Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes

TL;DR

This paper introduces a kernel-based similarity function for STL formulae on stochastic processes, enabling efficient and precise satisfaction prediction without manual feature extraction, backed by theoretical guarantees.

Contribution

It presents a novel kernel trick for STL formulae, simplifying the learning process and improving prediction accuracy on stochastic processes.

Findings

Efficient learning of satisfaction prediction for STL formulae.

High-precision predictions achieved without explicit feature vectors.

Theoretical PAC guarantee supports the method's reliability.

Abstract

We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick allows us to circumvent the complicated process of feature extraction, i.e. the (typically manual) effort to identify the decisive properties of formulae so that learning can be applied. We demonstrate this consequence and its advantages on the task of predicting (quantitative) satisfaction of STL formulae on stochastic processes: Using our kernel and the kernel trick, we learn (i) computationally efficiently (ii) a practically precise predictor of satisfaction, (iii) avoiding the difficult task of finding a way to explicitly turn formulae into vectors of numbers in a sensible way. We back the high precision we have achieved in the experiments by a theoretically sound PAC guarantee, ensuring our procedure efficiently delivers a close-to-optimal predictor.