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.

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.

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.

We consider the problem of identifying the best arm in a multi-armed bandit model. Despite a wealth of literature in the traditional fixed budget and fixed confidence regimes of the best arm identification problem, it still remains a mystery to most practitioners as to how to choose an approach and corresponding budget or confidence parameter. We propose a new formalism to avoid this dilemma altogether by minimizing a risk functional which explicitly balances the performance of the recommended arm and the cost incurred by learning this arm. In this framework, a cost is incurred for each observation during the sampling phase, and upon recommending an arm, a performance penalty is incurred for identifying a suboptimal arm. The learner's goal is to minimize the sum of the penalty and cost. This new regime mirrors the priorities of many practitioners, e.g.

In this paper, we develop a novel algorithm for constructing time-uniform, asymptotic confidence sequences for quantiles under local differential privacy (LDP). The procedure combines dynamically chained parallel stochastic gradient descent (P-SGD) with a randomized response mechanism, thereby guaranteeing privacy protection while simultaneously estimating the target quantile and its variance. A strong Gaussian approximation for the proposed estimator yields asymptotically anytime-valid confidence sequences whose widths obey the law of the iterated logarithm (LIL). Moreover, the method is fully online, offering high computational efficiency and requiring only O(κ)memory, where κdenotes the number of chains and is much smaller than the sample size. Rigorous mathematical proofs and extensive numerical experiments demonstrate the theoretical soundness and practical effectiveness of the algorithm.

We consider the problem of estimating a causal effect in a multi-domain setting. The causal effect of interest is confounded by an unobserved confounder and can change between the different domains. We assume that we have access to a proxy of the hidden confounder and that all variables are discrete or categorical. We propose methodology to estimate the causal effect in the target domain, where we assume to observe only the proxy variable. Under these conditions, we prove identifiability (even when treatment and response variables are continuous). We introduce two estimation techniques, prove consistency, and derive confidence intervals. The theoretical results are supported by simulation studies and a real-world example studying the causal effect of website rankings on consumer choices.

This paper addresses the problem of multi-risk measure agnostic multi-armed bandits in heavy-tailed reward settings. We propose a framework that leverages novel deviation inequalities for the 1-Wasserstein distance to construct confidence intervals for Lipschitz risk measures. The distributional LCB (DistLCB) algorithm is introduced, which achieves asymptotic optimality by deriving the first lower bounds for risk measure aware bandits with explicit sub-optimality gap dependencies. The DistLCB is further extended to multi-risk objectives, which enables Pareto-optimal solutions that consider multiple aspects of reward distributions. Additionally, we provide a regret analysis that includes both gap-dependent and gap-independent bounds for multi-risk settings. Experiments validate the effectiveness of the proposed methods in synthetic and real-world applications.

We consider the problem of estimating the correlation of two random variables X and Y, where the pairs (X, Y) are not observed together, but are instead separated co-ordinate-wise at two servers: server 1 contains all the X observations, and server 2 contains the corresponding Y observations. In this vertically distributed setting, we assume that each server has its own privacy constraints, owing to which they can only share suitably privatized statistics of their own component observations. We consider differing privacy budgets (ε1, δ1) and (ε2, δ2) for the two servers and determine the minimax optimal rates for correlation estimation allowing for both noninteractive and interactive mechanisms. We also provide correlation estimators that achieve these rates and further develop inference procedures, namely, confidence intervals, for the estimated correlations. Our results are characterized by an interesting rate in terms of the sample size n, ε1, ε2, which is strictly slower than the usual central privacy estimation rates. More interestingly, we find that the interactive mechanism is always better than its non-interactive counterpart whenever the two privacy budgets are different. Results from extensive numerical experiments support our theoretical findings.

Yet, modern machine learning pipelines offer a promising solution--provided their predictions yield correct conclusions. We focus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled target experiment, relying on training data with the same outcome annotated but potentially different treatment or effect modifiers.