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 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.
KeywordsOrdinary Differential Equation Learning Model Ordinary Differential Equation Good Generalization Performance Direct Learning
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