Classification Uncertainty of Deep Neural Networks Based on Gradient Information

Abstract

We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification accuracy -i.e. the task of classifying predictions as correct or incorrect without knowing the actual label -as for entropy thresholding. We apply meta classification to unknown concepts (out-of-distribution samples) -EMNIST/Omniglot letters, CIFAR10 and noise -and demonstrate that meta classification rates for unknown concepts can be increased when using entropy together with several gradient based metrics as input quantities for a meta classifier. Meta classifiers only trained on the uncertainty metrics of known concepts, i.e. EMNIST digits, usually do not perform equally well for all unknown concepts. If we however allow the meta classifier to be trained on uncertainty metrics for some out-ofdistribution samples, meta classification for concepts remote from EMNIST digits (then termed known unknowns) can be improved considerably.

Exploring the Limits of Epistemic Uncertainty Quantification in Low-Shot Settings

“…Uncertainty Methods. We evaluate MC-Dropout (DO) [4], MC-DropConnect (DC) [11], Deep Ensembles (DE) [10], Direct Uncertainty Quantification (DUQ) [15], Variational Inference with Flipout (VI) [16], and Gradient-based uncertainty (GD) [12]. This selection covers scalable as well as approximate methods and recent advances.…”

“…Gradient Uncertainty (GD) This method [12] computes the gradient of the loss with respect to trainable parameters, using a virtual label that is the one-hot encoded version of the predicted label, and passes the gradient vector through an aggregation function that produces a scalar, which can be used as an uncertainty measure. This can only be done in a classification setting.…”

Anomalous Example Detection in Deep Learning: A Survey

“…Supervised [19] Uncertainty measure based on the gradient of the negative log-likelihood is used as a measure of confidence Supervised [20] Confidence scores based on Mahalanobis distance from different layers is combined using weighted averaging Supervised [21] Invariance of classifier's softmax under various transformations to input image is used as a measure of confidence Supervised [22] Ratio of Hausdorff distances between test sample to the nearest non-predicted and the predicted classes is used as the trust score Semi-supervised [23] Likelihood ratio-based method is used to differentiate between in-distribution and OOD examples Semi-supervised [24] A two-head CNN consisting of a common feature extractor and two classifiers with different decision boundaries is trained to detect OOD examples Unsupervised [25] Predicted softmax probability is used to detect OOD examples Unsupervised [26] Temperature scaling and by adding small perturbations to the input is used to better separate the softmax score for OOD detection Unsupervised [27] GAN based architecture is used to compare the bottleneck features of the generated image with that of the test image Unsupervised [28] Degenerated prior network with concentration perturbation algorithm is used to get better uncertainty measure Unsupervised [29] Learning to discriminate between geometric transformations is used for learning unique features that are useful in OOD detection Unsupervised [30] Mahalanobis distance is applied in the latent space of the autoencoder to detect OOD examples Unsupervised [31] Resampling uncertainty estimation approach is proposed as an approximation to the bootstrap…”

“…In [19], an approach to measure uncertainty of a neural network based on gradient information of the negative loglikelihood at the predicted class label is presented. The gradient metrics are computed from all the layers in this method and scalarized using norm or min/max operations.…”

Ensemble-Based Out-of-Distribution Detection

“…Rather than relying on the maximum softmax score, some researchers tried to define the score functions based on different distance measures. For example, the Mahalanobis distance was calculated and calibrated on the intermediate features of DNNs to serve as the confidence score [9,10]; A measure of confidence was proposed by analyzing the invariance of softmax score under various transformations of inputs [11]; the uncertainty of DNNs was evaluated by using the gradient information from all the layers to serve as the score function [12]; the trust score for each input was defined as the ratio of the Hausdorff distances from the input to its closest and second closest labels, which is used to determine whether a classifier's prediction can be trusted or not [13]. By projecting the inputs into a new space, these newly defined score functions can distinguish the InD and OOD samples better than the methods relying on the softmax score.…”