Learning Specifications for Labelled Patterns

Abstract

In this work, we introduce a supervised learning framework for inferring temporal logic specifications from labelled patterns in signals, so that the formulae can then be used to correctly detect the same patterns in unlabelled samples. The input patterns that are fed to the training process are labelled by a Boolean signal that captures their occurrences. To express the patterns with quantitative features, we use parametric specifications that are increasing, which we call Increasing Parametric Pattern Predictor (IPPP). This means that augmenting the value of the parameters makes the predicted pattern true on a larger set. A particular class of parametric specification formalisms that we use is Parametric Signal Temporal Logic (PSTL). One of the main contributions of this paper is the definition of a new measure, called -count, to assess the quality of the learned formula. This measure enables us to compare two Boolean signals and, hence, quantifies how much the labelling signal induced by the formula differs from the true labelling signal (e.g. given by an expert). Therefore, the -count can measure the number of mismatches (either false positives or false negatives) up to some error tolerance . Our supervised learning framework can be expressed by a multicriteria optimization problem with two objective functions: the minimization of false positives and false negatives given by the parametric formula on a signal. We provide an algorithm to solve this multi-criteria optimization problem. Our approach is demonstrated on two case studies involving characterization and classification of labeled ECG (electrocardiogram) data.

Pattern Matching and Parameter Identification for Parametric Timed Regular Expressions

“…Additionally, we can restrict the scope to expressions with only magnitude parameters and efficiently handle them using a data structure that combines zones and boxes. Finally, we can explore how parametric identification of PSRE with monotonicity property can be efficiently performed using queries as it has been done for PSTL in [6,13].…”

“…For PSTL, to reduce the complexity of the problem, two alternative approaches have been explored. The first approach involves making the assumption that the PSTL formulae are monotonic and exploit it to efficiently compute approximate validity domains as in [6,13]. The second approach is to restrict the focus to formulae with only magnitude parameters and utilize specialized algorithms as in [9].…”

Differentiable Inference of Temporal Logic Formulas

“…Most existing methods learn Signal Temporal Logic (STL) formulas [7]- [9], while the work in [10] explicitly targets LTL learning. STL inference methods include the enumerative method of [8], which enumerates almost all formula structures, and the lattice method of [7] and follow-on works, which is restricted to a fragment of STL and searches over it by leveraging a lattice defined over the restricted search space.…”

“…The technique in [12] uses a pre-specified set of parametric formula templates from which to learn a root-cause for a system's failure. Finally, the algorithm in [9] takes a given formula structure and computes the set of parameters that achieve a given false positive and false negative rates, where possible.…”