Instrumental variables (IV) analysis is an important applied tool for areas such as healthcare and consumer economics. For IV analysis in high-dimensional settings, the Generalized Method of Moments (GMM) using deep neural networks offers an efficient approach. With non-i.i.d. data sourced from scattered decentralized clients, federated learning is a popular paradigm for training the models while promising data privacy. However, to our knowledge, no federated algorithm for either GMM or IV analysis exists to date. In this work, we introduce federated instrumental variables analysis (FedIV) via federated generalized method of moments (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a federated non-convex non-concave minimax optimization problem, which is solved using federated gradient descent ascent (FedGDA) algorithm. One key challenge arises in theoretically characterizing the federated local optimality. To address this, we present properties and existence results of clients' local equilibria via FedGDA limit points. Thereby, we show that the federated solution consistently estimates the local moment conditions of every participating client. The proposed algorithm is backed by extensive experiments to demonstrate the efficacy of our approach.

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally represents relationships in the data. We provide exact and approximate solutions to the decoding problem via constrained optimization, split relabeling, and nearest neighbors regression. These methods effectively invert the compression pipeline, establishing a map from the embedding space back to the input space using splits learned by the ensemble's constituent trees. The resulting decoders are universally consistent under common regularity assumptions. The procedure works with supervised or unsupervised models, providing a window into conditional or joint distributions. We demonstrate various applications of this autoencoder, including powerful new tools for visualization, compression, clustering, and denoising. Experiments illustrate the ease and utility of our method in a wide range of settings, including tabular, image, and genomic data.

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance, arising in cubature, data compression, and optimisation. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective precludes global minimisation in general. Instead, we consider \emph{stationary} points of the MMD which, in contrast to points globally minimising the MMD, can be accurately computed. Our main theoretical contribution is the (perhaps surprising) result that, for integrands in the associated reproducing kernel Hilbert space, the cubature error of stationary MMD points vanishes \emph{faster} than the MMD. Motivated by this \emph{super-convergence} property, we consider discretised gradient flows as a practical strategy for computing stationary points of the MMD, presenting a refined convergence analysis that establishes a novel non-asymptotic finite-particle error bound, which may be of independent interest.

The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue by modifying the Lasso loss function, this paper introduces an approach that simplifies the data processed by Lasso. We propose that decorrelating variables before applying the Lasso improves the stability of variable selection regardless of the direction of correlation among predictors. Furthermore, we highlight that the irrepresentable condition, which ensures consistency for the Lasso, is satisfied after variable decorrelation under two assumptions. In addition, by noting that the instability of the Lasso is not limited to high-dimensional settings, we demonstrate the effectiveness of the proposed approach for low-dimensional data. Finally, we present empirical results that indicate the efficacy of the proposed method across different variable selection techniques, highlighting its potential for broader application. The DVS R package is developed to facilitate the implementation of the methodology proposed in this paper.

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by outliers, standard GPs and their sparse approximations struggle with computational tractability and robustness. We introduce Robust Computation-aware Gaussian Process (RCaGP), a novel GP model that jointly addresses these challenges by combining a principled treatment of approximation-induced uncertainty with robust generalized Bayesian updating. The key insight is that robustness and approximation-awareness are not orthogonal but intertwined: approximations can exacerbate the impact of outliers, and mitigating one without the other is insufficient. Unlike previous work that focuses narrowly on either robustness or approximation quality, RCaGP combines both in a principled and scalable framework, thus effectively managing both outliers and computational uncertainties introduced by approximations such as low-rank matrix multiplications. Our model ensures more conservative and reliable uncertainty estimates, a property we rigorously demonstrate. Additionally, we establish a robustness property and show that the mean function is key to preserving it, motivating a tailored model selection scheme for robust mean functions. Empirical results confirm that solving these challenges jointly leads to superior performance across both clean and outlier-contaminated settings, both on regression and high-throughput Bayesian optimization benchmarks.

Regardless the amount of data a machine learning (ML) model is trained on, there will inevitably be data that differs from their training set, lowering model performance. Concept shift occurs when the distribution of labels conditioned on the features changes, making even a well-tuned ML model to have learned a fundamentally incorrect representation. Identifying these shifted features provides unique insight into how one dataset differs from another, considering the difference may be across a scientifically relevant dimension, such as time, disease status, population, etc. In this paper, we propose SGShift, a model for detecting concept shift in tabular data and attributing reduced model performance to a sparse set of shifted features. SGShift models concept shift with a Generalized Additive Model (GAM) and performs subsequent feature selection to identify shifted features. We propose further extensions of SGShift by incorporating knockoffs to control false discoveries and an absorption term to account for models with poor fit to the data. We conduct extensive experiments in synthetic and real data across various ML models and find SGShift can identify shifted features with AUC $>0.9$ and recall $>90\%$, often 2 or 3 times as high as baseline methods.

This paper investigates a general robust one-shot aggregation framework for distributed and federated Independent Component Analysis (ICA) problem. We propose a geometric median-based aggregation algorithm that leverages $k$-means clustering to resolve the permutation ambiguity in local client estimations. Our method first performs k-means to partition client-provided estimators into clusters and then aggregates estimators within each cluster using the geometric median. This approach provably remains effective even in highly heterogeneous scenarios where at most half of the clients can observe only a minimal number of samples. The key theoretical contribution lies in the combined analysis of the geometric median's error bound-aided by sample quantiles-and the maximum misclustering rates of the aforementioned solution of $k$-means. The effectiveness of the proposed approach is further supported by simulation studies conducted under various heterogeneous settings.

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this theoretically, recent works examine gradient descent and its variants in simplified training settings, often assuming vanishing learning rates. These studies reveal various forms of implicit regularization, such as $\ell_1$-norm minimizing parameters in regression and max-margin solutions in classification. Concurrently, empirical findings show that moderate to large learning rates exceeding standard stability thresholds lead to faster, albeit oscillatory, convergence in the so-called Edge-of-Stability regime, and induce an implicit bias towards minima of low sharpness (norm of training loss Hessian). In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate balances between low parameter norm and low sharpness of the trained model. We furthermore prove for diagonal linear networks trained on a simple regression task that neither implicit bias alone minimizes the generalization error. These findings demonstrate that focusing on a single implicit bias is insufficient to explain good generalization, and they motivate a broader view of implicit regularization that captures the dynamic trade-off between norm and sharpness induced by non-negligible learning rates.

Hollmann et al. ( Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time. " Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning" . If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification.

Diffusion models (DMs) have demonstrated remarkable ability to generate diverse and high-quality images by efficiently modeling complex data distributions. They have also been explored as powerful generative priors for signal recovery, resulting in a substantial improvement in the quality of reconstructed signals. However, existing research on signal recovery with diffusion models either focuses on specific reconstruction problems or is unable to handle nonlinear measurement models with discontinuous or unknown link functions. In this work, we focus on using DMs to achieve accurate recovery from semi-parametric single index models, which encompass a variety of popular nonlinear models that may have {\em discontinuous} and {\em unknown} link functions. We propose an efficient reconstruction method that only requires one round of unconditional sampling and (partial) inversion of DMs. Theoretical analysis on the effectiveness of the proposed methods has been established under appropriate conditions. We perform numerical experiments on image datasets for different nonlinear measurement models. We observe that compared to competing methods, our approach can yield more accurate reconstructions while utilizing significantly fewer neural function evaluations.