报告人：John S. Baras（Institute for Systems Research University of Maryland College Park）
We briefly review various instances of non-commutative probability models from quantum mechanics, directed information, nonlinear control systems, Web-based inference, multi-agent systems, collective human cognition and decision making from psychology. To illustrate and explain our new theory we consider the binary hypothesis-testing problem, as the simplest human decision-making problem. First, we consider a single observer. We analyze three approaches to this decision-making problem. In the first, we represent the available data via classical probability (Kolmogorov). In the second and third, we represent the available data via two versions of non-commutative probability (von Neumann): as coming from measurements modeled via projection valued measures (PVM), and then from measurements modeled via positive operator valued measures (POVM). We compare the performance achieved by these three approaches. Next, we consider the binary hypothesis testing problem with two collaborating observers. We analyze three approaches. In the first (centralized) approach, the observations collected by both observers are sent to a central coordinator where hypothesis testing is performed. In the second approach, each observer performs hypothesis testing based on locally collected observations. At every time step decision information is exchanged until consensus is achieved. In the third approach, the sequential hypothesis testing problem is formulated for each observer, and solved using locally collected observations. Taking into account the asymmetric and random stopping times of the observers, we design a consensus algorithm. We compare the performance of the three approaches via numerical methods. To explain the surprises found in the above results, and several other “paradoxes” for the behavioral and psychology communities, we investigate how the probability models for multi-agent systems could be constructed from observational. We develop an axiomatic method for such a construction that reveals some new foundational principles: multiple non-collocated observers, existence of incompatible events, notions of information sharing, directed information, constrained event algebras. We next describe independence-friendly logic and its multi-agent game theory semantics. We describe the resulting convex optimization problems. We close with our recent work on unifying these various non-commutative probability models and their utilization.
John S. Baras is a Distinguished University Professor and holds the endowed Lockheed Martin Chair in Systems Engineering at the Institute for Systems Research (ISR) and the Department of Electrical and Computer Engineering of the University of Maryland College Park. He received his Ph.D. degree in Applied Mathematics from Harvard University in 1973. Professor in the Applied Mathematics, Statistics and Scientific Computation Program. Affiliate Professor of: Fischell Department of Bioengineering; Department of Mechanical Engineering; Department of Decision, Operations and Information Technologies, Robert H. Smith School of Business; Department of Computer Science. From 1985 to 1991, he was the Founding Director of the ISR and since 1992 he has been the Director of the Maryland Center for Hybrid Networks, which he co-founded. He is an IEEE Life Fellow, SIAM Fellow, AAAS Fellow, NAI Fellow, IFAC Fellow, AIAA Associate Fellow, AMS Fellow, Member of the National Academy of Inventors and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA). Major honors and awards include the 1980 George Axelby Award from the IEEE Control Systems Society, the 2006 Leonard Abraham Prize from the IEEE Communications Society, the 2017 IEEE Simon Ramo Medal, the 2017 AACC Richard E. Bellman Control Heritage Award., and the 2018 AIAA Aerospace Communications Award. In 2016 he was inducted in the University of Maryland A. J. Clark School of Engineering Innovation Hall of Fame. In 2018 he was awarded a Doctorate Honoris Causa by his alma mater the National Technical University of Athens, Greece. His research interests include systems and control, optimization, communication networks, signal processing and understanding, robotics, computing systems, network security and trust, systems biology, healthcare management systems, model-based systems engineering. He has been awarded eighteen patents and has been honored worldwide with many awards as innovator and leader of economic development.