# Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes

arXiv: https://arxiv.org/abs/2211.02375 · HTML: https://mlsanity.com/paper/2211.02375/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Neural Simplex Architecture](https://mlsanity.com/paper/1908.00528/) (2019)
- [Predictive Runtime Monitoring for Mobile Robots using Logic-Based Bayesian Intent Inference](https://mlsanity.com/paper/2108.01227/) (2021)
- [Smoothed Model Checking for Uncertain Continuous Time Markov Chains](https://mlsanity.com/paper/1402.1450/) (2014)
- [Neural Predictive Monitoring under Partial Observability](https://mlsanity.com/paper/2108.07134/) (2021)
- [Neural State Classification for Hybrid Systems](https://mlsanity.com/paper/1807.09901/) (2018)
- [Time-Robust Control for STL Specifications](https://mlsanity.com/paper/2104.02677/) (2021)
- [Temporal Robustness of Stochastic Signals](https://mlsanity.com/paper/2202.02583/) (2022)

## Built on by (most cited first, 13 of 13)

- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [What Can Be Enforced? A Theory of Certified Runtime Safety for Tool-Using Agents](https://mlsanity.com/paper/2607.22868/) (2026)
- [Conformal Off-Policy Prediction for Multi-Agent Systems](https://mlsanity.com/paper/2403.16871/) (2024)
- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)
- [Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees](https://mlsanity.com/paper/2312.01959/) (2023)
- [Certified Guidance for Planning with Deep Generative Models](https://mlsanity.com/paper/2501.12815/) (2025)
- [CoCAI: Copula-based Conformal Anomaly Identification for Multivariate Time-Series](https://mlsanity.com/paper/2507.17796/) (2025)
- [Conformal Predictive Monitoring for Multi-Modal Scenarios](https://mlsanity.com/paper/2509.01338/) (2025)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations](https://mlsanity.com/paper/2605.13923/) (2026)
- [Guiding Neuro-Symbolic Scenario Generation with Spatio-Temporal Logic](https://mlsanity.com/paper/2605.19038/) (2026)
- [Conformal Sequential Decision Making With Cost and Sublinear Policy Regret Guarantees](https://mlsanity.com/paper/2610.15011/) (2026)

## Abstract (arXiv)

We consider the problem of predictive monitoring (PM), i.e., predicting at runtime the satisfaction of a desired property from the current system's state. Due to its relevance for runtime safety assurance and online control, PM methods need to be efficient to enable timely interventions against predicted violations, while providing correctness guarantees. We introduce textitquantitative predictive monitoring (QPM), the first PM method to support stochastic processes and rich specifications given in Signal Temporal Logic (STL). Unlike most of the existing PM techniques that predict whether or not some property φ is satisfied, QPM provides a quantitative measure of satisfaction by predicting the quantitative (aka robust) STL semantics of φ. QPM derives prediction intervals that are highly efficient to compute and with probabilistic guarantees, in that the intervals cover with arbitrary probability the STL robustness values relative to the stochastic evolution of the system. To do so, we take a machine-learning approach and leverage recent advances in conformal inference for quantile regression, thereby avoiding expensive Monte-Carlo simulations at runtime to estimate the intervals. We also show how our monitors can be combined in a compositional manner to handle composite formulas, without retraining the predictors nor sacrificing the guarantees. We demonstrate the effectiveness and scalability of QPM over a benchmark of four discrete-time stochastic processes with varying degrees of complexity.