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Journal Article

Dropout: a simple way to prevent neural networks from overfitting

01 Jan 2014-Journal of Machine Learning Research (JMLR.org)-Vol. 15, Iss: 1, pp 1929-1958
TL;DR: It is shown 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.
Abstract: 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.

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Citations
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Book
18 Nov 2016
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

38,208 citations

Proceedings Article
Sergey Ioffe1, Christian Szegedy1
06 Jul 2015
TL;DR: Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin.
Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.

30,843 citations

Proceedings ArticleDOI
21 Jul 2017
TL;DR: DenseNet as mentioned in this paper proposes to connect each layer to every other layer in a feed-forward fashion, which can alleviate the vanishing gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters.
Abstract: Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections—one between each layer and its subsequent layer—our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less memory and computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet.

27,821 citations

Posted Content
Sergey Ioffe1, Christian Szegedy1
TL;DR: Batch Normalization as mentioned in this paper normalizes layer inputs for each training mini-batch to reduce the internal covariate shift in deep neural networks, and achieves state-of-the-art performance on ImageNet.
Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.

17,184 citations

Posted Content
TL;DR: A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.
Abstract: We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.

15,696 citations


Cites background from "Dropout: a simple way to prevent ne..."

  • ...This assumption, however, might restrict modeling capacity, as graph edges need not necessarily encode node similarity, but could contain additional information....

    [...]

References
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Posted Content
TL;DR: This paper proposed marginalized SDA (mSDA) that addresses two crucial limitations of stacked denoising autoencoders: high computational cost and lack of scalability to high-dimensional features.
Abstract: Stacked denoising autoencoders (SDAs) have been successfully used to learn new representations for domain adaptation. Recently, they have attained record accuracy on standard benchmark tasks of sentiment analysis across different text domains. SDAs learn robust data representations by reconstruction, recovering original features from data that are artificially corrupted with noise. In this paper, we propose marginalized SDA (mSDA) that addresses two crucial limitations of SDAs: high computational cost and lack of scalability to high-dimensional features. In contrast to SDAs, our approach of mSDA marginalizes noise and thus does not require stochastic gradient descent or other optimization algorithms to learn parameters ? in fact, they are computed in closed-form. Consequently, mSDA, which can be implemented in only 20 lines of MATLAB^{TM}, significantly speeds up SDAs by two orders of magnitude. Furthermore, the representations learnt by mSDA are as effective as the traditional SDAs, attaining almost identical accuracies in benchmark tasks.

688 citations

Journal ArticleDOI
TL;DR: A more complicated penalty term is proposed in which the distribution of weight values is modeled as a mixture of multiple gaussians, which allows the parameters of the mixture model to adapt at the same time as the network learns.
Abstract: One way of simplifying neural networks so they generalize better is to add an extra term to the error function that will penalize complexity. Simple versions of this approach include penalizing the sum of the squares of the weights or penalizing the number of nonzero weights. We propose a more complicated penalty term in which the distribution of weight values is modeled as a mixture of multiple gaussians. A set of weights is simple if the weights have high probability density under the mixture model. This can be achieved by clustering the weights into subsets with the weights in each cluster having very similar values. Since we do not know the appropriate means or variances of the clusters in advance, we allow the parameters of the mixture model to adapt at the same time as the network learns. Simulations on two different problems demonstrate that this complexity term is more effective than previous complexity terms.

683 citations


"Dropout: a simple way to prevent ne..." refers background in this paper

  • ...These include stopping the training as soon as performance on a validation set starts to get worse, introducing weight penalties of various kinds such as L1 and L2 regularization and soft weight sharing (Nowlan and Hinton, 1992)....

    [...]

Proceedings Article
05 Dec 2013
TL;DR: By casting dropout as regularization, this work develops a natural semi-supervised algorithm that uses unlabeled data to create a better adaptive regularizer and consistently boosts the performance of dropout training, improving on state-of-the-art results on the IMDB reviews dataset.
Abstract: Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout regularizer is first-order equivalent to an L2 regularizer applied after scaling the features by an estimate of the inverse diagonal Fisher information matrix. We also establish a connection to AdaGrad, an online learning algorithm, and find that a close relative of AdaGrad operates by repeatedly solving linear dropout-regularized problems. By casting dropout as regularization, we develop a natural semi-supervised algorithm that uses unlabeled data to create a better adaptive regularizer. We apply this idea to document classification tasks, and show that it consistently boosts the performance of dropout training, improving on state-of-the-art results on the IMDB reviews dataset.

535 citations


"Dropout: a simple way to prevent ne..." refers background in this paper

  • ...Wager et al. (2013) describes how dropout can be seen as an adaptive regularizer....

    [...]

Book ChapterDOI
01 Jan 1980
TL;DR: Many inverse problems arising in optics and other fields like geophysics, medical diagnostics and remote sensing, present numerical instability: the noise affecting the data may produce arbitrarily large errors in the solutions.
Abstract: Many inverse problems arising in optics and other fields like geophysics, medical diagnostics and remote sensing, present numerical instability: the noise affecting the data may produce arbitrarily large errors in the solutions. In other words, these problems are ill-posed in the sense of Hadamard.

439 citations


"Dropout: a simple way to prevent ne..." refers methods in this paper

  • ...These include L2 weight decay (more generally Tikhonov regularization (Tikhonov, 1943)), lasso (Tibshirani, 1996), KL-sparsity and max-norm regularization....

    [...]

Proceedings Article
16 Jun 2013
TL;DR: This work shows how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective, which gives an order of magnitude speedup and more stability.
Abstract: Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (Hinton et al., 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.

422 citations


"Dropout: a simple way to prevent ne..." refers methods in this paper

  • ...Wang and Manning (2013) proposed a method for speeding up dropout by marginalizing dropout noise....

    [...]

Trending Questions (3)
¿Qué es el overfitting en machine learning?

Overfitting is mentioned in the paper. It refers to a problem in machine learning where a model performs well on the training data but fails to generalize well to new, unseen data.

How does the number of parameters affect overfitting in deep learning?

The paper does not directly address how the number of parameters affects overfitting in deep learning.

What are the most common methods used to address overfitting in RNN?

The most common method used to address overfitting in RNN is dropout.