Towards Learning Stochastic Population Models by Gradient Descent
This work addresses the challenge of learning mechanistic models for researchers in computational biology or ecology, but it is incremental as it builds on existing methods for dynamical systems discovery.
The paper tackles the problem of learning stochastic population models from data by exploring simulation-based optimization approaches, including stochastic gradient descent, and demonstrates accurate model estimation but finds that enforcing parsimonious, interpretable models significantly increases difficulty.
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.