A0880
Title: Modeling trajectories using functional linear first-order differential equations
Authors: Julia Wrobel - Colorado School of Public Health (United States) [presenting]
Abstract: A novel regression method is introduced that fuses concepts from functional linear regression and ordinary differential equations. The method models i.i.d. trajectories in a dynamical systems framework which captures in the influence of forces and derivatives on the path of an object. The motivation comes from novel data from an experiment exploring the relationship between neural firing rates and hand trajectories of mice performing a reaching task while under neurological assessment. This is an example from the increasingly common class of problems where outcome and responses are measured densely in parallel. For these data streams, we want to understand the relationship between inputs and outputs that are both functions measured on the same domain. Recent work using these data suggests that the dynamics of the arm during dexterous, voluntary movements are tightly coupled to neural control signals from the motor cortex. To better quantify how brain activity affects current and future paw position, our model incorporates initial position and has parameters that treat the relationship between the paw trajectory and the brain as a dynamical system of inputs and outputs, that state of which evolve over time. We compare our method to historical functional linear regression in simulations and on the mouse kinematic data.
