Journal Article•
Dropout: a simple way to prevent neural networks from overfitting
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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Book•
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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•
06 Jul 2015TL;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
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•
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....
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References
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01 Jan 2009
115 citations
TL;DR: This work forms the assembly of a splicing code as a problem of statistical inference and introduces a Bayesian method that uses an adaptively selected number of hidden variables to combine subgroups of features into a network, allows different tissues to share feature subgroups and uses a Gibbs sampler to hedge predictions and ascertain the statistical significance of identified features.
Abstract: Motivation: Alternative splicing is a major contributor to cellular diversity in mammalian tissues and relates to many human diseases. An important goal in understanding this phenomenon is to infer a ‘splicing code’ that predicts how splicing is regulated in different cell types by features derived from RNA, DNA and epigenetic modifiers.
Methods: We formulate the assembly of a splicing code as a problem of statistical inference and introduce a Bayesian method that uses an adaptively selected number of hidden variables to combine subgroups of features into a network, allows different tissues to share feature subgroups and uses a Gibbs sampler to hedge predictions and ascertain the statistical significance of identified features.
Results: Using data for 3665 cassette exons, 1014 RNA features and 4 tissue types derived from 27 mouse tissues ( http://genes.toronto.edu/wasp), we benchmarked several methods. Our method outperforms all others, and achieves relative improvements of 52% in splicing code quality and up to 22% in classification error, compared with the state of the art. Novel combinations of regulatory features and novel combinations of tissues that share feature subgroups were identified using our method.
Contact: frey@psi.toronto.edu
Supplementary information:Supplementary data are available at Bioinformatics online.
96 citations
"Dropout: a simple way to prevent ne..." refers background or methods in this paper
...Method Code Quality (bits) Neural Network (early stopping) (Xiong et al., 2011) 440 Regression, PCA (Xiong et al....
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...Xiong et al. (2011) used Bayesian neural nets for this task....
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...This can sometimes be approximated quite well for simple or small models (Xiong et al., 2011; Salakhutdinov and Mnih, 2008), but we would like to approach the performance of the Bayesian gold standard using considerably less computation....
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...The data set that we use (Xiong et al., 2011) comes from the domain of genetics....
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..., 2011) 463 SVM, PCA (Xiong et al., 2011) 487 Neural Network with dropout 567 Bayesian Neural Network (Xiong et al....
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01 Jan 2009
TL;DR: The feature set of CUDAMat is biased towards providing functionality useful for implementing standard machine learning algorithms, however, it is general enough to be useful in other elds.
Abstract: CUDAMat is an open source software package that provides a CUDA-based matrix class for Python. The primary goal of CUDAMat is to make it easy to implement algorithms that are easily expressed in terms of dense matrix operations on a GPU. At present, the feature set of CUDAMat is biased towards providing functionality useful for implementing standard machine learning algorithms, however, it is general enough to be useful in other elds. We have used CUDAMat to implement several common machine learning algorithms on GPUs oering speedups of up to 50x over numpy and MATLAB implementations.
82 citations
"Dropout: a simple way to prevent ne..." refers methods in this paper
...We used the excellent CUDA libraries—cudamat (Mnih, 2009) and cuda-convnet (Krizhevsky et al....
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TL;DR: It is demonstrated that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the recombination rate between them, respectively.
Abstract: The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the recombination rate between them, respectively. Implications for sex and evolution theory are discussed.
63 citations
"Dropout: a simple way to prevent ne..." refers background in this paper
...A motivation for dropout comes from a theory of the role of sex in evolution (Livnat et al., 2010)....
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