Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

Abstract

Abstract-The Volterra model is a well-established option in nonlinear black-box system identification. However, the estimated model is often over-parametrized. This paper presents an approach to reducing the number of parameters of a Volterra model with the kernels parametrized in the orthonormal basis of Laguerre functions by estimating it with a sparse estimation algorithm subject to constraints. The resulting parameter estimates are scrutinized for parameter redundancy and functional dependence by principal component analysis. The benefits of this approach are illustrated by identifying the human smooth pursuit system. Previous studies have suggested that the Volterra model structure is suitable for modeling the human smooth pursuit system both in health and disease. The data sets are obtained by eye tracking in a study performed on 7 test subjects diagnosed with Parkinson's disease and 22 healthy control subjects. In terms of output error, the reduced model has similar performance to that of the full model.

Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements

“…Second-order VL models capture the oculodynamics of the SPS well both in the patients and controls. This is in line with previous research on VL modeling of the SPS [8], [24], [25]. Therefore, higher-order nonlinearities appear to be insignificant in the oculodynamics.…”

“…The discrete and continuous VL model structures were chosen by means of the procedure described in [8]. Laguerre and nonlinearity orders N = 2, L = 2 were used initially, and in the explicit delay case the delay τ was also considered as a parameter.…”

“…Therefore, sparse estimation methods such as LASSO [5], [6] and SPICE [7] are applied to identify and estimate only the essential kernel components. To further promote model parsimonicity, an approach combining sparse estimation with estimated functional relations between the VL coefficients has been proposed and applied to the modeling of the human smooth pursuit system (SPS) [8].…”

“…Compute the output loss ε (τi) = ∥y − ŷ(τ i , γ)∥ 2 7: end for 8: (γ, τ ) = arg min τi∈T ε (τi) The estimation procedure on the population level is described in [8] and can be summarized as in Algorithm 2.…”

Nonlinear dynamics of the human smooth pursuit system in health and disease: Model structure and parameter estimation

“…PCA was used to identify possible functional relations between the coefficients, and a reduced model structure was selected. The VL-model reduction procedure is detailed in [2].…”