Contextual bandit is a widely used model for sequential decision making.

Contextual bandit is a widely used model for sequential decision making.

We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates $X$ and an outcome $Y$ under different experimental conditions (environments) but do not observe them jointly; we either observe $X$ or $Y$. Under appropriate regularity conditions, the problem can be cast as an instrumental variable (IV) regression with the environment acting as a (possibly high-dimensional) instrument. When there are many environments but only a few observations per environment, standard two-sample IV estimators fail to be consistent. We propose a GMM-type estimator based on cross-fold sample splitting of the instrument-covariate sample and prove that it is consistent as the number of environments grows but the sample size per environment remains constant. We further extend the method to sparse causal effects via $\ell_1$-regularized estimation and post-selection refitting.

Instrumental variable based estimation of a causal effect has emerged as a standard approach to mitigate confounding bias in the social sciences and epidemiology, where conducting randomized experiments can be too costly or impossible. However, justifying the validity of the instrument often poses a significant challenge. In this work, we highlight a problem generally neglected in arguments for instrumental variable validity: the presence of an ''aggregate treatment variable'', where the treatment (e.g., education, GDP, caloric intake) is composed of finer-grained components that each may have a different effect on the outcome. We show that the causal effect of an aggregate treatment is generally ambiguous, as it depends on how interventions on the aggregate are instantiated at the component level, formalized through the aggregate-constrained component intervention distribution. We then characterize conditions on the interventional distribution and the aggregate setting under which standard instrumental variable estimators identify the aggregate effect. The contrived nature of these conditions implies major limitations on the interpretation of instrumental variable estimates based on aggregate treatments and highlights the need for a broader justificatory base for the exclusion restriction in such settings.

We study the statistical-computational tradeoffs in a high dimensional single index model $Y=f(X^\top\beta^*) +\epsilon$, where $f$ is unknown, $X$ is a Gaussian vector and $\beta^*$ is $s$-sparse with unit norm. When $\cov(Y,X^\top\beta^*)\neq 0$, \cite{plan2016generalized} shows that the direction and support of $\beta^*$ can be recovered using a generalized version of Lasso. In this paper, we investigate the case when this critical assumption fails to hold, where the problem becomes considerably harder. Using the statistical query model to characterize the computational cost of an algorithm, we show that when $\cov(Y,X^\top\beta^*)=0$ and $\cov(Y,(X^\top\beta^*)^2)> 0$, no computationally tractable algorithms can achieve the information-theoretic limit of the minimax risk. This implies that one must pay an extra computational cost for the nonlinearity involved in the model.

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity on real-world data. Kernel methods using the partial covariance operator offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of the partial covariance operator and use them to construct a simple test statistic, reminiscent of the Hilbert-Schmidt Independence Criterion (HSIC). We also introduce a practical bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Preliminary experiments suggest that this approach offers a practical and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

Open-world learning (OWL) requires models that can adapt to evolving environments while reliably detecting out-of-distribution (OOD) inputs. Existing approaches, such as SCONE, achieve robustness to covariate and semantic shifts but assume static environments, leading to degraded performance in dynamic domains. In this paper, we propose Temp-SCONE, a temporally consistent extension of SCONE designed to handle temporal shifts in dynamic environments. Temp-SCONE introduces a confidence-driven regularization loss based on Average Thresholded Confidence (ATC), penalizing instability in predictions across time steps while preserving SCONE's energy-margin separation. Experiments on dynamic datasets demonstrate that Temp-SCONE significantly improves robustness under temporal drift, yielding higher corrupted-data accuracy and more reliable OOD detection compared to SCONE. On distinct datasets without temporal continuity, Temp-SCONE maintains comparable performance, highlighting the importance and limitations of temporal regularization. Our theoretical insights on temporal stability and generalization error further establish Temp-SCONE as a step toward reliable OWL in evolving dynamic environments.

Dependent data underlies many statistical studies in the social and health sciences, which often involve sensitive or private information. Differential privacy (DP) and in particular \textit{user-level} DP provide a natural formalization of privacy requirements for processing dependent data where each individual provides multiple observations to the dataset. However, dependence introduced, e.g., through repeated measurements challenges the existing statistical theory under DP-constraints. In \iid{} settings, noisy Winsorized mean estimators have been shown to be minimax optimal for standard (\textit{item-level}) and \textit{user-level} DP estimation of a mean $μ\in \R^d$. Yet, their behavior on potentially dependent observations has not previously been studied. We fill this gap and show that Winsorized mean estimators can also be used under dependence for bounded and unbounded data, and can lead to asymptotic and finite sample guarantees that resemble their \iid{} counterparts under a weak notion of dependence. For this, we formalize dependence via log-Sobolev inequalities on the joint distribution of observations. This enables us to adapt the stable histogram by Karwa and Vadhan (2018) to a non-\iid{} setting, which we then use to estimate the private projection intervals of the Winsorized estimator. The resulting guarantees for our item-level mean estimator extend to \textit{user-level} mean estimation and transfer to the local model via a randomized response histogram. Using the mean estimators as building blocks, we provide extensions to random effects models, longitudinal linear regression and nonparametric regression. Therefore, our work constitutes a first step towards a systematic study of DP for dependent data.

In many learning applications, data are collected from multiple sources, each providing a batch of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one of several unknown subgroups, each with an unknown input distribution and input-output relationship. We consider one of this setup's most fundamental and important manifestations where the output is a noisy linear combination of the inputs, and there are k subgroups, each with its own regression vector.