Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as multiaccuracy, or having low bias over a range of possible targets. In this paper, we consider a simple estimator, ridge boosting: starting with any initial predictor, perform a single boosting step with (kernel) ridge regression. Surprisingly, we show that ridge boosting simultaneously achieves both efficiency and distributional robustness: for target distribution shifts that lie within an RKHS unit ball, this estimator maintains low bias across all such shifts and has variance at the semiparametric efficiency bound for each target. In addition to bridging otherwise distinct research areas, this result has immediate practical value. Since ridge boosting uses only data from the source distribution, researchers can train a single model to obtain both robust and efficient estimates for multiple target estimands at the same time, eliminating the need to fit separate semiparametric efficient estimators for each target. We assess this approach through simulations and an application estimating the age profile of retirement income.

The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the tightest possible confidence intervals is vital every time the sampling of the random variables is expensive. The current state-of-the-art method to construct confidence intervals is by using betting algorithms. This is a very successful approach for deriving optimal confidence sequences, even matching the rate of law of iterated logarithms. However, in the fixed horizon setting, these approaches are either sub-optimal or based on heuristic solutions with strong empirical performance but without a finite-time guarantee.

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.

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

AI has the potential to transform scientific discovery by analyzing vast datasets with little human effort. However, current workflows often do not provide the accuracy or statistical guarantees that are needed. We introduce active measurement, a human-in-the-loop AI framework for scientific measurement. An AI model is used to predict measurements for individual units, which are then sampled for human labeling using importance sampling. With each new set of human labels, the AI model is improved and an unbiased Monte Carlo estimate of the total measurement is refined. Active measurement can provide precise estimates even with an imperfect AI model, and requires little human effort when the AI model is very accurate. We derive novel estimators, weighting schemes, and confidence intervals, and show that active measurement reduces estimation error compared to alternatives in several measurement tasks.

Multi-arm bandit experimental designs are increasingly being adopted over standard randomized trials due to their potential to improve outcomes for study participants, enable faster identification of the best-performing options, and/or enhance the precision of estimating key parameters. Current approaches for inference after adaptive sampling either rely on asymptotic normality under restricted experiment designs or underpowered martingale concentration inequalities that lead to weak power in practice. To bypass these limitations, we propose a simulation-based approach for conducting hypothesis tests and constructing confidence intervals for arm specific means and their differences. Our simulation-based approach uses positively biased nuisances to generate additional trajectories of the experiment, which we call simulation with optimism. Using these simulations, we characterize the distribution potentially non-normal sample mean test statistic to conduct inference. We provide guarantees for (i) asymptotic type I error control, (ii) convergence of our confidence intervals, and (iii) asymptotic strong consistency of our estimator over a wide variety of common bandit designs. Our empirical results show that our approach achieves the desired coverage while reducing confidence interval widths by up to 50%, with drastic improvements for arms not targeted by the design.

Estimating associations between spatial covariates and responses -- rather than merely predicting responses -- is central to environmental science, epidemiology, and economics. For instance, public health officials might be interested in whether air pollution has a strictly positive association with a health outcome, and the magnitude of any effect. Standard machine learning methods often provide accurate predictions but offer limited insight into covariate-response relationships. And we show that existing methods for constructing confidence (or credible) intervals for associations can fail to provide nominal coverage in the face of model misspecification and nonrandom locations -- despite both being essentially always present in spatial problems. We introduce a method that constructs valid frequentist confidence intervals for associations in spatial settings. Our method requires minimal assumptions beyond a form of spatial smoothness and a homoskedastic Gaussian error assumption. In particular, we do not require model correctness or covariate overlap between training and target locations. Our approach is the first to guarantee nominal coverage in this setting and outperforms existing techniques in both real and simulated experiments. Our confidence intervals are valid in finite samples when the noise of the Gaussian error is known, and we provide an asymptotically consistent estimation procedure for this noise variance when it is unknown.

Mixture-of-Experts (MoE) models have become popular in machine learning, boosting performance by partitioning tasks across multiple experts. However, the need for several experts often results in high computational costs, limiting their application on resource-constrained devices with stringent real-time requirements, such as cochlear implants (CIs). We introduce the Omni-Expert (OE) - a simple and efficient solution that leverages feature transformations to achieve the'divideand-conquer' functionality of a full MoE ensemble in a single expert model. We demonstrate the effectiveness of the OE using phoneme-specific time-frequency masking for speech dereverberation in a CI. Empirical results show that the OE delivers statistically significant improvements in objective intelligibility measures of CI vocoded speech at different levels of reverberation across various speech datasets at a much reduced computational cost relative to a counterpart MoE.

Foundation models have enabled rapid progress across many specialized domains by leveraging large-scale pre-training on unlabeled data, demonstrating strong generalization to a variety of downstream tasks. While such models have gained significant attention in fields like Earth Observation, their application to Mars science remains limited. A key enabler of progress in other domains has been the availability of standardized benchmarks that support systematic evaluation. In contrast, Mars science lacks such benchmarks and standardized evaluation frameworks, which have limited progress toward developing foundation models for Martian tasks. To address this gap, we introduce Mars-Bench, the first benchmark designed to systematically evaluate models across a broad range of Mars-related tasks using both orbital and surface imagery.