IS THE LABEL TRUSTFUL: TRAINING BETTER DEEP LEARNING MODEL VIA UNCERTAINTY MINING NET

1 INTRODUCTION . Deep Learning ( DL ) , to learn powerful representations , it usually requires a large amount of training data . However , for many real world problems , it is not always possible to obtain sufficiently large training data . What we can usually get is limited training data with corrupted labels which heavily affect the model performance . Although acquiring large data is not hard , considering the information explosion on the internet , accurate labeling is usually an expensive and error-prone task which involves humans ’ interaction , especially experts with knowledge in the specific field . Most of the time , we have to build DL models using limited training data with corrupted data labels . It becomes very challenging to apply current popular deep learning frameworks to solve this problem . Training a deep learning model via noisily labeled data is a challenging task ( Patrini et al. , 2017 ; Li et al. , 2017 ; Ding et al. , 2018 ; Menon et al. , 2015 ; Goldberger & Ben-Reuven , 2016 ; Jiang et al. , 2017 ) . Most of current explorations for dealing with such problems usually require large amount of labeled data as a prerequisite . It means that in these works , the designed pipelines and evaluations are based on having enough labeled training data , though they may include label noise . These approaches will suffer from the limited size of labeled training data as well as the label noise . As we know , the hierarchical representation learned by deep learning models mainly benefits from the amount of data . The deep learning model can easily overfit to the mislabeled samples especially when the data size is small ( Tarvainen & Valpola , 2017 ; Ren et al. , 2018 ) . Unfortunately , there is no general solutions to solve the problem of training on limited annotated data with label noise . If we directly train the deep learning model only with the labeled data , the small portion of labeled training data will limit the learning capability . Meanwhile , the label noise makes it very challenging to utilize the labeled data directly . In this work , our framework can handle these problems simultaneously . UMN includes two major components . The first part is used to learn a latent feature representation via a generative framework ( VAE ) using all the training data . Then the learned embedding is applied as the input to its subsequent semi-supervised learning component by conditional variational autoencoder to train the classifier . To handle the label noise , we integrate label uncertainty estimation module where the reliable data contributes more to the model training and noisy data contributes less . Though recent works ( Hataya & Nakayama , 2019 ; Ren et al. , 2018 ) discuss such problems , they usually assume to have a separate small clean dataset to begin with . It may not be possible to have an independent clean dataset in real scenarios . Current supervised robust learning approaches can not be directly adopted to our case since the labeled data is small and not reliable . The limited labeled training data makes the supervised model overfit very easily to the small size of noisy data . This will heavily hurt the model performance . The limited data labels and noise can also affect other related state-of-the-art semi-supervised learning approaches . We will present the comparisons with these approaches in the experiment section . In this paper , our major contributions can be summarized into the following aspects : First , our studied problem is very general in real scenarios : small mislabeled datasets with large amount of unlabeled data , and there are very few existing approaches to target this kind of problems . Second , instead of treating the label noise as the preknowledge , we explicitly use the deep generative architecture to model the noisy labels at the sample level precisely . This has been validated by the improved experimental results as well as the theoretical analysis . Third , we show how to use the moving average model to estimate the sample-wise uncertainty in labels . We have explained it in the theory analysis section and validated this assumption in the experiments . Furthermore , our experiments demonstrate that UMN can also help identify these mis-labeled data without any prior knowledge . Finally , we build one end-to-end deep learning pipeline to train against the noisy labeled data . 2 RELATED WORKS . Along with the popularity of deep neural network , the problem of training deep neural networks with noisy label data has started to draw our attention . Natarajan et al . ( Natarajan et al. , 2013 ) propose the unbiased estimator of the surrogate loss function and calculate theoretical bounds for empirical risk optimization . Modeling the consistency as the regularization for deep neural network is another route for robust learning with noisy labeled data . Reed et al . ( Reed et al. , 2015 ) design a robust loss to model the prediction consistency . In ( Li et al. , 2017 ) , the authors propose a knowledge distillation framework where they train an auxiliary model on a small set of clean data samples and linearly combine its predictions with the observed labels to form the new targets to train . In ( Ding et al. , 2018 ) , a two-stage approach is proposed . First a DNN model is trained on the noisy data and used to filter out these noisy samples . Then another model is trained on the filtered dataset using a semi-supervised approach