Unsupervised Anomaly Detection by Robust Collaborative Autoencoders

Unsupervised anomaly detection plays a critical role in many real-world applications , from computer security to healthcare . A common approach based on deep learning is to apply autoencoders to learn a feature representation of the normal ( non-anomalous ) observations and use the reconstruction error of each observation to detect anomalies present in the data . However , due to the high complexity brought upon by over-parameterization of the deep neural networks ( DNNs ) , the anomalies themselves may have small reconstruction errors , which degrades the performance of these methods . To address this problem , we present a robust framework for detecting anomalies using collaborative autoencoders . Unlike previous methods , our framework does not require supervised label information nor access to clean ( uncorrupted ) examples during training . We investigate the theoretical properties of our framework and perform extensive experiments to compare its performance against other DNN-based methods . Our experimental results show the superior performance of the proposed framework as well as its robustness to noise due to missing value imputation compared to the baseline methods . 1 INTRODUCTION . Anomaly detection ( AD ) is the task of identifying abnormal observations in the data . It has been successfully applied to many applications , from malware detection to medical diagnosis ( Chandola et al. , 2009 ) . Driven by the success of deep learning , AD methods based on deep neural networks ( DNNs ) ( Zhou & Paffenroth , 2017 ; Aggarwal & Sathe , 2017 ; Ruff et al. , 2018 ; Zong et al. , 2018 ; Hendrycks et al. , 2018 ) have attracted increasing attention recently . Unfortunately , DNN methods have several known drawbacks when applied to AD problems . First , since many of them are based on the supervised learning approach ( Hendrycks et al. , 2018 ) , this requires labeled examples of anomalies , which are often expensive to acquire and may not be representative enough in non-stationary environments . Supervised AD methods are also susceptible to the class imbalance problem as anomalies are rare compared to normal observations . Some DNN methods rely on having access to clean data to ensure that the feature representation learning is not contaminated by anomalies during training ( Zong et al. , 2018 ; Ruff et al. , 2018 ; Pidhorskyi et al. , 2018 ; Fan et al. , 2020 ) . This limits their applicability as acquiring a representative clean data itself is a tricky problem . Due to these limitations , there have been concerted efforts to develop robust unsupervised DNN methods that do not assume the availability of supervised labels nor clean training data ( Chandola et al. , 2009 ; Liu et al. , 2019 ) . Deep autoencoders are perhaps one of the most widely used unsupervised AD methods ( Sakurada & Yairi , 2014 ; Vincent et al. , 2010 ) . An autoencoder compresses the original data by learning a latent representation that minimizes the reconstruction loss . It is based on the working assumption that normal observations are easier to compress than anomalies . Unfortunately , such an assumption may not hold in practice since DNNs are often over-parameterized and have the capability to overfit the anomalies ( Zhang et al. , 2016 ) , thus degrading their overall performance . To improve their performance , the unsupervised DNN methods must consider the trade-off between model capacity and overfitting to the anomalies . One way to control the model capacity is through regularization . Many regularization methods for deep networks have been developed to control model capacity , e.g. , by constraining the norms of the model parameters or explicitly perturbing the training process ( Srivastava et al. , 2014 ) . However , these approaches do not prevent the networks from being able to perfectly fit random data ( Zhang et al. , 2016 ) . As a consequence , the regulariza- tion approaches can not prevent the anomalies from being memorized , especially in an unsupervised learning setting . Our work is motivated by recent advances in supervised learning on the robustness of DNNs for noisy labeled data by learning the weights of the training examples ( Jiang et al. , 2017 ; Han et al. , 2018 ) . Unlike previous studies , our goal is to learn the weights in an unsupervised learning fashion so that normal observations are assigned higher weights than the anomalies when calculating reconstruction error . The weights help to reduce the influence of anomalies when learning a feature representation of the data . Since existing approaches for weight learning are supervised , they are inapplicable to unsupervised AD . Instead , we propose an unsupervised robust collaborative autoencoders ( RCA ) method that trains a pair of autoencoders in a collaborative fashion and jointly learns their model parameters and sample weights . Each autoencoder selects a subset of samples with lowest reconstruction errors from a mini-batch to learn their feature representation . By discarding samples with high reconstruction errors , the algorithm is biased towards learning the representation for clean data , thereby reducing its risk of memorizing anomalies . However , by selecting only easyto-fit samples in each iteration , this may lead to premature convergence of the algorithm without sufficient exploration of the loss surface . Thus , instead of selecting the samples to update its own model parameters , each autoencoder will shuffle its selected samples to the other autoencoder , who will use the samples to update their model parameters . The sample selection procedure is illustrated in Figure 1 . During the testing phase , we apply the dropout mechanism used in training to produce multiple output predictions for each test point by repeating the forward pass multiple times . These ensemble of outputs are then aggregated to obtain a more robust estimate of the anomaly score . The main contributions of this paper are as follows . First , we present a novel framework for unsupervised AD using robust collaborative autoencoders ( RCA ) . Second , we provide rigorous theoretical analysis to understand the mechanism behind RCA . We also describe the convergence of RCA to the solution obtained if it was trained on clean data only . We show that the worst-case scenario for RCA is better than conventional autoencoders and analyze the conditions under which RCA is guaranteed to find the anomalies . Finally , we empirically demonstrate that RCA outperforms state-of-the-art unsupervised AD methods for the majority of the datasets used in this study , even in the presence of noise due to missing value imputation . 