Deep learning models with a large number of parameters, often referred to as over-parameterized models, have achieved exceptional performance across various tasks. Despite concerns about overfitting, these models frequently generalize well to unseen data, thanks to effective regularization techniques, with data augmentation being among the most widely used. While data augmentation has shown great success in classification tasks using label-preserving transformations, its application in regression problems has received less attention. Recently, a novel \emph{manifold learning} approach for generating synthetic data was proposed, utilizing a first-order approximation of the data manifold. Building on this foundation, we present a theoretical framework and practical tools for approximating and sampling general data manifolds. Furthermore, we introduce the Curvature-Enhanced Manifold Sampling (CEMS) method for regression tasks. CEMS leverages a second-order representation of the data manifold to enable efficient sampling and reconstruction of new data points. Extensive evaluations across multiple datasets and comparisons with state-of-the-art methods demonstrate that CEMS delivers superior performance in both in-distribution and out-of-distribution scenarios, while introducing only minimal computational overhead. Code is available at https://github.com/azencot-group/CEMS.

Causal effect estimation from observational data is fundamental across various applications. However, selecting an appropriate estimator from dozens of specialized methods demands substantial manual effort and domain expertise. We present CausalPFN, a single transformer that amortizes this workflow: trained once on a large library of simulated data-generating processes that satisfy ignorability, it infers causal effects for new observational datasets out-of-the-box. CausalPFN combines ideas from Bayesian causal inference with the large-scale training protocol of prior-fitted networks (PFNs), learning to map raw observations directly to causal effects without any task-specific adjustment. Our approach achieves superior average performance on heterogeneous and average treatment effect estimation benchmarks (IHDP, Lalonde, ACIC). Moreover, it shows competitive performance for real-world policy making on uplift modeling tasks. CausalPFN provides calibrated uncertainty estimates to support reliable decision-making based on Bayesian principles. This ready-to-use model does not require any further training or tuning and takes a step toward automated causal inference (https://github.com/vdblm/CausalPFN).

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise assumptions but often deteriorates in the presence of heavy-tailed errors or outliers commonly encountered in real data applications such as genomics, finance, and signal processing. To address these challenges, we propose a novel robust regression method, termed Heavy Lasso, which incorporates a loss function inspired by the Student's t-distribution within a Lasso penalization framework. This loss retains the desirable quadratic behavior for small residuals while adaptively downweighting large deviations, thus enhancing robustness to heavy-tailed noise and outliers. Heavy Lasso enjoys computationally efficient by leveraging a data augmentation scheme and a soft-thresholding algorithm, which integrate seamlessly with classical Lasso solvers. Theoretically, we establish non-asymptotic bounds under both $\ell_1$ and $\ell_2 $ norms, by employing the framework of localized convexity, showing that the Heavy Lasso estimator achieves rates comparable to those of the Huber loss. Extensive numerical studies demonstrate Heavy Lasso's superior performance over classical Lasso and other robust variants, highlighting its effectiveness in challenging noisy settings. Our method is implemented in the R package heavylasso available on Github.

Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. This paper studies the stability properties of the mean-field approximation when the target distribution varies within the class of strongly log-concave measures. We establish dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in the 2-Wasserstein distance, with Lipschitz constant inversely proportional to the log-concavity parameter. Under additional regularity conditions, we further show that the MFVI optimizer depends differentiably on the target potential and characterize the derivative by a partial differential equation. Methodologically, we follow a novel approach to MFVI via linearized optimal transport: the non-convex MFVI problem is lifted to a convex optimization over transport maps with a fixed base measure, enabling the use of calculus of variations and functional analysis. We discuss several applications of our results to robust Bayesian inference and empirical Bayes, including a quantitative Bernstein--von Mises theorem for MFVI, as well as to distributed stochastic control.

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data dimension or rely on unrealistic assumptions such as access to exact empirical risk minimizers. In this work, we provide a principled analysis of score estimation, establishing a sample complexity bound of $\widetilde{\mathcal{O}}(ε^{-6})$. Our approach leverages a structured decomposition of the score estimation error into statistical, approximation, and optimization errors, enabling us to eliminate the exponential dependence on neural network parameters that arises in prior analyses. It is the first such result which achieves sample complexity bounds without assuming access to the empirical risk minimizer of score function estimation loss.

