Towards Learning Stochastic Population Models by Gradient Descent
Justin N. Kreikemeyer Philipp Andelfinger Adelinde M. Uhrmacher
Increasing effort is put into the development of methods for learning
mechanistic models from data. This task entails not only the accurate
estimation of parameters, but also a suitable model structure. Recent work on
the discovery of dynamical systems formulates this problem as a linear equation
system. Here, we explore several simulation-based optimization approaches,
which allow much greater freedom in the objective formulation and weaker
conditions on the available data. We show that even for relatively small
stochastic population models, simultaneous estimation of parameters and
structure poses major challenges for optimization procedures. Particularly, we
investigate the application of the local stochastic gradient descent method,
commonly used for training machine learning models. We demonstrate accurate
estimation of models but find that enforcing the inference of parsimonious,
interpretable models drastically increases the difficulty. We give an outlook
on how this challenge can be overcome.