Recent advances in large-scale models, including deep neural networks and large language models, have substantially improved performance across a wide range of learning tasks. The widespread availability of such pre-trained models creates new opportunities for data-efficient statistical learning, provided they can be effectively integrated into downstream tasks. Motivated by this setting, we study few-shot personalization, where a pre-trained black-box model is adapted to a target domain using a limited number of samples. We develop a theoretical framework for few-shot personalization in nonparametric regression and propose algorithms that can incorporate a black-box pre-trained model into the regression procedure. We establish the minimax optimal rate for the personalization problem and show that the proposed method attains this rate. Our results clarify the statistical benefits of leveraging pre-trained models under sample scarcity and provide robustness guarantees when the pre-trained model is not informative. We illustrate the finite-sample performance of the methods through simulations and an application to the California housing dataset with several pre-trained models.

Clinical decision-making demands uncertainty quantification that provides both distribution-free coverage guarantees and risk-adaptive precision, requirements that existing methods fail to jointly satisfy. We present a hybrid Bayesian-conformal framework that addresses this fundamental limitation in healthcare predictions. Our approach integrates Bayesian hierarchical random forests with group-aware con-formal calibration, using posterior uncertainties to weight conformity scores while maintaining rigorous coverage validity. Evaluated on 61,538 admissions across 3,793 U.S. hospitals and 4 regions, our method achieves target coverage (94.3% vs 95% target) with adaptive precision: 21% narrower intervals for low-uncertainty cases while appropriately widening for high-risk predictions. Critically, we demonstrate that well-calibrated Bayesian uncertainties alone severely under-cover (14.1%), highlighting the necessity of our hybrid approach. This framework enables risk-stratified clinical protocols, efficient resource planning for high-confidence predictions, and conservative allocation with enhanced oversight for uncertain cases, providing uncertainty-aware decision support across diverse healthcare settings.

This paper develops a practical framework for using observational data to audit the consumer surplus effects of AI-driven decisions, specifically in targeted pricing and algorithmic lending. Traditional approaches first estimate demand functions and then integrate to compute consumer surplus, but these methods can be challenging to implement in practice due to model misspecification in parametric demand forms and the large data requirements and slow convergence of flexible nonparametric or machine learning approaches. Instead, we exploit the randomness inherent in modern algorithmic pricing, arising from the need to balance exploration and exploitation, and introduce an estimator that avoids explicit estimation and numerical integration of the demand function. Each observed purchase outcome at a randomized price is an unbiased estimate of demand and by carefully reweighting purchase outcomes using novel cumulative propensity weights (CPW), we are able to reconstruct the integral. Building on this idea, we introduce a doubly robust variant named the augmented cumulative propensity weighting (ACPW) estimator that only requires one of either the demand model or the historical pricing policy distribution to be correctly specified. Furthermore, this approach facilitates the use of flexible machine learning methods for estimating consumer surplus, since it achieves fast convergence rates by incorporating an estimate of demand, even when the machine learning estimate has slower convergence rates. Neither of these estimators is a standard application of off-policy evaluation techniques as the target estimand, consumer surplus, is unobserved. To address fairness, we extend this framework to an inequality-aware surplus measure, allowing regulators and firms to quantify the profit-equity trade-off. Finally, we validate our methods through comprehensive numerical studies.

Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target relationship. Our approach relies on a local transfer assumption: the covariate space is partitioned into finitely many cells such that, within each cell, the target regression function can be expressed as a low-complexity transformation of the source regression function. This localized structure enables effective transfer where similarity is present while limiting negative transfer elsewhere. We introduce estimators that jointly learn the local transfer functions and the target regression, together with fully data-driven procedures that adapt to unknown partition structure and transfer strength. We establish sharp minimax rates for target regression estimation, showing that local transfer can mitigate the curse of dimensionality by exploiting reduced functional complexity. Our theoretical guarantees take the form of oracle inequalities that decompose excess risk into estimation and approximation terms, ensuring robustness to model misspecification. Numerical experiments illustrate the benefits of the proposed approach.

Conformal prediction guarantees degrade under distribution shift. We study this using COVID-19 as a natural experiment across 8 supply chain tasks. Despite identical severe feature turnover (Jaccard approximately 0), coverage drops vary from 0% to 86.7%, spanning two orders of magnitude. Using SHapley Additive exPlanations (SHAP) analysis, we find catastrophic failures correlate with single-feature dependence (rho = 0.714, p = 0.047). Catastrophic tasks concentrate importance in one feature (4.5x increase), while robust tasks redistribute across many (10-20x). Quarterly retraining restores catastrophic task coverage from 22% to 41% (+19 pp, p = 0.04), but provides no benefit for robust tasks (99.8% coverage). Exploratory analysis of 4 additional tasks with moderate feature stability (Jaccard 0.13-0.86) reveals feature stability, not concentration, determines robustness, suggesting concentration effects apply specifically to severe shifts. We provide a decision framework: monitor SHAP concentration before deployment; retrain quarterly if vulnerable (>40% concentration); skip retraining if robust.

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.

Graphs are commonly used in machine learning to model relationships between instances. Consider the task of predicting the political preferences of users in a social network; to solve this task one should consider, both, the features of each individual user and the relationships between them. However, oftentimes one is not interested in the label of a single instance but rather in the distribution of labels over a set of instances; e.g., when predicting the political preferences of users, the overall prevalence of a given opinion might be of higher interest than the opinion of a specific person. This label prevalence estimation task is commonly referred to as quantification learning (QL). Current QL methods for tabular data are typically based on the so-called prior probability shift (PPS) assumption which states that the label-conditional instance distributions should remain equal across the training and test data. In the graph setting, PPS generally does not hold if the shift between training and test data is structural, i.e., if the training data comes from a different region of the graph than the test data. To address such structural shifts, an importance sampling variant of the popular adjusted count quantification approach has previously been proposed. In this work, we extend the idea of structural importance sampling to the state-of-the-art KDEy quantification approach. We show that our proposed method adapts to structural shifts and outperforms standard quantification approaches.

A first-order method for nonconvex-strongly-concave constrained minimax optimization Zhaosong Lu Sanyou Mei May 12, 2024 (Revised: October 23, 2025) Abstract In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax problems and suitably solved by a first-order method developed in this paper that leverages the strong concavity structure. Under suitable assumptions, the proposed method achieves an operation complexity of O(ε 3.5 log ε 1), measured in terms of its fundamental operations, for finding an ε-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of ε 0.5 . Keywords: minimax optimization, augmented Lagrangian method, first-order method, operation complexity Mathematics Subject Classification: 90C26, 90C30, 90C47, 90C99, 65K05 1 Introduction In this paper, we consider a nonconvex-strongly-concave constrained minimax problem F = min c(x) 0 max d(x,y) 0 {F (x,y):= f (x, y) + p(x) q(y)}. Assume that problem (1) has at least one optimal solution and the following additional assumptions hold.

The new Atlas will be deployed at Hyundai and Google DeepMind first. After years of testing its humanoid robot (and forcing it to dance), Boston Dynamics' Atlas is entering production . The robotics company says the final product version of the robot is being built now, and the first companies that will receive deployments are Hyundai, Boston Dynamics' majority shareholder, and Google DeepMind, the firm's newly minted AI partner. This final enterprise version of Atlas can perform a wide array of industrial tasks, according to Boston Dynamics, and is specifically designed with consistency and reliability in mind. Atlas can work autonomously, via a teleoperator or with a tablet steering interface, and the robot is both strong and durable.