State Estimation for Generalized Linear Dynamical Networks
Abstract
Summary Methods that can systematically characterize the structure and dynamics of neural circuits are fundamental to understanding information processing in the brain, including perception and cognition. However, unlocking the connectivity and interactions of large neural populations from limited measurements is dauntingly complex. From a mathematical perspective, the key challenge is that neural populations as observed through modern technologies such micro-electrocortiography ( ECoG) are, in essence, high-dimensional nonlinear dynamical systems with large numbers of hidden states. Generically, estimation and identification problems in high-dimensional dynamical systems suffer from the curse of dimensionality – the complexity of performing many computations grows exponentially in the state dimension. To address these challenges, the broad goals of this proposal are twofold: develop succinct mathematical models that can describe high-dimensional nonlinear dynamical systems with a particular focus on these systems as the arise in neural cortical circuits; and develop computationally scalable algorithms that can identify these models from limited observations including ECoG data. Toward this end, the key insight that we pursue in this project is that neural systems – and many other high-dimensional systems in engineering and science – can be described as networks of low-dimensional nonlinear dynamical systems with linear, memoryless interactions. We call these networks Generalized Linear Dynamical Networks (GLDNs). These models can readily capture a wide range of complex phenomena including neural systems. At the same time, we argue that the models are amenable to decomposition methods that enable tractable and scalable approaches for high-dimensional inference and system identification – the critical task in neural modeling. The focus of this short-term project (approximately one year) is on developing the foundational algorithmic and theoretical methods for GLDNs. The focus on the first year is on state estimation. The two challenges we address in this work are handling the nonlinearities and making the algorithms work on very large scale. The PI will leverage existing works based on graphical models for static problems where she was able to obtain scalable algorithms for high-dimensional nonlinear estimation algorithms with provable guarantees. The study of state estimation can in turn be used for subsequent work in system identification and work targeted specifically to neural systems. 1
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512677
Entities
People
- Alyson Fletcher
Organizations
- Office of Naval Research
- United States Navy
- University of California, Santa Cruz