Uncertainties in Neural Networks : A System Identification Approach

Malmstrom, Magnus

doi:10.3384/lic.diva-174720

Cited by 6 publications

(12 citation statements)

References 41 publications

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“…. In [3], it is shown that given that the model set for the choose model is flexible enough to include the true system, the parameter covariance is computed as…”

Section: B Linearization Methodsmentioning

confidence: 99%

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Modeling of the tire-road friction using neural networks including quantification of the prediction uncertainty

Malmstrom

Skog

Axehill

et al. 2021

2021 IEEE 24th International Conference on Information Fusion (FUSION)

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Despite the great success of neural networks (NN) in many application areas, it is still not obvious how to integrate an NN in a sensor fusion framework. The reason is that the computation of the for fusion required variance of NN is still a rather immature area. Here, we apply a methodology from system identification where uncertainty of the parameters in the NN are first estimated in the training phase, and then this uncertainty is propagated to the output in the prediction phase. This local approach is based on linearization, and it implicitly assumes a good signal-to-noise ratio and persistency of excitation. We illustrate the proposed method on a fundamental problem in advanced driver assistance systems (ADAS), namely to estimate the tire-road friction. This is a single input single output static nonlinear relation that is simple enough to provide insight and it enables comparisons with other parametric approaches. We compare both to existing methods for how to assess uncertainty in NN and standard methods for this problem, and evaluate on real data. The goal is not to improve on simpler methods for this particular application, but rather to validate that our method is on par with simpler model structures, where output variance is immediately provided.

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“…. In [3], it is shown that given that the model set for the choose model is flexible enough to include the true system, the parameter covariance is computed as…”

Section: B Linearization Methodsmentioning

confidence: 99%

“…A method to compute output variance from an NN was proposed in [3]. It relies on well-established methodology in system identification [4].…”

Section: Introductionmentioning

confidence: 99%

Modeling of the tire-road friction using neural networks including quantification of the prediction uncertainty

Malmstrom

Skog

Axehill

et al. 2021

2021 IEEE 24th International Conference on Information Fusion (FUSION)

View full text Add to dashboard Cite

show abstract

“…Given that the covariance of the parameters Cov( θN ) has been computed during the training phase. Using the linearization approach [15], the uncertainty can be propagated to the output as…”

Section: Quantify Uncertainty In the Classificationmentioning

confidence: 99%

“…The idea of MC dropout is to use dropout to create an ensemble of classifications Z M CD during the validation phase. From this ensemble, similarly to (15), one could create a classification of the input where uncertainty is taken into consideration. That is Fig.…”

Section: B Classification With Uncertainty: Monte Carlo Dropoutmentioning

confidence: 99%

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Detection of outliers in classification by using quantified uncertainty in neural networks

Malmstrom

Skog

Axehill

et al. 2022

2022 25th International Conference on Information Fusion (FUSION)

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Neural Networks (NNs) can solve very hard classification and estimation tasks but are less well suited to solve complex sensor fusion challenges, such as end-to-end control of autonomous vehicles. Nevertheless, NN can still be a powerful tool for particular sub-problems in sensor fusion. This would require a reliable and quantifiable measure of the stochastic uncertainty in the predictions that can be compared to classical sensor measurements. However, current NN's output some figure of merit, that is only a relative model fit and not a stochastic uncertainty. We propose to embed the NN's in a proper stochastic system identification framework. In the training phase, the stochastic uncertainty of the parameters in the (last layers of the) NN is quantified. We show that this can be done recursively with very few extra computations. In the classification phase, Monte-Carlo (MC) samples are used to generate a set of classifier outputs. From this set, a distribution of the classifier output is obtained, which represents a proper description of the stochastic uncertainty of the predictions. We also show how to use the calculated uncertainty for outlier detection by including an artificial outlier class. In this way, the NN fits a sensor fusion framework much better. We evaluate the approach on images of handwritten digits. The proposed method is shown to be on par with MC dropout, while having lower computational complexity, and the outlier detection almost completely eliminates false classifications.

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Integrating Physical and Data-Driven System Frequency Response Modelling for Wind-PV-Thermal Power Systems

Zhang

Wang

Zhou

et al. 2024

IEEE Trans. Power Syst.

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Uncertainties in Neural Networks : A System Identification Approach

Cited by 6 publications

References 41 publications

Modeling of the tire-road friction using neural networks including quantification of the prediction uncertainty

Modeling of the tire-road friction using neural networks including quantification of the prediction uncertainty

Detection of outliers in classification by using quantified uncertainty in neural networks

Integrating Physical and Data-Driven System Frequency Response Modelling for Wind-PV-Thermal Power Systems

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