by treating these filtered out samples as unlabeled . Menon et al . model the corruption process of a dataset by learning the class-probability estimator ( Menon et al. , 2015 ) . Another way of regularization for training on noisy labels is to estimate the class conditional corruption ratio . Goldberger et al . ( Goldberger & Ben-Reuven , 2016 ) propose a softmax layer along with the classifier to predict the class conditional corruption ratio . In ( Jiang et al. , 2017 ) , they propose MentorNet which learns a data driven dynamic curriculum to be followed by the StudentNet . Semi-supervised learning with few labeled samples is also a well studied area . Some of the closely related works are ( Gordon & Hernández-Lobato , 2017 ) , ( Kingma et al. , 2014 ) , ( Tarvainen & Valpola , 2017 ) . Kingma et al ( Kingma et al. , 2014 ) propose a stacked deep generative semi-supervised model for training on partially labeled datasets . They first train a variational autoencoder on the labeled data , then stack on top of it a conditional variational autoencoder and continue training in semi-supervised fashion to get a robust classifier . In ( Tarvainen & Valpola , 2017 ) , the authors train a classifier in semi-supervised way using temporal ensemble approach . They train a student network and maintain a teacher network as the exponential moving average of the student . They use classification loss for labeled data and enforce consistency loss between teacher and student for unlabeled data . There have been limited works dealing with bi-quality data ( Hataya & Nakayama , 2019 ) , ( Langevin et al. , 2018 ) . Bi-quality data is defined in ( Hataya & Nakayama , 2019 ) as datasets with few labeled samples where the labels are potentially corrupted . In ( Langevin et al. , 2018 ) , the authors discuss to use the deep generative semi-supervised model to model noisy labels . They assume that the labels are also randomly corrupted with a probability ρ . Their idea relies on the predefined ρ to train the classifier . However , the corruption probability ρ is not known as a prior in reality . Compared to these work , we present a new architecture for training a robust classifier with dataset including noisy labels . We assume that there is no preknowledge of the label corruption rate and we do not have access to a separate clean dataset which is more close to the real scenario . 3 METHOD . The goal of our work is to learn a better model with the limited labeled data including the noise . Since the labeled data only occupies a small portion of the training data , the labeled data alone is not sufficient to train a good model . At the same time , we also need to solve the label noise problem . To deal with these issues , our pipeline consists of two major components . In the first part , we apply unsupervised learning scheme to learn a latent feature representation via all the available training data . Then we utilize the label via semi-supervised learning pipeline to train the classifier . At the same time , we incorporate the label uncertainty estimation to reduce the influences coming from these mislabeled data . We estimate the uncertainty of the given sample from the prediction of the updating model and its guider model ( exponential moving average of the updating model ) , part of this idea is inspired by work ( Polyak & Juditsky , 1992 ) . The estimated uncertainty is then used to assign weights to the training data samples . This is an end-to-end framework . We call it Uncertainty Mining Nets ( UMN ) . In the following subsection , we will introduce UMN in more details . 3.1 LATENT-FEATURE LEARNING . In this work , we represent the given data as the set of ( X , Y ) = { ( x1 , y1 ) , . . . , ( xN , yN ) } where xi is the observed data sample and yi is its corresponding label which may be potentially corrupted . If xi is unlabeled , then yi becomes empty . To be concise , we omit the index i in the rest of the paper . Motivated by the recent success of generative models in semi-supervised learning related applications , firstly , we apply the variational autoencoder ( VAE ) on all the training data . VAE consists of two modules : an Encoder that maps the variables x to the latent variables z to approximate the prior distribution of p ( z ) and a Generator pθ ( x|z ) that samples the the input variables x given the latent variables z . It can be formulated as p ( z ) = N ( z|0 , I ) , pθ ( x|z ) = f ( x ; z , θ ) ; ( 1 ) where f ( x ; z , θ ) is the likelihood function and N indicates the Gaussian distribution . θs are network parameters . The goal of VAE is to maximize the evidence variational lower bound ( ELBO ) of pθ ( x ) as log pθ ( x ) > Eqφ ( z|x ) log pθ ( x|z ) −DKL ( qφ ( z|x ) ||p ( x ) ) . The learned latent variables obtained from VAE can be used as the feature representation to train the classifier . Based on this , we can fully utilize the knowledge from the training data without the constraint of the labeled data size limitation . The low-dimensional embedding z can well cover the distribution of the input data x . Our hypothesis is that the unlabeled data helps training robustly against the noisy labels via the deep generative modeling . We will see this in the next subsection . 