Novelty detection using ensembles with regularized disagreement

Despite their excellent performance on in-distribution ( ID ) data , deep neural networks often confidently predict on out-of-distribution ( OOD ) samples that come from novel classes instead of flagging them for expert evaluation . Even though conventional OOD detection algorithms can distinguish far OOD samples , current methods that can identify near OOD samples require training with labeled data that is very similar to these near OOD samples . In turn , we develop a new ensemble-based procedure for semi-supervised novelty detection ( SSND ) that only utilizes a mixture of unlabeled ID and OOD samples to achieve good detection performance on near OOD data . It crucially relies on regularization to promote diversity on the OOD data while preserving agreement on ID data . Extensive comparisons of our approach to state-of-the-art SSND methods on standard image data sets ( SVHN/CIFAR-10/CIFAR-100 ) and medical image data sets reveal significant gains with negligible increase in computational cost 1 . 1 INTRODUCTION . Despite achieving great in-distribution ( ID ) performance , deep neural networks ( DNN ) often have trouble dealing with samples in the test set that are out-of-distribution ( OOD ) , i.e . test inputs that are unlike the data seen during training . For example , DNNs often make incorrect predictions with high confidence when new unseen classes emerge over time ( e.g . undiscovered bacteria Ren et al . ( 2019 ) , new diseases Katsamenis et al . ( 2020 ) ) , or when data suffers from distribution shift ( e.g . corruptions Lu et al . ( 2019 ) , environmental changes Kumar et al . ( 2020 ) ) . If the labels of these OOD samples follow the same conditional probability distribution as the training set Shimodaira ( 2000 ) , it is most desirable to output calibrated uncertainty estimates in addition to a single predicted value , as in Neal ( 1996 ) ; Gal & Ghahramani ( 2016 ) ; Malinin & Gales ( 2018 ) ; Lakshminarayanan et al . ( 2017 ) . In contrast , when this assumption does not hold and some inputs might come from previously unseen classes , we would like to detect such novel samples and bring them to the attention of experts . More specifically , in novelty detection , we want to detect inputs x that satisfy PX ( x ) < α for a small threshold α , where PX is the marginal training ( ID ) distribution . Previous works that have tackled this problem are known as open-set recognition and OOD detection methods . In what follows , we use the terms novelty detection ( ND ) and OOD detection interchangeably . Related problems such as aforementioned uncertainty estimation or one-class ( OC ) classification have slightly different objectives but also include methods that are applicable to novelty detection . 1Our code is publicly available at https : //bit.ly/3a7aQyN Numerous novelty detection methods are successful for simple benchmarks where the OOD samples are far from the training samples ( such as SVHN vs CIFAR10 ) . As Winkens et al . ( 2020 ) and a number of concurrent works ( Tack et al. , 2020 ; Fort et al. , 2021 ) recently noted , these methods however have subpar performance on near OOD data , for instance when OOD samples are drawn from unseen classes from the same data set ( e.g . CIFAR100 vs CIFAR10 ) . A recent method that is reported to have high near OOD detection performance involves tuning large models pretrained on ImageNet21k ( Fort et al. , 2021 ) and , hence , arguably relies on using during training OOD data that contains classes that are close to the unseen CIFAR classes during test time . However , in many scientific applications that use , for instance , medical or satellite images , such large data sets for pretraining are not available . In particular , truly novel classes will be inherently dissimilar from any previously available data while still sharing some of the same characteristics . Instead , a more realistic scenario assumes access to a small batch of unlabeled test data that includes ID and OOD samples without knowing which are the outliers . We can use this set during training to ultimately perform well on future samples ( i.e . semi-supervised novelty detection ( SSND ) ( Blanchard et al. , 2010 ) ) or to detect outliers from that particular test batch itself ( reminiscent of transductive OOD detection ( Scott & Blanchard , 2008 ) ) . Even though using unlabeled data has the potential to improve detection performance as argued in Scott & Blanchard ( 2009 ) , existing SSND methods for deep neural networks ( Kiryo et al. , 2017 ; Yu & Aizawa , 2019 ; Guo et al. , 2020 ; Zhang et al. , 2020b ) do not leverage the unlabeled set well enough to improve near OOD detection performance , as shown in Figure 1 . This includes previous methods that try to obtain a diverse ensemble and use it for novelty detection , such as MCD ( Yu & Aizawa , 2019 ) . In this paper , we introduce Ensembles with Regularized Disagreement ( ERD ) , an ensemble method for SSND that successfully takes advantage of the unlabeled data to achieve the right amount of disagreement between the model predictions . The models in our ensemble are trained to not only fit the training data but also the artificially labeled samples from the unlabeled set , while aiming to achieve good validation accuracy . In particular , • we argue why regularizing disagreement is crucial for OOD detection with ensemble methods . • we give a justification , backed by theoretical arguments , as to why training with early stopping and with artificial labels assigned to the unlabeled set achieves the right amount of disagreement . • we test our method on many near OOD tasks , including medical data , demonstrating significant gains with a negligible increase in computation cost compared to vanilla ensembles . 2 RELATED WORK AND A TAXONOMY OF OOD DETECTION METHODS . In this section we give an overview of approaches that are related to ours and categorize them with respect to 1 ) data availability and 2 ) the final objective . Further , we list a few representative approaches in Table 1 and refer the reader to surveys such as Bulusu et al . ( 2020 ) for a thorough literature overview . 