论文标题
数据科学的固定点策略
Fixed Point Strategies in Data Science
论文作者
论文摘要
本文的目的是通过表明它们为建模，分析和解决各种问题提供简化和统一的框架来促进数据科学中的固定点策略。他们被认为构成了一种自然环境，以解释高级凸优化方法的行为以及数据科学中最新的非线性方法，这些方法是根据范式提出的，这些范式超出了最小化的概念，并涉及纳什均衡或单调包含物等构建体。我们回顾了固定点理论的相关工具，并描述了可证明是收敛固定点构建的主要最新算法。我们还结合了其他成分，例如随机性，块状实施和非欧国人指标，这些成分可提供进一步的增强。讨论了信号和图像处理，机器学习，统计，神经网络和反问题的应用。
The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a natural environment to explain the behavior of advanced convex optimization methods as well as of recent nonlinear methods in data science which are formulated in terms of paradigms that go beyond minimization concepts and involve constructs such as Nash equilibria or monotone inclusions. We review the pertinent tools of fixed point theory and describe the main state-of-the-art algorithms for provably convergent fixed point construction. We also incorporate additional ingredients such as stochasticity, block-implementations, and non-Euclidean metrics, which provide further enhancements. Applications to signal and image processing, machine learning, statistics, neural networks, and inverse problems are discussed.