I present a novel approach to estimating the temporal and spatial patterns of violent conflict. I show how we can use highly temporally and spatially disaggregated data on conflict events in tandem with Gaussian processes to estimate temporospatial conflict trends. These trends can be studied to gain insight into conflict traps, diffusion and tempo-spatial conflict exposure in general; they can also be used to control for such phenomenons given other estimation tasks; lastly, the approach allow us to extrapolate the estimated tempo-spatial conflict patterns into future temporal units, thus facilitating powerful, stat-of-the-art, conflict forecasts. Importantly, these results are achieved via a relatively parsimonious framework using only one data source: past conflict patterns.

Dynamic treatment regimes (DTRs) are critical to precision medicine, optimizing long-term outcomes through personalized, real-time decision-making in evolving clinical contexts, but require careful supervision for unsafe treatment risks. Existing efforts rely primarily on clinician-prescribed gold standards despite the absence of a known optimal strategy, and predominantly using structured EHR data without extracting valuable insights from clinical notes, limiting their reliability for treatment recommendations. In this work, we introduce SAFER, a calibrated risk-aware tabular-language recommendation framework for DTR that integrates both structured EHR and clinical notes, enabling them to learn from each other, and addresses inherent label uncertainty by assuming ambiguous optimal treatment solution for deceased patients. Moreover, SAFER employs conformal prediction to provide statistical guarantees, ensuring safe treatment recommendations while filtering out uncertain predictions. Experiments on two publicly available sepsis datasets demonstrate that SAFER outperforms state-of-the-art baselines across multiple recommendation metrics and counterfactual mortality rate, while offering robust formal assurances. These findings underscore SAFER potential as a trustworthy and theoretically grounded solution for high-stakes DTR applications.

How does the training data affect a model's behavior? This is the question we seek to answer with data attribution. The leading practical approaches to data attribution are based on influence functions (IF). IFs utilize a first-order Taylor approximation to efficiently predict the effect of removing a set of samples from the training set without retraining the model, and are used in a wide variety of machine learning applications. However, especially in the high-dimensional regime (# params $\geq Ω($# samples$)$), they are often imprecise and tend to underestimate the effect of sample removals, even for simple models such as logistic regression. We present rescaled influence functions (RIF), a new tool for data attribution which can be used as a drop-in replacement for influence functions, with little computational overhead but significant improvement in accuracy. We compare IF and RIF on a range of real-world datasets, showing that RIFs offer significantly better predictions in practice, and present a theoretical analysis explaining this improvement. Finally, we present a simple class of data poisoning attacks that would fool IF-based detections but would be detected by RIF.

The Popularity Adjusted Block Model (PABM) provides a flexible framework for community detection in network data by allowing heterogeneous node popularity across communities. However, this flexibility increases model complexity and raises key unresolved challenges, particularly in effectively adapting spectral clustering techniques and efficiently achieving strong consistency in label recovery. To address these challenges, we first propose the Thresholded Cosine Spectral Clustering (TCSC) algorithm and establish its weak consistency under the PABM. We then introduce the one-step Refined TCSC algorithm and prove that it achieves strong consistency under the PABM, correctly recovering all community labels with high probability. We further show that the two-step Refined TCSC accelerates clustering error convergence, especially with small sample sizes. Additionally, we propose a data-driven approach for selecting the number of communities, which outperforms existing methods under the PABM. The effectiveness and robustness of our methods are validated through extensive simulations and real-world applications.

We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of $Ω(1/k)$. However, prior work using an unregularized scheme has only established an upper bound of $O(1/k^{1/4})$, leaving a significant gap. Our paper proves that this gap can be narrowed, or even closed, using two frequently used regularization schemes: (1) explicit isotropic $\ell_2$ regularization, and (2) implicit regularization via finite step budgets. We show that these approaches, which are used in practice to mitigate forgetting, reduce to stochastic gradient descent (SGD) on carefully defined surrogate losses. Through this lens, we identify a fixed regularization strength that yields a near-optimal rate of $O(\log k / k)$. Moreover, formalizing and analyzing a generalized variant of SGD for time-varying functions, we derive an increasing regularization strength schedule that provably achieves an optimal rate of $O(1/k)$. This suggests that schedules that increase the regularization coefficient or decrease the number of steps per task are beneficial, at least in the worst case.