2 RELATED WORK . There are numerous methods developed for anomaly detection , a survey of which can be found in Chandola et al . ( 2009 ) . Reconstruction-based methods , such as principal component analysis ( PCA ) and autoencoders , are popular approaches , whereby the input data is projected to a lowerdimensional space before it was transformed back to its original feature space . The distance between the input and reconstructed data is used to determine the anomaly scores of the data points . More advanced unsupervised AD methods have been developed recently . Zhou & Paffenroth ( 2017 ) combined robust PCA with an autoencoder to decompose the data into a mixture of normal and anomaly parts . Zong et al . ( 2018 ) jointly learned a low dimensional embedding and density of the data , using the density of each point as its anomaly score while Ruff et al . ( 2018 ) extended the traditional one-class SVM approach to a deep learning setting . Wang et al . ( 2019 ) applied an end-to-end selfsupervised learning approach to the unsupervised AD problem . However , their approach is designed for image data , requiring operations such as rotation and patch reshuffling . Despite the recent progress on deep unsupervised AD , current methods do not explicitly prevent the neural network from incorporating anomalies into their learned representation , thereby degrading the model performance . One way to address the issue is by assigning a weight to each data point , giving higher weights to the normal data to make the model more robust against anomalies . The idea of learning a weight for each data point is not new in supervised learning . A classic example is boosting ( Freund et al. , 1996 ) , where hard to classify examples are assigned higher weights to encourage the model to classify them more accurately . An opposite strategy is used in self-paced learning ( Kumar et al. , 2010 ) , where the algorithm assigns higher weights to easier-to-classify examples and lower weights to harder ones . This strategy was also used by other methods for learning from noisy labeled data , including Jiang et al . ( 2017 ) and Han et al . ( 2018 ) . Furthermore , there are many studies providing theoretical analysis on the benefits of choosing samples with smaller loss to drive the optimization algorithm ( Shen & Sanghavi , 2018 ; Shah et al. , 2020 ) . 3 METHODOLOGY . This section introduces the proposed robust collaborative autoencoder ( RCA ) framework and analyze its properties . Let X ∈ Rn×d denote the input data , where n is the number of observations and d is the number of features . Our goal is to classify each data point xi ∈ X as an anomaly or a normal observation . Let O ⊂ X denote the set of true anomalies in the data . We assume the anomaly ratio , = |O|/n , is given1 or can be approximately estimated . The RCA framework trains a pair of autoencoders , A1 andA2 , with different initializations . In each iteration during training , the autoencoders will each apply a forward pass on a mini-batch randomly sampled from the training data and compute the reconstruction error of each data point in the minibatch . The data points in the mini-batch are then sorted according to their reconstruction errors and each mini-batch selects the points with lowest errors to be exchanged with the other autoencoder . Each autoencoder subsequently performs a back-propagation step to update its model parameters using the samples it receives from the other autoencoder . Upon convergence , the averaged reconstruction error of each data point is used to determine the anomaly score . A pseudocode of the training phase for RCA is given in Algorithm 1 , while the testing phase is given in Algorithm 2 . Algorithm 1 : Robust Collaborative Autoencoders ( Training Phase ) input : training data Xtrn , test data Xtst , reconstruction loss function L , anomaly ratio , dropout rate r > 0 , and maximum training epochs : max epoch ; return trained autoencoders , A∗1 andA ∗ 2 ; Initialize autoencodersA1 andA2 ; sample selection rate β = 1 and best loss ξ∗ = +∞ ; while epoch≤ max epoch do for minibatch S in Xtrn do Ŝ1 ← forward ( A1 , S , dropout = 0 ) , Ŝ2 ← forward ( A2 , S , dropout = 0 ) ; c1 ← sample selection ( L ( Ŝ1 , S ) , β ) , c2 ← sample selection ( L ( Ŝ2 , S ) , β ) ; Ŝ1 ← forward ( A1 , S [ c2 ] , dropout = r ) , Ŝ2 ← forward ( A2 , S [ c1 ] , dropout = r ) ; A1 ←backprop ( Ŝ1 , S [ c2 ] , dropout = r ) , A2 ← backprop ( Ŝ2 , S [ c1 ] , dropout = r ) ; end X̂tst1 ← forward ( A1 , Xtst , dropout = 0 ) , X̂tst2 ← forward ( A2 , Xtst , dropout = 0 ) ; ξtest ← L ( X̂tst1 , Xtst ) + L ( X̂tst2 , Xtst ) ; if ξtest < ξ∗ then ξ∗ = ξtest , A ∗ 1 = A1 , A ∗ 2 = A2 end ; β = max ( β − max epoch , 1− ) end Algorithm 2 : Robust Collaborative Autoencoders ( Testing Phase ) input : test data Xtst , trained autoencodersA∗1 , A ∗ 2 , dropout rate r > 0 , size of ensemble v ; return anomaly score ; Initialize an empty set of reconstruction errors : ξ = { } . for i = 1 to v do ξ1= forward ( A∗1 , Xtst , dropout = r ) , ξ2=forward ( A ∗ 2 , Xtst , dropout = r ) ; ξ = ξ ∪ ( ξ1 + ξ2 ) /2 end anomaly score = average ( ξ ) ; RCA differs from conventional autoencoders in several ways . First , its autoencoders are trained using only selected data points with small reconstruction errors . The selected points are then exchanged between the autoencoders to avoid premature convergence . Furthermore , in the testing phase , each autoencoder applies a dropout mechanism to generate multiple predicted outputs . The averaged ensemble output is used as the final anomaly score . Details of these steps are given next . 1In practice , users would typically specify the top-k anomalies to be examined and verified , where k = n .

Summary: The submission tackles unsupervised anomaly detection, specifically in a scenario where supervision labels are not available, only information about the ratio of anomalous examples in the data set. They suggest an architecture consisting of two auto-encoders collaboratively determining anomalous samples and updating their weights based on data that is deemed normal. The authors provide a theoretical analysis of the selection process, and validate anomaly detection performance on a range of experiments.