explores when ZNet might be used as a module for causal inference in general observational settings.

Stepped-wedge designs are increasingly used in randomized experiments to accommodate logistical and ethical constraints by staggering treatment roll-out over time. Despite their popularity, existing analytical methods largely rely on parametric models with linear covariate adjustment and prespecified correlation structures, which may limit achievable precision in practice. We propose a new class of estimators for the causal average treatment effect in stepped-wedge designs that optimizes precision through flexible, machine-learning-based covariate adjustment to capture complex outcome-covariate relationships, together with quadratic inference functions to adaptively learn the correlation structure. We establish consistency and asymptotic normality under mild conditions requiring only $L_2$ convergence of nuisance estimators, even under model misspecification, and characterize when the estimator attains the minimal asymptotic variance. Moreover, we prove that the proposed estimator never reduces efficiency relative to an independence working correlation. The proposed method further accommodates treatment-effect heterogeneity across both exposure duration and calendar time. Finally, we demonstrate our methods through simulation studies and reanalyses of two empirical studies that differ substantially in research area and key design parameters.

In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to obtain an estimator of the parameter of interest with asymptotic variance no greater than that which would be obtained using only the labeled observations. While existing PPI proposals consider estimators arising from M-estimation, in this paper we generalize PPI to any regular asymptotically linear estimator. Furthermore, by situating PPI within the context of an existing rich literature on missing data and semi-parametric efficiency theory, we show that while PPI does not achieve the semi-parametric efficiency lower bound outside of very restrictive and unrealistic scenarios, it can be viewed as a computationally-simple alternative to proposals in that literature. We exploit connections to that literature to propose modified PPI estimators that can handle three distinct forms of covariate distribution shift. Finally, we illustrate these developments by constructing PPI estimators of true positive rate, false positive rate, and area under the curve via numerical studies.

Predicting time-to-event outcomes when event times are interval censored is challenging because the exact event time is unobserved. Many existing survival analysis approaches for interval-censored data rely on strong model assumptions or cannot handle high-dimensional predictors. We develop ICODEN, an ordinary differential equation-based neural network for interval-censored data that models the hazard function through deep neural networks and obtains the cumulative hazard by solving an ordinary differential equation. ICODEN does not require the proportional hazards assumption or a prespecified parametric form for the hazard function, thereby permitting flexible survival modeling. Across simulation settings with proportional or non-proportional hazards and both linear and nonlinear covariate effects, ICODEN consistently achieves satisfactory predictive accuracy and remains stable as the number of predictors increases. Applications to data from multiple phases of the Alzheimer's Disease Neuroimaging Initiative (ADNI) and to two Age-Related Eye Disease Studies (AREDS and AREDS2) for age-related macular degeneration (AMD) demonstrate ICODEN's robust prediction performance. In both applications, predicting time-to-AD or time-to-late AMD, ICODEN effectively uses hundreds to more than 1,000 SNPs and supports data-driven subgroup identification with differential progression risk profiles. These results establish ICODEN as a practical assumption-lean tool for prediction with interval-censored survival data in high-dimensional biomedical settings.

We prove asymptotic equivalence of nonparametric additive regression and an appropriate Gaussian white noise experiment in which a multidimensional shifted Wiener process is observed, whose dimension equals the number of additive components. The shift depends on the additive components of the regression function and solely the one- and two-dimensional marginal distributions of the covariates via an explicitly specified bounded but non-compact linear operator~$\Gamma$. The number of additive components $d$ is allowed to increase moderately with respect to the sample size. In the special case of pairwise independent components of the covariates, the white noise model decomposes into $d$ independent univariate processes. Moreover, we study approximation in some semiparametric setting where $\Gamma$ splits into a multiplication operator and an asymptotically negligible Hilbert-Schmidt operator.

Reasoning ability in large language models is often attributed to distribution sharpening: concentrating output probability on high-likelihood sequences. Recent works show that this sharpening effect can be obtained at inference time, without modifying model parameters, and can elicit strong reasoning performance. A natural formalization is the sequence-level power distribution, which is proportional to the model's probability raised to an exponent $\alpha>1$. Prior work leveraged Metropolis–Hastings (MH) sampling to draw samples from this distribution and achieves strong results, however, at order-of-magnitude inference slowdowns. We introduce Power-SMC, a `training-free' sampling method that targets the same power distribution yielding close to standard decoding latency. Power-SMC maintains multiple candidate sequences in parallel. Each candidate sequence is assigned a score, namely the importance weight, that measures how well it matches the power distribution. It then periodically prunes low-scoring candidate sequences in favor of high-scoring ones. We further provide a theoretical justification for the design choices in Power-SMC. Among all next-token sampling strategies that do not rely on future tokens, we prove that sampling temperature $\tau{=}1/\alpha$ uniquely eliminates per-step weight variance. Finally, we characterize the remaining source of weight instability and introduce a gradual sharpening schedule to reduce weight collapse, while targeting the same power distribution. Extensive evaluations on MATH500, GSM8K, GPQA, and HumanEval show that Power-SMC matches or exceeds MH sampling in accuracy, preserves output diversity unlike RL-finetuned models, while accelerating inference speed by up to {$\mathbf{17.6}\times$}. The code is available at https://github.com/ArminAzizi98/Power-SMC.