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It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity,…

Machine Learning · Computer Science 2021-05-25 Daniel Alabi

This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…

Machine Learning · Statistics 2021-03-03 Jie Shen , Chicheng Zhang

Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the…

Statistics Theory · Mathematics 2018-10-05 Christian Borgs , Jennifer Chayes , Adam Smith , Ilias Zadik

One of the big challenges in machine learning applications is that training data can be different from the real-world data faced by the algorithm. In language modeling, users' language (e.g. in private messaging) could change in a year and…

Computation and Language · Computer Science 2018-03-07 Vadim Popov , Mikhail Kudinov , Irina Piontkovskaya , Petr Vytovtov , Alex Nevidomsky

In this work we address the practical challenges of training machine learning models on privacy-sensitive datasets by introducing a modular approach that minimizes changes to training algorithms, provides a variety of configuration…

Machine Learning · Computer Science 2019-03-05 H. Brendan McMahan , Galen Andrew , Ulfar Erlingsson , Steve Chien , Ilya Mironov , Nicolas Papernot , Peter Kairouz

In this paper, we consider the task of answering linear queries under the constraint of differential privacy. This is a general and well-studied class of queries that captures other commonly studied classes, including predicate queries and…

Data Structures and Algorithms · Computer Science 2011-01-20 Aaron Roth

We study the difficulties in learning that arise from robust and differentially private optimization. We first study convergence of gradient descent based adversarial training with differential privacy, taking a simple binary classification…

Machine Learning · Computer Science 2022-01-10 Jamie Hayes , Borja Balle , M. Pawan Kumar

We study the optimal sample complexity of a given workload of linear queries under the constraints of differential privacy. The sample complexity of a query answering mechanism under error parameter $\alpha$ is the smallest $n$ such that…

Data Structures and Algorithms · Computer Science 2016-12-12 Assimakis Kattis , Aleksandar Nikolov

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Numerical Analysis · Mathematics 2024-05-10 Yan Xie , Minrui Lv , Chensong Zhang

In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in…

Data Structures and Algorithms · Computer Science 2025-09-26 Hadley Black , Kasper Green Larsen , Arya Mazumdar , Barna Saha , Geelon So

The realizable-to-agnostic transformation (Beimel et al., 2015; Alon et al., 2020) provides a general mechanism to convert a private learner in the realizable setting (where the examples are labeled by some function in the concept class) to…

Machine Learning · Statistics 2025-10-03 Bo Li , Wei Wang , Peng Ye

Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…

Numerical Analysis · Mathematics 2024-12-04 Zhongshuo Lin , Yifan Wang , Hehu Xie

Learning the structure of a Bayesian network from decentralized data poses two major challenges: (i) ensuring rigorous privacy guarantees for participants, and (ii) avoiding communication costs that scale poorly with dimensionality. In this…

Machine Learning · Statistics 2026-04-13 Ghita Fassy El Fehri , Aurélien Bellet , Philippe Bastien

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…

Optimization and Control · Mathematics 2023-03-07 Mohammadreza Chamanbaz , Roland Bouffanais

We design differentially private learning algorithms that are agnostic to the learning model. Our algorithms are interactive in nature, i.e., instead of outputting a model based on the training data, they provide predictions for a set of…

Machine Learning · Computer Science 2018-03-15 Raef Bassily , Om Thakkar , Abhradeep Thakurta

Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure -- such as meta-learning and hyperparameter optimization. Such applications often…

Machine Learning · Computer Science 2025-11-10 Andrew Lowy , Daogao Liu

In this work, we study trade-offs between accuracy and privacy in the context of linear queries over histograms. This is a rich class of queries that includes contingency tables and range queries, and has been a focus of a long line of…

Data Structures and Algorithms · Computer Science 2013-08-05 Aleksandar Nikolov , Kunal Talwar , Li Zhang

We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach…

Cryptography and Security · Computer Science 2026-01-09 Hao WU , Hanwen Zhang

We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of…

Machine Learning · Computer Science 2025-07-30 Chao Yan
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