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Model confidence or uncertainty is critical in autonomous systems as they directly tie to the safety and trustworthiness of the system. The quantification of uncertainty in the output decisions of deep neural networks (DNNs) is a challenging problem. The Bayesian framework enables the estimation of the predictive uncertainty by introducing probability distributions over the (unknown) network weights; however, the propagation of these high-dimensional distributions through multiple layers and non-linear transformations is mathematically intractable. In this work, we propose an extended variational inference (eVI) framework for convolutional neural network (CNN) based on tensor Normal distributions (TNDs) defined over convolutional kernels. Our proposed eVI framework propagates the first two moments (mean and covariance) of these TNDs through all layers of the CNN. We employ first-order Taylor series linearization to approximate the mean and covariances passing through the non-linear activations. The uncertainty in the output decision is given by the propagated covariance of the predictive distribution. Furthermore, we show, through extensive simulations on the MNIST and CIFAR-10 datasets, that the CNN becomes more robust to Gaussian noise and adversarial attacks.
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BaSIS-Net: From Point Estimate to Predictive Distribution in Neural Networks - A Bayesian Sequential Importance Sampling Framework
Data-driven Deep Learning (DL) models have revolutionized autonomous systems, but ensuring their safety and reliability necessitates the assessment of predictive confidence or uncertainty. Bayesian DL provides a principled approach to quantify uncertainty via probability density functions defined over model parameters. However, the exact solution is intractable for most DL models, and the approximation methods, often based on heuristics, suffer from scalability issues and stringent distribution assumptions and may lack theoretical guarantees. This work develops a Sequential Importance Sampling framework that approximates the posterior probability density function through weighted samples (or particles), which can be used to find the mean, variance, or higher-order moments of the posterior distribution. We demonstrate that propagating particles, which capture information about the higher-order moments, through the layers of the DL model results in increased robustness to natural and malicious noise (adversarial attacks). The variance computed from these particles effectively quantifies the model’s decision uncertainty, demonstrating well-calibrated and accurate predictive confidence.
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- Award ID(s):
- 2234468
- PAR ID:
- 10599137
- Publisher / Repository:
- TMLR
- Date Published:
- Journal Name:
- Transactions on Machine Learning Research
- ISSN:
- 2835-8856
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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