Online Learning of Temporal Logic Formulae for Signal Classification

Abstract

This paper introduces a method for online inference of temporal logic properties from data. Specifically, we tackle the online supervised learning problem. In this setting, the data is in form of a set of pairs of signals and labels and it becomes available over time. We propose an approach for efficiently processing the data incrementally. In particular, when a new instance is presented, the proposed method updates a binary tree that is linked with the inferred Signal Temporal Logic (STL) formula. This approach presents several benefits. Primarily, it allows the refinement of the current formula when more data is acquired. Moreover, the incremental construction offers insights on the trade-off between formula complexity and classification accuracy. We present two case studies to emphasize the characteristics of the proposed algorithm: 1) a fault classification problem in an automotive system and 2) an anomaly detection problem in the maritime environment.