Reformulated Parametric Learning Based on Ordinary Differential Equations

Abstract

This paper presents a new parametric learning scheme, namely, Reformulated Parametric Learning (RPL). Instead of learning the parameters directly on the original model, this scheme reformulates the model into a simpler yet equivalent one, and all parameters are estimated on the reformulated model. While a set of simpler equivalent models can be obtained from deriving Equivalent Decomposition Models (EDM) through their associated ordinary differential equations, to achieve the simplest EDM is a combination optimization problem. For a preliminary study, we apply the RPL to a simple class of models, named ’Additive Pseudo-Exponential Models’ (APEM). While conventional approaches have to adopt nonlinear programming to learn APEM, the proposed RPL can obtain equivalent solutions through Linear Least -Square (LLS) method. Numeric work confirms the better performance of the proposed scheme in comparing with conventional learning scheme.