Date Approved


Embargo Period


Document Type


Degree Name

PhD Doctor of Philosophy


Electrical and Computer Engineering


Henry M. Rowan College of Engineering


Bouaynaya, Nidhal

Committee Member 1

Rasool, Ghulam

Committee Member 2

Ramachandran, Ravi


Convolutional Neural Networks, Deep neural networks, Tensor Normal Distribution, Unscented Transformation, Variational Density Propagation, Variational Inference


Neural networks (Computer science); Uncertainty--Mathematical models


Electrical and Computer Engineering


Deep neural networks (DNNs) have surpassed human-level accuracy in various fields, including object recognition and classification. However, DNNs being inherently deterministic, are unable to evaluate their confidence in the decisions. Bayesian inference provides a principled approach to reason about model confidence or uncertainty by estimating the posterior distribution of the unknown parameters. The challenge in DNNs is the multi-layer stages of non-linearities, which makes propagation of high-dimensional distributions mathematically intractable. This dissertation establishes the theoretical and algorithmic foundations of uncertainty or belief propagation by developing new deep learning models that can quantify their uncertainty in the decision and self-assess their performance. We introduce Tensor Normal distributions as priors over the network parameters and derive a first-order Taylor series mean-covariance propagation framework. We subsequently extend the first-order approximation to an unscented framework that propagates sigma points through the model layers and is shown to be accurate to at least the second-order approximation. The uncertainty in the output decision is given by the propagated covariance of the predictive distribution. Experiments on benchmark datasets demonstrate: 1) superior robustness against Gaussian noise and adversarial attacks; 2) self-assessment through predictive confidence that decreases quickly with increasing levels of ambient noise or attack; and 3) an ability to detect a targeted attack from ambient noise.