# Interpretable Classification of Time-Series Data using Efficient Enumerative Techniques

arXiv: https://arxiv.org/abs/1907.10265 · HTML: https://mlsanity.com/paper/1907.10265/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 20 of 20)

- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Differentiable Inference of Temporal Logic Formulas](https://mlsanity.com/paper/2208.05440/) (2022)
- [Retrieval-Augmented Mining of Temporal Logic Specifications from Data](https://mlsanity.com/paper/2405.14355/) (2024)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Interactive Learning from Natural Language and Demonstrations using Signal Temporal Logic](https://mlsanity.com/paper/2207.00627/) (2022)
- [STL: Surprisingly Tricky Logic (for System Validation)](https://mlsanity.com/paper/2305.17258/) (2023)
- [Learning Probabilistic Temporal Logic Specifications for Stochastic Systems](https://mlsanity.com/paper/2505.12107/) (2025)
- [Mining Interpretable Spatio-temporal Logic Properties for Spatially Distributed Systems](https://mlsanity.com/paper/2106.08548/) (2021)
- [Joint Learning of Policy with Unknown Temporal Constraints for Safe Reinforcement Learning](https://mlsanity.com/paper/2305.00576/) (2023)
- [ECATS: Explainable-by-design concept-based anomaly detection for time series](https://mlsanity.com/paper/2405.10608/) (2024)
- [Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformers](https://mlsanity.com/paper/2507.07808/) (2025)
- [Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2508.03269/) (2025)
- [Time-Incremental Learning from Data Using Temporal Logics](https://mlsanity.com/paper/2112.14300/) (2021)
- [Learning Optimal Signal Temporal Logic Decision Trees for Classification: A Max-Flow MILP Formulation](https://mlsanity.com/paper/2407.21090/) (2024)
- [Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons](https://mlsanity.com/paper/2505.18030/) (2025)
- [Guided by Stars: Interpretable Concept Learning Over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2511.04244/) (2025)
- [On Synthesis of Metric Interval Temporal Logics](https://mlsanity.com/paper/2609.01032/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

Cyber-physical system applications such as autonomous vehicles, wearable devices, and avionic systems generate a large volume of time-series data. Designers often look for tools to help classify and categorize the data. Traditional machine learning techniques for time-series data offer several solutions to solve these problems; however, the artifacts trained by these algorithms often lack interpretability. On the other hand, temporal logics, such as Signal Temporal Logic (STL) have been successfully used in the formal methods community as specifications of time-series behaviors. In this work, we propose a new technique to automatically learn temporal logic formulae that are able to cluster and classify real-valued time-series data. Previous work on learning STL formulas from data either assumes a formula-template to be given by the user, or assumes some special fragment of STL that enables exploring the formula structure in a systematic fashion. In our technique, we relax these assumptions, and provide a way to systematically explore the space of all STL formulas. As the space of all STL formulas is very large, and contains many semantically equivalent formulas, we suggest a technique to heuristically prune the space of formulas considered. Finally, we illustrate our technique on various case studies from the automotive, transportation and healthcare domain.