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Analysis of dynamical data
Special Events| Speaker: | Sui Tang, Johns Hopkins University |
| Location: | 1147 MSB |
| Start time: | Mon, Jan 27 2020, 4:10PM |
High-dimensional dynamical data arise in many fields of modern science and introduce new challenges in statistical learning and data recovery. In this talk, I will present two sets of problems. One is related to the data-driven discovery of dynamics in systems of interacting agents: given only observed trajectories of the system, we are interested in estimating the interaction laws between the agents using tools from statistical/machine learning. We show that at least in particular circumstances, where the interactions are governed by (unknown) functions of distances, the high-dimensionality of the state space of the system does not affect the learning rates. We can achieve an optimal learning rate for the interaction kernel, equal to that of a one-dimensional regression problem. The other one is related to the dynamical sampling: a new area in sampling theory that deals with processing a linear time series of evolving signals and aims at recovering the initial state and the forward operator from its coarsely sampled evolving states. We provide mathematical theories to show how the dynamics can inform feasible space-time sampling locations and the fundamental limit of space-time trade-off.
Meet the speaker at a reception starting 3:45pm in front of MSB. Refreshments will be served.