In this work we investigate the reasons why Batch Normalization (BN) improves the generalization performance of deep networks. We argue that one major reason, distinguishing it from data-independent normalization methods, is randomness of batch statistics. This randomness appears in the parameters rather than in activations and admits an interpretation as a practical Bayesian learning. We apply this idea to other (deterministic) normalization techniques that are oblivious to the batch size. We show that their generalization performance can be improved significantly by Bayesian learning of the same form. We obtain test performance comparable to BN and, at the same time, better validation losses suitable for subsequent output uncertainty estimation through approximate Bayesian posterior.
The improved methods that we propose are also closely related to variational drop -out @cite_0 as discussed below. We give a new interpretation to variational dropout and apply it in combination with normalization techniques.
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Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of common deep learning techniques such as dropout. This grounding of dropout in approximate Bayesian inference suggests an extension of the theoretical results, offering insights into the use of dropout with RNN models. We apply this new variational inference based dropout technique in LSTM and GRU models, assessing it on language modelling and sentiment analysis tasks. The new approach outperforms existing techniques, and to the best of our knowledge improves on the single model state-of-the-art in language modelling with the Penn Treebank (73.4 test perplexity). This extends our arsenal of variational tools in deep learning. Dropout prediction in MOOCs is a well-researched problem where we classify which students are likely to persist or drop out of a course. Most research into creating models which can predict outcomes is based on student engagement data. Why these students might be dropping out has only been studied through retroactive exit surveys. This helps identify an important extension area to dropout prediction- how can we interpret dropout predictions at the student and model level? We demonstrate how existing MOOC dropout prediction pipelines can be made interpretable, all while having predictive performance close to existing techniques. We explore each stage of the pipeline as design components in the context of interpretability. Our end result is a layer which longitudinally interprets both predictions and entire classification models of MOOC dropout to provide researchers with in-depth insights of why a student is likely to dropout. We introduce DropAll, a generalization of DropOut [1] and DropConnect [2], for regularization of fully-connected layers within convolutional neural networks. Applying these methods amounts to sub-sampling a neural network by dropping units. Training with DropOut, a randomly selected subset of activations are dropped, when training with DropConnect we drop a randomly subsets of weights. With DropAll we can perform both methods. We show the validity of our proposal by improving the classification error of networks trained with DropOut and DropConnect, on a common image classification dataset. To improve the classification, we also used a new method for combining networks, which was proposed in [3]. Recurrent neural networks show state-of-the-art results in many text analysis tasks but often require a lot of memory to store their weights. Recently proposed Sparse Variational Dropout eliminates the majority of the weights in a feed-forward neural network without significant loss of quality. We apply this technique to sparsify recurrent neural networks. To account for recurrent specifics we also rely on Binary Variational Dropout for RNN. We report 99.5 sparsity level on sentiment analysis task without a quality drop and up to 87 sparsity level on language modeling task with slight loss of accuracy. We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy. We propose zoneout, a novel method for regularizing RNNs. At each timestep, zoneout stochastically forces some hidden units to maintain their previous values. Like dropout, zoneout uses random noise to train a pseudo-ensemble, improving generalization. But by preserving instead of dropping hidden units, gradient information and state information are more readily propagated through time, as in feedforward stochastic depth networks. We perform an empirical investigation of various RNN regularizers, and find that zoneout gives significant performance improvements across tasks. We achieve competitive results with relatively simple models in character- and word-level language modelling on the Penn Treebank and Text8 datasets, and combining with recurrent batch normalization yields state-of-the-art results on permuted sequential MNIST. Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves gener- alization but also leads to extremely sparse neural architectures by automatically setting the individual noise magnitude per weight. However, this sparsity can hardly be used for acceleration since it is unstructured. In the paper, we propose a new Bayesian model that takes into account the computational structure of neural net- works and provides structured sparsity, e.g. removes neurons and or convolutional channels in CNNs. To do this we inject noise to the neurons outputs while keeping the weights unregularized. We establish the probabilistic model with a proper truncated log-uniform prior over the noise and truncated log-normal variational approximation that ensures that the KL-term in the evidence lower bound is com- puted in closed-form. The model leads to structured sparsity by removing elements with a low SNR from the computation graph and provides significant acceleration on a number of deep neural architectures. The model is easy to implement as it can be formulated as a separate dropout-like layer. The numerical treatment of contact problems involves the formulation of the geometry, the statement of interface laws, the variational formulation and the development of algorithms. In this paper we give an overview with regard to the different topics which are involved when contact problems have to be simulated. To be most general we will derive a geometrical model for contact which is valid for large deformations. Furthermore interface laws will be discussed for the normal and tangential stress components in the contact area. Different variational formulations can be applied to treat the variational inequalities due to contact. Several of these different techniques will be presented. Furthermore the discretization of a contact problem in time and space is of great importance and has to be chosen with regard to the nature of the contact problem. Thus the standard discretization schemes will be discussed as well as techiques to search for contact in case of large deformations. Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its applications to relatively simple phenomena. In this work, we propose hierarchical nonparametric variational autoencoders, which combines tree-structured Bayesian nonparametric priors with VAEs, to enable infinite flexibility of the latent representation space. Both the neural parameters and Bayesian priors are learned jointly using tailored variational inference. The resulting model induces a hierarchical structure of latent semantic concepts underlying the data corpus, and infers accurate representations of data instances. We apply our model in video representation learning. Our method is able to discover highly interpretable activity hierarchies, and obtain improved clustering accuracy and generalization capacity based on the learned rich representations. The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference. We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the mini-batch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments. Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (, 2012) does this by randomly dropping out (zeroing) hidden units and input features during training of neural networks. However, repeatedly sampling a random subset of input features makes training much slower. Based on an examination of the implied objective function of dropout training, we show how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective. This approximation, justified by the central limit theorem and empirical evidence, gives an order of magnitude speedup and more stability. We show how to do fast dropout training for classification, regression, and multilayer neural networks. Beyond dropout, our technique is extended to integrate out other types of noise and small image transformations. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from other multiplicative noise based variational distributions has not been investigated in depth. We evaluated Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We tested the calibration of the probabilistic predictions of Bayesian convolutional neural networks (CNNs) on MNIST and CIFAR-10. Sampling at prediction time increased the calibration of the DNNs' probabalistic predictions. Sampling weights, whether Gaussian or Bernoulli, led to more robust representation of uncertainty compared to sampling of units. However, using either Gaussian or Bernoulli dropout led to increased test set classification accuracy. Based on these findings we used both Bernoulli dropout and Gaussian dropconnect concurrently, which we show approximates the use of a spike-and-slab variational distribution without increasing the number of learned parameters. We found that spike-and-slab sampling had higher test set performance than Gaussian dropconnect and more robustly represented its uncertainty compared to Bernoulli dropout. Generating versatile and appropriate synthetic speech requires control over the output expression separate from the spoken text. Important non-textual speech variation is seldom annotated, in which case output control must be learned in an unsupervised fashion. In this paper, we perform an in-depth study of methods for unsupervised learning of control in statistical speech synthesis. For example, we show that popular unsupervised training heuristics can be interpreted as variational inference in certain autoencoder models. We additionally connect these models to VQ-VAEs, another, recently-proposed class of deep variational autoencoders, which we show can be derived from a very similar mathematical argument. The implications of these new probabilistic interpretations are discussed. We illustrate the utility of the various approaches with an application to acoustic modelling for emotional speech synthesis, where the unsupervised methods for learning expression control (without access to emotional labels) are found to give results that in many aspects match or surpass the previous best supervised approach. Mesh surface denoising is a fundamental problem in geometry processing. The main challenge is to remove noise while preserving sharp features (such as edges and corners) and preventing generating false edges. We propose in this paper to combine total variation (TV) and piecewise constant function space for variational mesh denoising. We first give definitions of piecewise constant function spaces and associated operators. A variational mesh denoising method will then be presented by combining TV and piecewise constant function space. It is proved that, the solution of the variational problem (the key part of the method) is in some sense continuously dependent on its parameter, indicating that the solution is robust to small perturbations of this parameter. To solve the variational problem, we propose an efficient iterative algorithm (with an additional algorithmic parameter) based on variable splitting and augmented Lagrangian method, each step of which has closed form solution. Our denoising method is discussed and compared to several typical existing methods in various aspects. Experimental results show that our method outperforms all the compared methods for both CAD and non-CAD meshes at reasonable costs. It can preserve different levels of features well, and prevent generating false edges in most cases, even with the parameters evaluated by our estimation formulae. © 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. The cross-entropy loss commonly used in deep learning is closely related to the defining properties of optimal representations, but does not enforce some of the key properties. We show that this can be solved by adding a regularization term, which is in turn related to injecting multiplicative noise in the activations of a Deep Neural Network, a special case of which is the common practice of dropout. We show that our regularized loss function can be efficiently minimized using Information Dropout, a generalization of dropout rooted in information theoretic principles that automatically adapts to the data and can better exploit architectures of limited capacity. When the task is the reconstruction of the input, we show that our loss function yields a Variational Autoencoder as a special case, thus providing a link between representation learning, information theory and variational inference. Finally, we prove that we can promote the creation of optimal disentangled representations simply by enforcing a factorized prior, a fact that has been observed empirically in recent work. Our experiments validate the theoretical intuitions behind our method, and we find that Information Dropout achieves a comparable or better generalization performance than binary dropout, especially on smaller models, since it can automatically adapt the noise to the structure of the network, as well as to the test sample. This paper describes a temporal expression identification and normalization system, ManTIME, developed for the TempEval-3 challenge. The identification phase combines the use of conditional random fields along with a post-processing identification pipeline, whereas the normalization phase is carried out using NorMA, an open-source rule-based temporal normalizer. We investigate the performance variation with respect to different feature types. Specifically, we show that the use of WordNet-based features in the identification task negatively affects the overall performance, and that there is no statistically significant difference in using gazetteers, shallow parsing and propositional noun phrases labels on top of the morphological features. On the test data, the best run achieved 0.95 (P), 0.85 (R) and 0.90 (F1) in the identification phase. Normalization accuracies are 0.84 (type attribute) and 0.77 (value attribute). Surprisingly, the use of the silver data (alone or in addition to the gold annotated ones) does not improve the performance. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modelling uncertainty is one of the key features of Bayesian methods. Bayesian DNNs that use dropout-based variational distributions and scale to complex tasks have recently been proposed. We evaluate Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We compare these Bayesian DNNs ability to represent their uncertainty about their outputs through sampling during inference. We tested the calibration of these Bayesian fully connected and convolutional DNNs on two visual inference tasks (MNIST and CIFAR-10). By adding different levels of Gaussian noise to the test images, we assessed how these DNNs represented their uncertainty about regions of input space not covered by the training set. These Bayesian DNNs represented their own uncertainty more accurately than traditional DNNs with a softmax output. We find that sampling of weights, whether Gaussian or Bernoulli, led to more accurate representation of uncertainty compared to sampling of units. However, sampling units using either Gaussian or Bernoulli dropout led to increased convolutional neural network (CNN) classification accuracy. Based on these findings we use both Bernoulli dropout and Gaussian dropconnect concurrently, which approximates the use of a spike-and-slab variational distribution. We find that networks with spike-and-slab sampling combine the advantages of the other methods: they classify with high accuracy and robustly represent the uncertainty of their classifications for all tested architectures.