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.

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or words across texts). While the factors explaining variation in data are undoubtedly shared across subsets of contexts, no tools currently exist to systematically recover such factors. We develop multi-context principal component analysis (MCPCA), a theoretical and algorithmic framework that decomposes data into factors shared across subsets of contexts. Applied to gene expression, MCPCA reveals axes of variation shared across subsets of cancer types and an axis whose variability in tumor cells, but not mean, is associated with lung cancer progression. Applied to contextualized word embeddings from language models, MCPCA maps stages of a debate on human nature, revealing a discussion between science and fiction over decades. These axes are not found by combining data across contexts or by restricting to individual contexts. MCPCA is a principled generalization of PCA to address the challenge of understanding factors underlying data across contexts.

Robust machine learning for regulatory genomics is studied under biologically and technically induced distribution shifts. Deep convolutional and attention based models achieve strong in distribution performance on DNA regulatory sequence prediction tasks but are usually evaluated under i.i.d. assumptions, even though real applications involve cell type specific programs, evolutionary turnover, assay protocol changes, and sequencing artifacts. We introduce a robustness framework that combines a mechanistic simulation benchmark with real data analysis on a massively parallel reporter assay (MPRA) dataset to quantify performance degradation, calibration failures, and uncertainty based reliability. In simulation, motif driven regulatory outputs are generated with cell type specific programs, PWM perturbations, GC bias, depth variation, batch effects, and heteroscedastic noise, and CNN, BiLSTM, and transformer models are evaluated. Models remain accurate and reasonably calibrated under mild GC content shifts but show higher error, severe variance miscalibration, and coverage collapse under motif effect rewiring and noise dominated regimes, revealing robustness gaps invisible to standard i.i.d. evaluation. Adding simple biological structural priors motif derived features in simulation and global GC content in MPRA improves in distribution error and yields consistent robustness gains under biologically meaningful genomic shifts, while providing only limited protection against strong assay noise. Uncertainty-aware selective prediction offers an additional safety layer that risk coverage analyses on simulated and MPRA data show that filtering low confidence inputs recovers low risk subsets, including under GC-based out-of-distribution conditions, although reliability gains diminish when noise dominates.

The rapid progress of diffusion models highlights the growing need for detecting generated images. Previous research demonstrates that incorporating diffusion-based measurements, such as reconstruction error, can enhance the gener-alizability of detectors. However, ignoring the differing impacts of aleatoric and epistemic uncertainty on reconstruction error can undermine detection performance. Aleatoric uncertainty, arising from inherent data noise, creates ambiguity that impedes accurate detection of generated images. As it reflects random variations within the data (e.g., noise in natural textures), it does not help distinguish generated images. In contrast, epistemic uncertainty, which represents the model's lack of knowledge about unfamiliar patterns, supports detection. In this paper, we propose a novel framework, Diffusion Epistemic Uncertainty with Asymmetric Learning (DEUA), for detecting diffusion-generated images. W e introduce Diffusion Epistemic Uncertainty (DEU) estimation via the Laplace approximation to assess the proximity of data to the manifold of diffusion-generated samples. Additionally, an asymmetric loss function is introduced to train a balanced classifier with larger margins, further enhancing generalizability.

Privacy-preserving model co-training in medical research is often hindered by server-dependent architectures incompatible with protected hospital data systems and by the predominant focus on relative effect measures (hazard ratios) which lack clinical interpretability for absolute survival risk assessment. We propose FedRD, a communication-efficient framework for federated risk difference estimation in distributed survival data. Unlike typical federated learning frameworks (e.g., FedAvg) that require persistent server connections and extensive iterative communication, FedRD is server-independent with minimal communication: one round of summary statistics exchange for the stratified model and three rounds for the unstratified model. Crucially, FedRD provides valid confidence intervals and hypothesis testing--capabilities absent in FedAvg-based frameworks. We provide theoretical guarantees by establishing the asymptotic properties of FedRD and prove that FedRD (unstratified) is asymptotically equivalent to pooled individual-level analysis. Simulation studies and real-world clinical applications across different countries demonstrate that FedRD outperforms local and federated baselines in both estimation accuracy and prediction performance, providing an architecturally feasible solution for absolute risk assessment in privacy-restricted, multi-site clinical studies.

