Abstract: Disclosed are various approaches for estimating uncertainty in deep neural networks. A respective tensor normal distribution can be applied to each of a plurality of convolutional kernels of a convolutional neural network, wherein the respective tensor normal distribution captures a correlation and a variance heterogeneity of each of the plurality of convolutional kernels. Then, the mean and covariance of each respective tensor normal distribution passing through the non-linear activation function of each nonlinear perceptron can be approximated. Next, a max-pool operation can be performed on a plurality of outputs of the plurality of non-linear perceptrons to generate an output tensor. Then, the output tensor can be vectorized to create an input vector for a fully-connected layer of the convolutional neural network. Subsequently, an output vector can be generated using the fully-connected layer. Then, a mean matrix and a covariance matrix for the output vector can be computed.