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An Automatic Sparse Model Estimation Method Guided by Constraints That Encode System Properties

Finding efficient methods to estimate model parameters or build models from time-series data is a central quest in Systems and Synthetic Biology. To aid this search, existing parameter estimation methods were adapted from other fields, or new ones were developed. In this paper, we use the Sparse Bayesian Learning (SBL) framework, which was first developed in the field of signal processing, and implement it as an iterative convex optimization problem. We extend the existing SBL framework to accommodate constraints that enforce certain system properties, such as nonnegative state variables or bounded state trajectories. These properties are vital parts of a dynamical model in biology and chemistry but are often overlooked in the parameter estimation literature. As a result of this work, the extended framework can automatically build “proper” dynamical models from time-series data. Finally, the examples show that such framework complemented with appropriate constraints can aid the model building process.