Reformulated Parametric Learning Based on Ordinary Differential Equations

This paper presents a new parametric learning scheme, namely, Reformulated Parametric Learning (RPL). Instead of learning the parameters directly by using 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 combinatorial optimization problem. As a case study, we apply RPL to a simple class of models, named 'Additive Pseudo-Exponential Models' (APEM). While conventi -onal approaches have to adopt nonlinear programming to learn APEM, the proposed RPL can obtain equivalent solutions merely through solving linear least square (thus has close form solutions). Numeric testing confirms the advantages of the proposed scheme.