EE Seminar: No Equations, No Parameters, No Variables: Data-driven Geometry Learning for Parametrically-Dependent Dynamical Systems
(The talk will be given in English)
Speaker: Prof. Ronen Talmon,
Department of Electrical Engineering, Technion
Sunday, April 2nd, 2017
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
No Equations, No Parameters, No Variables: Data-driven Geometry Learning for Parametrically-Dependent Dynamical Systems
Abstract
The extraction of models from data is a fundamental cognitive as well as scientific challenge. We demonstrate a geometric/analytic learning algorithm capable of creating minimal descriptions of parametrically-dependent unknown nonlinear dynamical systems. This is accomplished by the data-driven discovery of useful intrinsic state variables and parameters, in terms of which one can empirically model the underlying dynamics. We present an approach based on informed observation geometry that enables us to formulate models without first principles, as well as without closed-form equations. Our toolbox consists of data-driven hierarchical structures, multiscale bases and metrics, and intrinsic minimal data representations.
We will show applications to simulated data as well as to in-vivo recordings of neuronal activity from awake animals. The application of our technique to such recordings demonstrates its capability of capturing the relations between time-dependent neural activities in different cortical regions (motor and sensory) and associate them to behavior. Specifically, our approach gives rise to the joint organization of neurons and dynamic patterns in data-driven hierarchical structures, as well as to multi-resolution representations, discovering latent driving structures and connectivity patterns as they develop and vary over the course of weeks, days, and within individual trials. By jointly organizing neurons along time segments, our methodology reveals co-dependencies and patterns of activation related to external triggers (e.g., a tone) and behavioral events (e.g., the sequence of motor actions). In addition, we will discuss a preliminary attempt to relate the extracted model from the same animal at different stages of its training and to reveal a proficiency phase shift: from beginner through learner to expert.
