Seminar Meeting Link:
Dennis Picard Chaired Professor
Electrical and Computer Engineering
?Easy, hard or convex?: the role of sparsity and structure in learning dynamical models?
Abstract: Arguably,one of the hardest challenges faced now by the dynamical systemscommunity stems from the exponential explosion in the availability of data,fueled by recent advances in sensing and actuationcapabilities. Simply stated,classical techniques are ill equipped to handle very large volumes of(heterogeneous) data, due to poor scaling properties, and to impose thestructural constraints required to implement ubiquitous sensing andcontrol. For example, the powerful Linear Matrix Inequality frameworkdeveloped in the past 20 years and associated semidefinite program basedmethods have proven very successful in providing global solutions to manycontrol and identification problems. However, in may cases these methods breakdown when considering problems involving just a few hundred data points. On theother hand, several in-principle non-convex problems (e.gidentification and robust control of classes of switched systems) can beefficiently solved in cases involving large amounts of data. Thus thetraditional convex/non-convex dichotomy may fail to completely capture theintrinsic difficulty of some problems.
Thegoal of this talk is to explorehow this ?curse of dimensionality? can be potentially overcome byexploiting the twin ?blessings? of self-similarity (high degree of spatio-temporal correlation in the data)and inherent underlying sparsity, and to answer the question of “what is Big Data in dynamical systems theory?”. Whilethese ideas have already been recently usedin machine learning (for instancein the context of dimensionality reduction and variable selection), theyhave hitherto not been fully exploited in systems theory. By appealing toa deep connection to semi-algebraic optimization, rank minimization andmatrix completion we will show that, in the context of systems theory, thelimiting factor is given by the “memory” of the system rather thanthe size of the data itself, and discuss the implications of this fact. These concepts will be illustrated by examining examples of “easy” and “hard” problems, including identificationand control of hybrid systems and (in)validation of switched models. We willconclude the talk by exploring the connection between hybrid systemsidentification, information extraction, and machine learning, and point out tonew research directions in systems theory and in machine learning motivated bythese problems.
Bio: Mario Sznaier iscurrently the Dennis Picard Chaired Professor at the Electrical and ComputerEngineering Department, Northeastern University,Boston. Prior to joiningNortheastern University, Dr. Sznaier wasa Professor of Electrical Engineering at the Pennsylvania State University andalso held visiting positions at the California Institute of Technology. Hisresearch interest include robust identification and control of hybrid systems,robust optimization, and dynamical vision. Dr. Sznaier iscurrently serving as an associate editor for the journal Automatica andas chair of the IFAC Technical Committee on Robust Control. Past recent serviceinclude Program Chair of the 2017 IEEE Conf. on Decision and Control, GeneralChair of the 2016 IEEE Multi Systems Conference, Chair of the IEEEControl Systems Society Technical Committee on Computational Aspects of ControlSystems Design (2013-2017), Executive Director of the IEEE CSS(2007-2011)and member of the Board of Governors of the CSS (2006-2014).He is adistinguished member of the IEEE Control Systems Society and aFellow of the IEEE for his contributions to robust control, identification anddynamic vision. A list of publications and current research projects can befound at:https://nam02.safelinks.protection.outlook.com/?url=http%3A%2F%2Frobustsystems.coe.neu.edu%2F&data=04%7C01%7Cjsulam1%40jhu.edu%7Cc568d7e5a82f414e8e4508d8cc50bc47%7C9fa4f438b1e6473b803f86f8aedf0dec%7C0%7C0%7C637483994418193664%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=2ngKt8DuptQ9d2M7QVeM5wvURHtKesMpAgueOo4hwNM%3D&reserved=0