Learning and Designing Stochastic Processes from Logical Constraints

TL;DR

This paper introduces a novel method for learning and designing stochastic processes using logical constraints, enabling system identification and design from qualitative temporal logic properties rather than quantitative data.

Contribution

It proposes a unified framework that combines system identification and design by leveraging satisfaction of linear temporal logic formulas for parameter inference.

Findings

Effective in modeling rumour spreading in social networks

Applicable to hybrid gene regulation models

Demonstrates broad applicability with simple examples

Abstract

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation.