Performance Bounds for Neural Network Estimators: Applications in Fault Detection
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Abstract (arXiv)
We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the data-driven estimator model is provided by an autoregressive neural network. In tuning, we specifically provide upper bounds on the rate of false alarms expected under normal operation. To accomplish this, we provide a theory extension to allow for the propagation of multiple confidence ellipsoids through a neural network. The ellipsoid that bounds the output of the neural network under the input variation informs the sensitivity - and thus the threshold tuning - of the detector. We demonstrate this approach on a linear and nonlinear dynamical system.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 10 of its 23 references that are in the map. First posted on arXiv 22 Mar 2021.
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References · 10
- 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
- 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
- 2016Safety Verification of Deep Neural Networkscited by 262
- 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
- 2017An approach to reachability analysis for feed-forward ReLU neural networkscited by 126
- 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
- 2017Output Range Analysis for Deep Neural Networkscited by 30
- 2020Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimizationcited by 17
- 2019Probabilistic Verification and Reachability Analysis of Neural Networks via Semidefinite Programmingcited by 14
- 2018Uncertainty Propagation in Deep Neural Networks Using Extended Kalman Filteringcited by 8
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