2.1 TAXONOMY ACCORDING TO DATA AVAILABILITY . In this section we present methods that are ordered by a decreasing necessary amount of labeled OOD data or data similar to OOD data at test time . Supervised and augmented unsupervised ND . We call methods that use labeled OOD samples from the test distribution for calibration or hyperparameter tuning supervised ND ( SND ) ( Yu & Aizawa , 2019 ; Lee et al. , 2018 ; Liang et al. , 2018 ; Ruff et al. , 2020 ) . Alternatively , some works use during training either real , known outliers Hendrycks et al . ( 2019 ) ; Malinin & Gales ( 2018 ) or OOD-like synthetically generated data to simulate the test OOD distribution , in what we call the augmented unsupervised ND ( A-UND ) . However , the performance of these methods relies on proxy OOD data that is similar to test OOD . Concurrent works also propose to use models large-scale models that are pretrained on datasets that contain classes similar to the novel classes ( Fort et al. , 2021 ; Reiss & Hoshen , 2021 ) , referred to as pretrained unsupervised ND . Semi-supervised novelty detection ( SSND , ours ) . This setting is the one we study in this work.2 We assume that , apart from class-labeled training data , we also have access to a small batch of unlabeled data drawn from the test distribution . It consists of ID and OOD data without explicitly knowing which samples are ID and OOD . SSND methods attempt to detect OOD samples from a new batch drawn from the same test distribution ( Blanchard et al. , 2010 ; Mũnoz-Marı́ et al. , 2010 ; du Plessis et al. , 2014 ; Liu et al. , 2018 ) . This is similar to the goal of approaches that use unlabeled data for learning with augmented classes ( U-LAC ) ( Da et al. , 2014 ; Guo et al. , 2020 ; Zhang et al. , 2020b ) . The SSND setting is related to transductive novelty detection ( Scott & Blanchard , 2008 ; Guo et al. , 2020 ) , where the test set coincides with the unlabeled set used for training . Unsupervised novelty detection ( UND ) . In this less restrictive setting , only ID data is available during training ( Lakshminarayanan et al. , 2017 ; Sastry & Oore , 2019 ; Nalisnick et al. , 2019 ; Choi et al. , 2018 ) , which generally leads to a poorer performance . Even though Scott & Blanchard ( 2009 ) prove for shallow models that unlabeled data available in SSND should significantly improve detection , it remains unclear how well deep neural networks can leverage the unlabeled data set effectively . 2.2 TAXONOMY ACCORDING TO OVERALL OBJECTIVE . We now discuss the different objectives of methods in the literature that can be used to detect OOD samples and explicitly list those that do not explicitly mention this keyword . Learning the ID marginal PX . Since we define OOD samples as all x for which PX ( x ) < α , if we had access to the marginal training distribution PX , we would have perfect OOD detection for any x 6∈ XID . Generative models ( Choi et al. , 2018 ; Akçay et al. , 2018 ; Nalisnick et al. , 2019 ) , however , struggle to learn the density from finite samples when the data is high-dimensional . Alternatively , one-class classification ( Mũnoz-Marı́ et al. , 2010 ; Ruff et al. , 2020 ; Sohn et al. , 2021 ) and PU learning approaches ( du Plessis et al. , 2014 ; Kiryo et al. , 2017 ) try to directly learn a discriminator between ID and OOD data , but tend to produce indistinguishable representations for inliers and outliers when the ID distribution consists of many diverse classes . Learning PX using label information . ( ours ) When the ID training set has class labels , one can take advantage of that additional information to distinguish points in the support of PX from OOD data , for instance , by using the intermediate representations of trained neural networks ( Lee et al. , 2018 ; Sastry & Oore , 2019 ) . Often the task is to also simultaneously predict well on ID data , known in the literature as the problem open-set recognition ( Zhang et al. , 2020a ; Geng et al. , 2021 ) . Learning uncertainty estimates for PY |X . Uncertainty estimates optimized for minimal calibration error can naturally be used for OOD samples . Many uncertainty quantification methods are based on a Bayesian framework ( Gal & Ghahramani , 2016 ; Malinin & Gales , 2018 ; Graves , 2011 ; Blundell et al. , 2015 ) or calibration improvement ( Liang et al. , 2018 ; Hafner et al. , 2019 ) – neither of them however perform as well as other OOD methods mentioned above ( Ovadia et al. , 2019 ) . 3 PROPOSED METHOD . In this section we introduce our proposed algorithm , ERD , and provide a principled justification for the key ingredients that lead to the improved performance of our method . 2We use the same definition of SSND as the survey by Bulusu et al . ( 2020 ) , whereas some works use the term to refer to SND ( Gornitz et al. , 2013 ; Daniel et al. , 2019 ; Ruff et al. , 2020 ) or UND ( Song et al. , 2017 ; Akçay et al. , 2018 ) according to our taxonomy .

Summary: The paper presents an ensemble-based semi-supervised learning method for novelty detection.  The goal of their training scheme is to create an ensemble of models that has a high disagreement on the out-of-distribution (OOD) samples in the unlabeled set. The training resembles a self-training algorithm that labels the unlabeled pool and uses implicit regularization via early-stopping to find a "sweet spot" in terms of disagreement on OOD samples between the models in the ensemble. The final decision of whether an input is considered as out- or in-distribution is based on a hypothesis test using the average disagreement between the softmax outputs in the ensemble. In-distribution samples should be accurately classified with high confidence and show little disagreement in the ensemble while out-distribution samples should be detectable as the different models will produce different outputs.