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These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

Optimization and Control · Mathematics 2024-10-28 Charles Dossal , Samuel Hurault , Nicolas Papadakis

Machine unlearning is an emerging field that selectively removes specific data samples from a trained model. This capability is crucial for addressing privacy concerns, complying with data protection regulations, and correcting errors or…

Machine Learning · Computer Science 2025-01-29 Zitong Li , Qingqing Ye , Haibo Hu

Additional training of a deep learning model can cause negative effects on the results, turning an initially positive sample into a negative one (degradation). Such degradation is possible in real-world use cases due to the diversity of…

Machine Learning · Computer Science 2022-05-19 Akihito Yoshii , Susumu Tokumoto , Fuyuki Ishikawa

The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…

Machine Learning · Computer Science 2020-07-22 Abbas Raza Ali , Marcin Budka , Bogdan Gabrys

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Machine Learning · Statistics 2015-11-13 Mengdi Wang , Yichen Chen , Jialin Liu , Yuantao Gu

Machine unlearning refers to removing the influence of a specified subset of training data from a machine learning model, efficiently, after it has already been trained. This is important for key applications, including making the model…

Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…

Information Theory · Computer Science 2020-06-01 Sundara Rajan Srinivasavaradhan , Michelle Du , Suhas Diggavi , Christina Fragouli

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

Machine Learning · Computer Science 2022-11-07 Ioannis A. Nellas , Sotiris K. Tasoulis , Vassilis P. Plagianakos , Spiros V. Georgakopoulos

Machine Unlearning allows participants to remove their data from a trained machine learning model in order to preserve their privacy, and security. However, the machine unlearning literature for generative models is rather limited. The…

Machine Learning · Computer Science 2025-06-25 Ayush K. Varshney , Vicenç Torra

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Optimization and Control · Mathematics 2018-07-03 Vyacheslav Kungurtsev , Tomas Pevny

Machine learning systems increasingly face requirements to remove entire domains of information--such as toxic language or biases--rather than individual user data. This task presents a dilemma: full removal of the unwanted domain data is…

Machine Learning · Computer Science 2026-01-15 Youssef Allouah , Rachid Guerraoui , Sanmi Koyejo

Delays and asynchrony are inevitable in large-scale machine-learning problems where communication plays a key role. As such, several works have extensively analyzed stochastic optimization with delayed gradients. However, as far as we are…

Machine Learning · Computer Science 2023-08-28 Arman Adibi , Aritra Mitra , Hamed Hassani

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

Machine Learning · Computer Science 2019-04-08 Craig Wilson , Yuheng Bu , Venugopal Veeravalli

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

Machine Learning · Statistics 2025-08-07 Arnab Ganguly , Tobias Sutter

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…

Optimization and Control · Mathematics 2015-02-18 Stephen J. Wright

This study investigates the machine unlearning techniques within the context of large language models (LLMs), referred to as \textit{LLM unlearning}. LLM unlearning offers a principled approach to removing the influence of undesirable data…

Computation and Language · Computer Science 2025-06-03 Jiahui Geng , Qing Li , Herbert Woisetschlaeger , Zongxiong Chen , Fengyu Cai , Yuxia Wang , Preslav Nakov , Hans-Arno Jacobsen , Fakhri Karray

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

Machine Learning · Computer Science 2020-11-19 Giorgos Mamakoukas , Orest Xherija , T. D. Murphey

Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…

Machine Learning · Statistics 2017-08-16 Alexander Jung

Machine unlearning aims to remove the influence of specific data from trained models while preserving general utility. Existing approximate unlearning methods often rely on performance-degradation heuristics, such as loss maximization or…

Machine Learning · Computer Science 2026-03-13 Jonas Mirlach , Sonia Laguna , Julia E. Vogt

As deep learning models are becoming larger and data-hungrier, there are growing ethical, legal and technical concerns over use of data: in practice, agreements on data use may change over time, rendering previously-used training data…

Machine Learning · Computer Science 2024-05-20 Nazanin Mohammadi Sepahvand , Vincent Dumoulin , Eleni Triantafillou , Gintare Karolina Dziugaite
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