Likelihood-Based Adaptive Learning in Stochastic State-Based Models

This letter presents an adaptive learning framework for estimating structural parameters in stochastic state-based models (SSMs). SSMs are a useful modeling tool in systems biology and medicine. While models in these disciplines are traditionally hand-crafted, an automated generation based on experimental data becomes a topic of research interest. In particular, our goal is to classify measured processes using the generated models. An innovative likelihood-based adaptive learning approach capable of learning the structural parameters, i.e., the arc weights of SSMs from data and exploiting the reliability of detected inputs is presented in this letter. Its convergence behavior is analyzed and an expression for the error at steady state is derived. Simulations assess the performance of the proposed and existing algorithms for a gene regulatory network.

I. Introduction

Modelling of complex systems may be performed using manifold approaches. One method often used in molecular and systems biology are Petri nets (PNs) [1], [2]. They have the advantage of a precise mathematical description of a model that can be illustrated at the same time. Various forms of PNs have been reported and tools have been developed for them [3]–[11]. In biomedical applications, PNs are particularly popular because of their ability to model concurrency which is a characteristic of reactions in biochemical systems [2]. Furthermore, they can be considered as a white box approach as their quantities and structure are interpretable and understandable unlike classical machine learning concepts such as neural networks.