机器学习

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

This paper develops the algorithmic and dynamical foundations of recursive ensemble learning driven by Fibonacci-type update flows. In contrast with classical boosting Freund and Schapire (1997); Friedman (2001), where the ensemble evolves…

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…

High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…

We establish a general statistical optimality theory for estimation problems where the target parameter is a linear functional of an unknown nuisance component that must be estimated from data. This formulation covers many causal and…

Neural networks have become a widely adopted tool for modeling nonlinear dynamical systems from data. However, the choice of training strategy remains a key design decision, particularly for simulation tasks. This paper compares two…

Neural networks have become a popular tool in predictive modelling, more commonly associated with machine learning and artificial intelligence than with statistics. Generalised Additive Models (GAMs) are flexible non-linear statistical…

Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a…

Differential privacy is a well-established framework for safeguarding sensitive information in data. While extensively applied across various domains, its application to network data -- particularly at the node level -- remains…

Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…

A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process. The proposition states that a lossy compression process is equivalent to {\it…

Backdoor and data-poisoning attacks can flip predictions with tiny training corruptions, yet a sharp theory linking poisoning strength, overparameterization, and regularization is lacking. We analyze ridge least squares with an unpenalized…

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

We propose a computationally efficient algorithm that achieves anytime regret of order $\mathcal{O}(\sqrt{t})$, with explicit dependence on the system dimensions and on the solution of the Discrete Algebraic Riccati Equation (DARE). Our…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Robustness of deep neural networks to input noise remains a critical challenge, as naive noise injection often degrades accuracy on clean (uncorrupted) data. We propose a novel training framework that addresses this trade-off through two…

Although Multi Armed Bandit (MAB) on one hand and the policy gradient approach on the other hand are among the most used frameworks of Reinforcement Learning, the theoretical properties of the policy gradient algorithm used for MAB have not…

In various practical situations, matrix factorization methods suffer from poor data quality, such as high data sparsity and low signal-to-noise ratio (SNR). Here, we consider a matrix factorization problem by utilizing auxiliary…

In this study, we introduce a sophisticated generative conditional strategy designed to impute missing values within datasets, an area of considerable importance in statistical analysis. Specifically, we initially elucidate the theoretical…

Detecting unobserved confounders is crucial for reliable causal inference in observational studies. Existing methods require either linearity assumptions or multiple heterogeneous environments, limiting applicability to nonlinear…