Constructing parsimonious analytic models for dynamic systems via symbolic regression

An approach for constructing parsimonious generalized Gaussian kernel regression models

The paper proposes a novel construction algorithm for generalized Gaussian kernel regression models. Each kernel regressor in the generalized Gaussian kernel regression model has an individual diagonal covariance matrix, which is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. The standard...

Envelope Models for Parsimonious and Efficient Multivariate Linear Regression

We propose a new parsimonious version of the classical multivariate normal linear model, yielding a maximum likelihood estimator (MLE) that is asymptotically less variable than the MLE based on the usual model. Our approach is based on the construction of a link between the mean function and the covariance matrix, using the minimal reducing subspace of the latter that accommodates the former. T...

Parsimonious classification via generalised linear mixed models

We devise a classification algorithm based on generalised linear mixed model (GLMM) technology. The algorithm incorporates spline smoothing, additive model-type structures and model selection. For reasons of speed we employ the Laplace approximation, rather than Monte Carlo methods. Tests on real and simulated data show the algorithm to have good classification performance. Moreover, the result...

Parsimonious Classification Via Generalized Linear Mixed Models

Constructing dynamical systems with specified symbolic dynamics.

In this paper we demonstrate how to construct signals (time series) of continuous-time dynamical systems that exhibit a given symbolic dynamics. This is achieved without construction of the ordinary differential equations that generate the flow. This construction is of theoretical interest and is useful as a source of dynamical data that can be used to test various data analysis algorithms.