3.2 SEMI-SUPERVISED LEARNING . After building the unsupervised learning framework via VAE , we apply the label information to improve the learning capability of the neural network . Instead of using the raw data x , we directly use the latent vector za obtained from VAE of latent-feature learning part along with the pre-defined labels . We follow the idea of conditional generative model . Our generative process can be formulated as , y , zb ∼M ( y ) , p ( zb ) , za ∼ pθ ( za|zb , y ) , ( 2 ) x ∼ pθ ( x|za ) , ŷ ∼ pθ ( ŷ | y , za ) ; ( 3 ) where M is the multinomial distribution . y indicates the true label . za is jointly generated from zb and y and zb is the latent representation of the input . In this work , we treat y as the latent variables . We use ŷ to denote the observed labels . To more accurately capture the reliability of labels , we estimate each labeled sample uncertainty via pθ ( ŷ | y , za ) . the posterior distribution can be factorised as q ( za , zb , y|x , ŷ ) = q ( za|x ) q ( y|za ) q ( zb|za , y ) . ( 4 ) Following this , the Evidence Lower Bound ( ELBO ) can be derived as follows : − ∑ x∈ { L , U } Eqφ ( za|x ) ∑ y∈C qφ ( y|za ) KL ( qφ ( zb|za , y ) ‖ p ( zb ) ) − ∑ x∈ { L , U } Eqφ ( za|x ) ∑ y∈C qφ ( y|za ) KL ( qφ ( y|za ) ‖ p ( y ) ) − ∑ x∈ { L , U } Eqφ ( za|x ) ∑ y∈C qφ ( y|za ) Eqφ ( zb|za , y ) ( log pθ ( za|zb , y ) − log qφ ( za|x ) ) + ∑ x∈ { L , U } Eqφ ( za|x ) log pθ ( x|za ) + ∑ x∈ { L } Eqφ ( za|x ) ∑ yk∈C qφ ( yk|za ) log pθ ( ŷ|yk , za ) , ( 5 ) where qφ ( y|za ) , qφ ( za|x ) , qφ ( zb|za , y ) , pθ ( za|zb , y ) , pθ ( x|za ) indicate the classifier , encoder , conditional encoder , conditional decoder and decoder functions respectively . L indicates labeled data . U means unlabeled data and C denotes the set of used classes . The last term can be treated as labeled loss term as the supervised portion of Eq . 5 . For a more detailed derivation of the ELBO , please refer to the Appendix . As indicated in Eq . 5 , except the last term , all other terms in the equation are calculated over all training data samples . The last term serves as the supervised factor for semi-supervised learning where the observed labels may be incorrect . It uses an uncertainty related function pθ ( ŷ|yk , za ) to modulate the sample weights during the gradient back-propagation . As indicated in Fig . 1 , pθ ( ŷ|yk , za ) is approximated based on the sample-wise uncertainty . More details are given in the following . For simplicity , we can also represent the generative process of the observed ŷ by Fig . 2 . One plausible way to estimate the uncertainty of the sample label is to model the class conditional corruption ratio p ( ŷ|y ) , which is a mean field approximation . As discussed in ( Langevin et al. , 2018 ) , the class conditional probability can be computed as p ( ŷ | y ) = { 1− , if ŷ = y / ( C − 1 ) , otherwise ( 6 ) and the labeled loss term can be formulated as Eqφ ( za|x ) [ f ( ) qφ ( y|za ) ] . ( 7 ) where f ( ) = log [ ( C−1 ) ( 1− ) ] is a function with constant . From Eq . 7 , we can see that it assigns the same weight for all samples belonging to the same category , i.e. , all labeled terms contribute equally to the gradient back propagated regardless of their label correctness as Eqφ ( za|x ) [ f ( ) ∇φqφ ( y|za ) ] . ( 8 ) Although this idea is simple and easy to follow , the assumption may not be the case in the real scenario . In general , the value of which is the class conditional corruption rate , remains unknown beforehand . Another issue is that it ’ s not accurate to apply the same categorical corruption ratio to all data samples of a given class . Our approach solves these problems by estimating sample-wise uncertainty during the training stage . We replace the class conditional in Eq . 9 with a point-wise estimation of the label uncertainty ( za ) , where we follow the generative process of Eq . 3 . The uncertainty of label is hence ( za ) . Pointwise label uncertainty is calculated as p ( ŷ | y , za ) = { 1− ( za ) , if ŷ = y ( za ) / ( C − 1 ) . otherwise ( 9 ) So f ( ) in Eq . 7 becomes f ( ) = log [ ( C−1 ) ( 1− ( za ) ) ( za ) ] . That is , samples contribute relatively more to the gradient backpropagation when the estimated is small which indicates there is a high probability that the given label is correct . By focusing on these reliable targets during training , we can train a more robust classifier . From this , we can see that the key is to approximate ( za ) precisely . In the following subsection , we discuss the proposed approach to model ( za ) using the differences in predictions from the updating classifier model and its moving average model . We want to emphasize that although UMN is based on VAE framework , its architecture can be flexible . Depending on the task , the encoder of its generative model-VAE can be implemented using various deep learning networks , e.g. , AlexNet , GoogLeNet , ResNet , etc . Meanwhile , UMN is not limited to one specific task , like image classification . It can be easily extended to other classification problems .

Summary: In this paper, the authors proposed a novel framework, Uncertainty Mining Net (UMN), to address the problem of learning on limited labeled data with label noise. First, UMN applied the unsupervised variational autoencoder to learn a more representative latent feature representation by involving large amounts of unlabeled data. Second, in the training process, ELBO integrates information from all the training data and sample-wise uncertainty estimated from the predictions of the updating model and its exponential moving average is incorporated to enable the learning process to focus on the data with reliable labels. Experimental results show that UMN outpuroms several state-of-the-art methods on multiple benchmark datasets.