In classification applications, we often want probabilistic predictions to reflect confidence or uncertainty. Dropout, a commonly used training technique, has recently been linked to Bayesian inference, yielding an efficient way to quantify uncertainty in neural network models. However, as previously demonstrated, confidence estimates computed with a naive implementation of dropout can be poorly calibrated, particularly when using convolutional networks. In this paper, through the lens of ensemble learning, we associate calibration error with the correlation between the models sampled with dropout. Motivated by this, we explore the use of structured dropout to promote model diversity and improve confidence calibration. We use the SVHN, CIFAR-10 and CIFAR-100 datasets to empirically compare model diversity and confidence errors obtained using various dropout techniques. We also show the merit of structured dropout in a Bayesian active learning application.
Dropout was first introduced as a stochastic regularization technique for NNs @cite_42 . Inspired by the success of dropout, numerous variants have recently been proposed @cite_9 @cite_47 @cite_35 @cite_27 . Unlike regular dropout, most of these methods drop parts of the NNs in a structured manner. For instance, DropBlock @cite_41 applies dropout to small patches of the feature map in convolutional networks, SpatialDrop @cite_30 drops out entire channels, while Stochastic Depth Net @cite_21 drops out entire ResNet blocks. These methods were proposed to boost test time accuracy. In this paper, we show that these structured dropout techniques can be successfully applied to obtain better confidence estimates as well.
@cite_30 @cite_35 @cite_41 @cite_9 @cite_42 @cite_21 @cite_27 @cite_47
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Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully connected layers, it is often less effective for convolutional layers. This lack of success of dropout for convolutional layers is perhaps due to the fact that neurons in a contiguous region in convolutional layers are strongly correlated so information can still flow through convolutional networks despite dropout. Thus a structured form of dropout is needed to regularize convolutional networks. In this paper, we introduce DropBlock, a form of structured dropout, where neurons in a contiguous region of a feature map are dropped together. Extensive experiments show that DropBlock works much better than dropout in regularizing convolutional networks. On ImageNet, DropBlock with ResNet-50 architecture achieves 77.65 accuracy, which is more than 1 improvement on the previous result of this architecture. Multi-layer neural networks have lead to remarkable performance on many kinds of benchmark tasks in text, speech and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting and misspecification. One approach to these estimation and related problems (local minima, colinearity, feature discovery etc.) is called Dropout (Hinton, et al 2012, 2016). The Dropout algorithm removes hidden units according to a Bernoulli random variable with probability @math prior to each update, creating random "shocks" to the network that are averaged over updates. In this paper we will show that Dropout is a special case of a more general model published originally in 1990 called the Stochastic Delta Rule, or SDR (Hanson, 1990). SDR redefines each weight in the network as a random variable with mean @math and standard deviation @math . Each weight random variable is sampled on each forward activation, consequently creating an exponential number of potential networks with shared weights. Both parameters are updated according to prediction error, thus resulting in weight noise injections that reflect a local history of prediction error and local model averaging. SDR therefore implements a more sensitive local gradient-dependent simulated annealing per weight converging in the limit to a Bayes optimal network. Tests on standard benchmarks (CIFAR) using a modified version of DenseNet shows the SDR outperforms standard Dropout in test error by approx. @math with DenseNet-BC 250 on CIFAR-100 and approx. @math in smaller networks. We also show that SDR reaches the same accuracy that Dropout attains in 100 epochs in as few as 35 epochs. Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weighted pooling. We also empirically show that the effect of convolutional dropout is not trivial, despite the dramatically reduced possibility of over-fitting due to the convolutional architecture. Elaborately designing dropout training simultaneously in max-pooling and fully-connected layers, we achieve state-of-the-art performance on MNIST, and very competitive results on CIFAR-10 and CIFAR-100, relative to other approaches without data augmentation. Finally, we compare max-pooling dropout and stochastic pooling, both of which introduce stochasticity based on multinomial distributions at pooling stage. © 2018 by authors.All right reserved. Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.