
Evaluation of Granger causality measures for constructing networks from multivariate time series
Granger causality and variants of this concept allow the study of comple...
read it

Metric on Nonlinear Dynamical Systems with Koopman Operators
The development of a metric for structural data is a longterm problem i...
read it

Reconstruction and prediction of random dynamical systems under borrowing of strength
We propose a Bayesian nonparametric model based on Markov Chain Monte Ca...
read it

Moment State Dynamical Systems for Nonlinear ChanceConstrained Motion Planning
Chanceconstrained motion planning requires uncertainty in dynamics to b...
read it

The FisherRao geometry of beta distributions applied to the study of canonical moments
This paper studies the FisherRao geometry on the parameter space of bet...
read it

The Hermitian Jacobi process: simplified formula for the moments and application to optical fibers MIMO channels
Using a change of basis in the algebra of symmetric functions, we comput...
read it

Shape Distributions of Nonlinear Dynamical Systems for Videobased Inference
This paper presents a shapetheoretic framework for dynamical analysis o...
read it
An informationgeometric approach to feature extraction and moment reconstruction in dynamical systems
We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data space of the observables themselves as in more conventional methods. Our approach is based on the fact that orbits of a dynamical system induce probability measures over the measurable space defined by (partial) observations of the system. We equip the space of these probability measures with a divergence, i.e., a distance between probability distributions, and use this divergence to define a kernel integral operator. The eigenfunctions of this operator create an orthonormal basis of functions that capture different timescales of the dynamical system. One of our main results shows that the evolution of the moments of the dynamicsdependent probability measures can be related to a timeaveraging operator on the original dynamical system. Using this result, we show that the moments can be expanded in the eigenfunction basis, thus opening up the avenue for nonparametric forecasting of the moments. If the collection of probability measures is itself a manifold, we can in addition equip the statistical manifold with the Riemannian metric and use techniques from information geometry. We present applications to ergodic dynamical systems on the 2torus and the Lorenz 63 system, and show on a realworld example that a small number of eigenvectors is sufficient to reconstruct the moments (here the first four moments) of an atmospheric time series, i.e., the realtime multivariate MaddenJulian oscillation index.
READ FULL TEXT
Comments
There are no comments yet.