Machine Learning for Signal Analysis and System Modeling: Sparse and Event Driven Strategies

拟议的研究是在机器学习（ML）及其应用领域的信号处理和系统建模。ML是计算机科学发展最快的领域之一，具有深远的应用。 这些不同的应用需要新的ML算法，能够科普大量的高维数据集。 在这个提案中，我描述了我的计划，将我目前对非参数/半参数学习方法的研究扩展到由两个概念驱动的ML问题：稀疏性和事件。 * 这一挑战不仅包括开发新的基本方法，而且还包括在信号和系统分析的框架内对其进行验证。还计划在电力工程和生物信号处理领域的具体应用中测试所提出的方法。* 我的研究建议依赖于将现代非参数/半参数学习方法与稀疏性和事件的概念相结合的想法。ML的稀疏性方法是基于这样的观察，即与原始空间的维度相比，真实世界的信号和系统的相关参数相对较少。 稀疏建模深深植根于古老的简约原则，可以与我们的日常生活。 关键问题是发现一个稀疏表示及其在给定环境中的形式。 目前对具有稀疏性的ML的研究大多局限于有限维线性模型。在这种设置中，稀疏性是指大多数变量接近于零的条件。稀疏线性模型的有效解决方案是基于凸松弛的惩罚最小二乘准则产生著名的拉索算法及其扩展。* 事件驱动的方法可以被视为一种特定形式的稀疏性，它通过基于仅在事件触发条件成立时获取的观测值生成无限维对象的表示。因此，对象由稀疏且随机分布的实例表示。在信号分析中，具体的基于事件的表示可以从一系列事件中获得，如平交道口和局部极值。各种事件类型可导致不同的稀疏表示。研究计划选择或联合收割机各种事件方案，以实现基于事件的学习的最大准确性和效率。*这个建议的挑战是要彻底检查由经典和基于事件的稀疏表示产生的无限维对象的稀疏性。我相信，所提出的稀疏和事件驱动的ML范式可以大大扩大ML应用的范围，并在案例研究的背景下改进现有的算法。在这个为期5年的周期中，我建议培养6名博士生（3名现任+ 3名新生）和3名硕士生（1名现任+ 2名新生）。

The proposed research is in the area of machine learning (ML) and its applications to signal processing and system modelling. ML is one the fastest growing fields of computer science, with far-reaching applications. These diverse applications demand for new ML algorithms able to cope with massive data sets of high dimensionality. In this proposal, I describe my plan to extend my current research on nonparametric/semiparametric learning methods to ML problems that are driven by two concepts: sparsity and events. ***This challenge includes not only the development of the new basic methodology, but also to verify it in the framework of signal and system analysis. Testing of the proposed methods in concrete applications within the areas of power engineering and biological signal processing is also planned. ***My research proposal relies on the idea of blending the modern nonparametric/semiparametric learning methodology with the concepts of sparsity and events. The sparsity approach to ML is based on the observation that real-world signals and systems are well characterized by a relatively small number of relevant parameters when compared to the dimension of their original space. Sparse modeling is deeply rooted in the ancient principle of parsimony and can be related to our daily lives. The key problem is to discover a sparse representation and its form in a given setting. The current research on ML with sparsity is mostly confined to finite-dimensional linear models. In this set-up the sparsity refers to the condition that most variables are close to zero. Efficient solutions for sparse linear models are based on the convex relaxation of the penalized least-squares criteria yielding the celebrated Lasso algorithm and its extensions. ***The event-driven approach can be viewed as a specific form of obtaining sparsity by generating a representation of the infinite-dimensional object based on observations that are acquired only when the event triggering condition holds. As a result, the object is represented by sparsely and randomly distributed instances. In signal analysis concrete event-based representations can be obtained from a sequence of events like level crossings and local extremes. Various event types may result in different sparse representations. Research is planned to select or combine various event schemes for the maximum accuracy and efficiency of the event-based learning.***The challenge of this proposal is to give thorough examination of the sparsity of infinite-dimensional objects generated by classical and event-based sparse representations. I believe that the proposed sparse and event driven ML paradigm can substantially enlarge a scope of ML applications and improve the existing algorithms within the context of examined case studies. Over this 5-year cycle I propose to train 6 PhD students (3 current + 3 new) and 3 MSc students (1 current + 2 new).