We study the optimal design of additive mechanisms for vector-valued queries under $ε$-differential privacy (DP). Given only the sensitivity of a query and a norm-monotone cost function measuring utility loss, we ask which noise distribution minimizes expected cost among all additive $ε$-DP mechanisms. Using convex rearrangement theory, we show that this infinite-dimensional optimization problem admits a reduction to a one-dimensional compact and convex family of radially symmetric distributions whose extreme points are the staircase distributions. As a consequence, we prove that for any dimension, any norm, and any norm-monotone cost function, there exists an $ε$-DP staircase mechanism that is optimal among all additive mechanisms. This result resolves a conjecture of Geng, Kairouz, Oh, and Viswanath, and provides a geometric explanation for the emergence of staircase mechanisms as extremal solutions in differential privacy.

Omics data, such as transcriptomics, proteomics, and metabolomics, provide critical insights into disease mechanisms and clinical outcomes. However, their high dimensionality, small sample sizes, and intricate biological networks pose major challenges for reliable prediction and meaningful interpretation. Graph Neural Networks (GNNs) offer a promising way to integrate prior knowledge by encoding feature relationships as graphs. Yet, existing methods typically rely solely on either an externally curated feature graph or a data-driven generated one, which limits their ability to capture complementary information. To address this, we propose the external and generated Graph Neural Network (engGNN), a dual-graph framework that jointly leverages both external known biological networks and data-driven generated graphs. Specifically, engGNN constructs a biologically informed undirected feature graph from established network databases and complements it with a directed feature graph derived from tree-ensemble models. This dual-graph design produces more comprehensive embeddings, thereby improving predictive performance and interpretability. Through extensive simulations and real-world applications to gene expression data, engGNN consistently outperforms state-of-the-art baselines. Beyond classification, engGNN provides interpretable feature importance scores that facilitate biologically meaningful discoveries, such as pathway enrichment analysis. Taken together, these results highlight engGNN as a robust, flexible, and interpretable framework for disease classification and biomarker discovery in high-dimensional omics contexts.

Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph constructed from the full dataset. In finite dimensions the asymptotics in the large (unlabeled) data limit are well understood with convergence from the graph setting to a continuum Sobolev semi-norm weighted by the Lebesgue density of the data-generating measure. The lack of the Lebesgue measure on infinite-dimensional spaces requires rethinking the analysis if the data aren't finite-dimensional. In this paper we make a first step in this direction by analyzing the setting when the data are generated by a Gaussian measure on a Hilbert space and proving pointwise convergence of the graph Dirichlet energy.

Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion models remains largely unexplored. In this work we investigate whether it provides tangible benefits for generative modelling. We find that while ensembling the scores generally improves the score-matching loss and model likelihood, it fails to consistently enhance perceptual quality metrics such as FID on image datasets. We confirm this observation across a breadth of aggregation rules using Deep Ensembles, Monte Carlo Dropout, on CIF AR-10 and FFHQ. We attempt to explain this discrepancy by investigating possible explanations, such as the link between score estimation and image quality. We also look into tabular data through random forests, and find that one aggregation strategy outperforms the others. Finally, we provide theoretical insights into the summing of score models, which shed light not only on ensembling but also on several model composition techniques (e.g.

A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. The same framework has been generalized to empirical cross-covariance matrices, whose singular value decomposition identifies canonical comovement modes between two asset sets, with singular values quantifying the strength of each mode and providing natural targets for shrinkage. Existing analytical cross-covariance cleaners are derived under strong stationarity and large-sample assumptions, and they typically rely on mesoscopic regularity conditions such as bounded spectra; macroscopic common modes (e.g., a global market factor) violate these conditions. When applied to real equity returns, where dependence structures drift over time and global modes are prominent, we find that these theoretically optimal formulas do not translate into robust out-of-sample performance. We address this gap by designing a random-matrix-inspired neural architecture that operates in the empirical singular-vector basis and learns a nonlinear mapping from empirical singular values to their corresponding cleaned values. By construction, the network can recover the analytical solution as a special case, yet it remains flexible enough to adapt to non-stationary dynamics and mode-driven distortions. Trained on a long history of equity returns, the proposed method achieves a more favorable bias-variance trade-off than purely analytical cleaners and delivers systematically lower out-of-sample cross-covariance prediction errors. Our results demonstrate that combining random-matrix theory with machine learning makes asymptotic theories practically effective in realistic time-varying markets.