A method for parameter estimation of biochemical networks has recently been proposed using dynamic Bayesian network (DBN) approximations. Although it has proven to be more efficient than ODE-based methods, it still suffers from the curse of dimensionality. To maximize the effectiveness of the learning method, we suggest using model reduction as a preliminary step to simplify the biochemical networks before performing the actual parameter estimation. In this paper, we discuss the most common reduction methods and highlight their limitations when applied to this framework, and propose adaptions that aim to significantly improve the parameter estimation method.