Fixed Point Strategies in Data Science
Fixed Point Strategies in Data Science
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DOI：
10.1109/tsp.2021.3069677
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发表时间：
2020-08
影响因子：
5.4
通讯作者：
P. Combettes;J. Pesquet
中科院分区：
文献类型：
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作者：
P. Combettes;J. Pesquet
本文的目标是通过展示定点策略为建模、分析和解决各种各样的问题提供了一个简化和统一的框架，从而促进定点策略在数据科学中的使用。它们被视为构成了一个自然的环境来解释高级凸优化方法的行为，以及数据科学中最近的非线性方法，这些方法是根据超越最小化概念的范式制定的，涉及纳什均衡或单调包含等结构。我们回顾了不动点理论的相关工具，并描述了证明收敛不动点构造的主要最新算法。我们还加入了额外的成分，如随机性、块实现和非欧几里得度量，它们提供了进一步的增强。讨论了信号和图像处理、机器学习、统计学、神经网络和逆问题的应用。
The goal of this article 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 provenly 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.