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

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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).