Abstract
Neural State Classification (NSC) is a recently proposed method for runtime predictive monitoring of Hybrid Automata (HA) using deep neural networks (DNNs). NSC trains a DNN as an approximate reachability predictor that labels a given HA state x as positive if an unsafe state is reachable from x within a given time bound, and labels x as negative otherwise. NSC predictors have very high accuracy, yet are prone to prediction errors that can negatively impact reliability. To overcome this limitation, we present Neural Predictive Monitoring (NPM), a technique based on NSC and conformal prediction that complements NSC predictions with statistically sound estimates of uncertainty. This yields principled criteria for the rejection of predictions likely to be incorrect, without knowing the true reachability values. We also present an active learning method that significantly reduces both the NSC predictor’s error rate and the percentage of rejected predictions. Our approach is highly efficient, with computation times on the order of milliseconds, and effective, managing in our experimental evaluation to successfully reject almost all incorrect predictions.
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Notes
- 1.
The only assumption is exchangeability, a weaker version of the independent and identically distributed assumption.
- 2.
In [21], the PM problem is called “state classification problem”, and its solution a “state classifier”.
- 3.
We will interchangeably use the term “predictor” for the function returning a vector of class likelihoods, and for the function returning the class with highest likelihood.
- 4.
The choice of \(\varDelta \) is not very important, as long as it is symmetric.
- 5.
As opposed to learning a linear combination of confidence and credibility, which is less interpretable.
- 6.
Note indeed that the \(\alpha \)-score of a sample \((x_i,y_i)\) is zero only if h both correctly predicts \(y_i\) and the corresponding class likelihood \(P_h(y_i\mid x_i)\) is 1.
- 7.
Evaluating our rejection criterion reduces to computing two p-values (confidence and credibility). Each p-value is derived by computing a nonconformity score, which requires one execution of the underlying predictor h, and one search over the array of calibration scores.
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Acknowledgements
This material is based on work supported in part by NSF Grants CCF-1414078, CCF-1918225, CPS-1446832, and IIS-1447549.
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Bortolussi, L., Cairoli, F., Paoletti, N., Smolka, S.A., Stoller, S.D. (2019). Neural Predictive Monitoring. In: Finkbeiner, B., Mariani, L. (eds) Runtime Verification. RV 2019. Lecture Notes in Computer Science(), vol 11757. Springer, Cham. https://doi.org/10.1007/978-3-030-32079-9_8
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