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首页> 外文期刊>IEEE Signal Processing Magazine >Submodularity in Action: From Machine Learning to Signal Processing Applications
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Submodularity in Action: From Machine Learning to Signal Processing Applications

机译：潜水机在行动中：从机器学习到信号处理应用

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摘要

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners, as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: 1) relaxation into the continuous domain to obtain an approximate solution or 2) the development of a tailored algorithm that applies directly in the discrete domain. In both approaches, worst-case performance guarantees are often hard to establish. Furthermore, they are often complex and thus not practical for large-scale problems. In this article, we show how certain scenarios lend themselves to exploiting submodularity for constructing scalable solutions with provable worst-case performance guarantees. We introduce a variety of submodular-friendly applications and elucidate the relation of submodularity to convexity and concavity, which enables efficient optimization. With a mixture of theory and practice, we present different flavors of submodularity accompanying illustrative real-world case studies from modern SP and ML. In all of the cases, optimization algorithms are presented along with hints on how optimality guarantees can be established.
机译：子骨折是一个离散的域功能属性，可以解释为模拟连续域中的众所周知的凸起/凹版属性的作用。子模具功能表现出强大的结构，导致有效的优化算法，具有可提供的近乎最优的保证。这些特性，即效率和可提供的性能界限，对于信号处理（SP）和机器学习（ML）从业者特别感兴趣，因为在各种应用中遇到了各种离散的优化问题。传统上，存在两种常规方法来解决离散问题：1）放松进入连续域以获得近似解决方案或2），其在离散域中直接应用的定制算法的开发。在这两种方法中，最坏的情况担保通常很难建立。此外，它们通常是复杂的，因此对于大规模问题而不是实用。在本文中，我们展示了某些方案如何利用潜水机，以利用具有可证明最坏情况担保的可扩展解决方案。我们介绍了各种子模型友好的应用，并阐明了潜水线对凸性和凹陷的关系，这使得能够有效优化。随着理论和实践的混合，我们伴随着现代SP和ML的说明性真实案例研究的不同口蹄疫表现。在所有情况下，优化算法随着如何建立最佳保证的提示。

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