Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSquared Earth Movers Distance-based Loss for Training Deep Neural Networks
75
0
0.0
(
0
)
Added by
Le Hou
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In the context of single-label classification, despite the huge success of deep learning, the commonly used cross-entropy loss function ignores the intricate inter-class relationships that often exist in real-life tasks such as age classification. In this work, we propose to leverage these relationships between classes by training deep nets with the exact squared Earth Movers Distance (also known as Wasserstein distance) for single-label classification. The squared EMD loss uses the predicted probabilities of all classes and penalizes the miss-predictions according to a ground distance matrix that quantifies the dissimilarities between classes. We demonstrate that on datasets with strong inter-class relationships such as an ordering between classes, our exact squared EMD losses yield new state-of-the-art results. Furthermore, we propose a method to automatically learn this matrix using the CNNs own features during training. We show that our method can learn a ground distance matrix efficiently with no inter-class relationship priors and yield the same performance gain. Finally, we show that our method can be generalized to applications that lack strong inter-class relationships and still maintain state-of-the-art performance. Therefore, with limited computational overhead, one can always deploy the proposed loss function on any dataset over the conventional cross-entropy.
rate research
Read More
Contour tracking in adverse environments is a challenging problem due to cluttered background, illumination variation, occlusion, and noise, among others. This paper presents a robust contour tracking method by contributing to some of the key issues involved, including (a) a region functional formulation and its optimization; (b) design of a robust and effective feature; and (c) development of an integrated tracking algorithm. First, we formulate a region functional based on robust Earth Movers distance (EMD) with kernel density for distribution modeling, and propose a two-phase method for its optimization. In the first phase, letting the candidate contour be fixed, we express EMD as the transportation problem and solve it by the simplex algorithm. Next, using the theory of shape derivative, we make a perturbation analysis of the contour around the best solution to the transportation problem. This leads to a partial differential equation (PDE) that governs the contour evolution. Second, we design a novel and effective feature for tracking applications. We propose a dimensionality reduction method by tensor decomposition, achieving a low-dimensional description of SIFT features called Tensor-SIFT for characterizing local image region properties. Applicable to both color and gray-level images, Tensor-SIFT is very distinctive, insensitive to illumination changes, and noise. Finally, we develop an integrated algorithm that combines various techniques of the simplex algorithm, narrow-band level set and fast marching algorithms. Particularly, we introduce an inter-frame initialization method and a stopping criterion for the termination of PDE iteration. Experiments in challenging image sequences show that the proposed work has promising performance.
In this paper, we tackle a problem of predicting phenotypes from structural connectomes. We propose that normalized Laplacian spectra can capture structural properties of brain networks, and hence graph spectral distributions are useful for a task of connectome-based classification. We introduce a kernel that is based on earth movers distance (EMD) between spectral distributions of brain networks. We access performance of an SVM classifier with the proposed kernel for a task of classification of autism spectrum disorder versus typical development based on a publicly available dataset. Classification quality (area under the ROC-curve) obtained with the EMD-based kernel on spectral distributions is 0.71, which is higher than that based on simpler graph embedding methods.
Modern deep neural networks have a large number of parameters, making them very hard to train. We propose DSD, a dense-sparse-dense training flow, for regularizing deep neural networks and achieving better optimization performance. In the first D (Dense) step, we train a dense network to learn connection weights and importance. In the S (Sparse) step, we regularize the network by pruning the unimportant connections with small weights and retraining the network given the sparsity constraint. In the final D (re-Dense) step, we increase the model capacity by removing the sparsity constraint, re-initialize the pruned parameters from zero and retrain the whole dense network. Experiments show that DSD training can improve the performance for a wide range of CNNs, RNNs and LSTMs on the tasks of image classification, caption generation and speech recognition. On ImageNet, DSD improved the Top1 accuracy of GoogLeNet by 1.1%, VGG-16 by 4.3%, ResNet-18 by 1.2% and ResNet-50 by 1.1%, respectively. On the WSJ93 dataset, DSD improved DeepSpeech and DeepSpeech2 WER by 2.0% and 1.1%. On the Flickr-8K dataset, DSD improved the NeuralTalk BLEU score by over 1.7. DSD is easy to use in practice: at training time, DSD incurs only one extra hyper-parameter: the sparsity ratio in the S step. At testing time, DSD doesnt change the network architecture or incur any inference overhead. The consistent and significant performance gain of DSD experiments shows the inadequacy of the current training methods for finding the best local optimum, while DSD effectively achieves superior optimization performance for finding a better solution. DSD models are available to download at https://songhan.github.io/DSD.
The Earth Movers Distance (EMD) computes the optimal cost of transforming one distribution into another, given a known transport metric between them. In deep learning, the EMD loss allows us to embed information during training about the output space structure like hierarchical or semantic relations. This helps in achieving better output smoothness and generalization. However EMD is computationally expensive.Moreover, solving EMD optimization problems usually require complex techniques like lasso. These properties limit the applicability of EMD-based approaches in large scale machine learning. We address in this work the difficulties facing incorporation of EMD-based loss in deep learning frameworks. Additionally, we provide insight and novel solutions on how to integrate such loss function in training deep neural networks. Specifically, we make three main contributions: (i) we provide an in-depth analysis of the fastest state-of-the-art EMD algorithm (Sinkhorn Distance) and discuss its limitations in deep learning scenarios. (ii) we derive fast and numerically stable closed-form solutions for the EMD gradient in output spaces with chain- and tree- connectivity; and (iii) we propose a relaxed form of the EMD gradient with equivalent computational complexity but faster convergence rate. We support our claims with experiments on real datasets. In a restricted data setting on the ImageNet dataset, we train a model to classify 1000 categories using 50K images, and demonstrate that our relaxed EMD loss achieves better Top-1 accuracy than the cross entropy loss. Overall, we show that our relaxed EMD loss criterion is a powerful asset for deep learning in the small data regime.
Sparse coding (Sc) has been studied very well as a powerful data representation method. It attempts to represent the feature vector of a data sample by reconstructing it as the sparse linear combination of some basic elements, and a $L_2$ norm distance function is usually used as the loss function for the reconstruction error. In this paper, we investigate using Sc as the representation method within multi-instance learning framework, where a sample is given as a bag of instances, and further represented as a histogram of the quantized instances. We argue that for the data type of histogram, using $L_2$ norm distance is not suitable, and propose to use the earth movers distance (EMD) instead of $L_2$ norm distance as a measure of the reconstruction error. By minimizing the EMD between the histogram of a sample and the its reconstruction from some basic histograms, a novel sparse coding method is developed, which is refereed as SC-EMD. We evaluate its performances as a histogram representation method in tow multi-instance learning problems --- abnormal image detection in wireless capsule endoscopy videos, and protein binding site retrieval. The encouraging results demonstrate the advantages of the new method over the traditional method using $L_2$ norm distance.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
