Related papers: Fixed Point Strategies in Data Science

Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the…

This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary…

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…

We propose a method that combines fixed point algorithms with a neural network to optimize jointly discrete and continuous variables in millimeter-wave communication systems, so that the users' rates are allocated fairly in a well-defined…

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…

Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

Feature selection, as a data preprocessing strategy, has been proven to be effective and efficient in preparing data (especially high-dimensional data) for various data mining and machine learning problems. The objectives of feature…

The main topic of this paper are algorithms for computing Nash equilibria. We cast our particular methods as instances of a general algorithmic abstraction, namely, a method we call {\em algorithmic boosting}, which is also relevant to…

This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…