Adversarial Inductive Transfer Learning with input and output space adaptation

1 INTRODUCTION . Deep neural networks ( Goodfellow et al. , 2016 ) have demonstrated the state-of-the-art performance in different problems , ranging from computer vision and natural language processing to genomics ( Eraslan et al. , 2019 ) and medicine ( Topol , 2019 ) . However , these networks often require a large number of samples for training , which is challenging and sometimes impossible to obtain in the real world applications . Transfer learning ( Pan & Yang , 2009 ) attempts to solve this challenge by leveraging the knowledge in a source domain , a large data-rich dataset , to improve the generalization performance on a small target domain . Training a model on the source domain and testing it on the target domain violates the i.i.d assumption that the train and test data are from the same distribution . The discrepancy in the input space decreases the prediction accuracy on the test data , which leads to poor generalization ( Zhang et al. , 2019 ) . Many methods have been proposed to minimize the discrepancy between the source and the target domains using different metrics such as Jensen Shannon Divergence ( Ganin & Lempitsky , 2014 ) , Maximum Mean Discrepancy ( Gretton et al. , 2012 ) , and Margin Disparity Discrepancy ( Zhang et al. , 2019 ) . While transductive transfer learning ( e.g . domain adaptation ) uses a labeled source domain to improve generalization on an unlabeled target domain , inductive transfer learning ( e.g . few-shot learning ) uses a labeled source domain to improve the generalization on a labeled target domain where label spaces are different in the source and the target domains ( Pan & Yang , 2009 ) . Adversarial domain adaptation has shown great performance in addressing the discrepancy in the input space for different applications ( Schoenauer-Sebag et al. , 2019 ; Hosseini-Asl et al. , 2018 ; Pinheiro , 2018 ; Zou et al. , 2018 ; Tsai et al. , 2018 ; Long et al. , 2018 ; Chen et al. , 2017 ; Tzeng et al. , 2017 ) , however , adversarial adaptation to address the discrepancies in both the input and output spaces has not yet been explored . Our motivating application is pharmacogenomics ( Smirnov et al. , 2017 ) where the goal is to predict response to a cancer drug given the genomic data ( e.g . gene expression ) . Since clinical datasets in pharmacogenomics ( patients ) are small and hard to obtain , many studies have focused on large pre-clinical pharmacogenomics datasets such as cancer cell lines as a proxy to patients ( Barretina et al. , 2012 ; Iorio et al. , 2016 ) . A majority of the current methods are trained on cell line datasets and then tested on other cell line or patient datasets ( Sharifi-Noghabi et al. , 2019b ; Geeleher et al. , 2014 ) . However , cell lines and patients data , even with the same set of genes , do not have identical distributions due to the lack of an immune system and the tumor microenvironment in cell lines ( Mourragui et al. , 2019 ) . Moreover , in cell lines , the response is often measured by the drug concentration that reduces viability by 50 % ( IC50 ) , whereas in patients , it is often based on changes in the size of the tumor and measured by metrics such as response evaluation criteria in solid tumors ( RECIST ) ( Schwartz et al. , 2016 ) . This means that drug response prediction is a regression problem in cell lines but a classification problem in patients . Therefore , discrepancies exist in both the input and output spaces in pharmacogenomics datasets . Table A1 provides the definition of these biological terms . In this paper , we propose Adversarial Inductive Transfer Learning ( AITL ) , the first adversarial method of inductive transfer learning . Different from existing methods for transfer learning , AITL adapts not only the input space but also the output space . Our motivating application is transfer learning for pharmacogenomics datasets . In our driving application , the source domain is the gene expression data obtained from the cell lines and the target domain is the gene expression data obtained from patients . Both domains have the same set of genes ( i.e. , raw feature representation ) . Discrepancies exist between the gene expression data in the input space , and the measure of the drug response in the output space . AITL learns features for the source and target samples and uses these features as input for a multi-task subnetwork to predict drug response for both the source and the target samples . The output space discrepancy is addressed by the multi-task subnetwork , which has one shared layer and separate classification and regression towers , and assigns binary labels ( called cross-domain labels ) to the source samples . The multi-task subnetwork also alleviates the problem of small sample size in the target domain by sharing the first layer with the source domain . To address the discrepancy in the input space , AITL performs adversarial domain adaptation . The goal is that features learned for the source samples should be domain-invariant and similar enough to the features learned for the target samples to fool a global discriminator that receives samples from both domains . Moreover , with the cross-domain binary labels available for the source samples , AITL further regularizes the learned features by class-wise discriminators . A class-wise discriminator receives source and target samples from the same class label and should not be able to predict the domain accurately . We evaluated the performance of AITL and state-of-the-art inductive and adversarial transductive transfer learning baselines on pharmacogenimcs datasets in terms of the Area Under the Receiver Operating Characteristic curve ( AUROC ) and the Area Under the Precision-Recall curve ( AUPR ) . In our experiments , AITL achieved a substantial improvement compared to the baselines , demonstrating the potential of transfer learning for drug response prediction , a crucial task of precision oncology . 2 RELATED WORK . 2.1 TRANSFER LEARNING . Following the notation of ( Pan & Yang , 2009 ) , a domain like DM is defined by a raw input feature space1 X and a probability distribution p ( X ) , where X = { x1 , x2 , ... , xn } and xi is the i-th raw feature vector of X . A task T is associated with DM = { X , p ( X ) } , where T = { Y , F ( . ) } is defined by a label space Y and a predictive function F ( . ) which is learned from training data of the form ( X , Y ) , where X ∈ X and Y ∈ Y . A source domain is defined as DMS = { ( xs1 , ys1 ) , ( xs2 , ys2 ) , ... , ( xsnS , ysnS ) } and a target domain is defined as DMT = { ( xt1 , yt1 ) , ( xt2 , yt2 ) , ... , ( xtnT , ytnT ) } , where xs ∈ XS , xt ∈ XT , ys ∈ YS , and yt ∈ YT . Since nT < < nS and it is challenging to train a model only on the target domain , transfer learning aims to improve the generalization on a target task TT using the knowledge in DMS and DMT and their corresponding tasks TS and TT . Transfer learning can be categorized into three categories : 1 ) unsupervised transfer learning , 2 ) transductive transfer learning , and 3 ) inductive transfer learning . In unsupervised transfer learning , there is no label in the source and target domains . In transductive transfer learning , source domain is labeled but target domain is unlabeled , domains can be either the same or different ( domain adaptation ) , but source and target tasks are the same . In inductive transfer learning , target domain is labeled and source domain can be either labeled or unlabeled , and 1This is different from learned features by the network domains can be the same or different , but in this category tasks are always different ( Pan & Yang , 2009 ) . 2.2 INDUCTIVE TRANSFER LEARNING . There are three approaches to inductive transfer learning : 1 ) deep metric learning , 2 ) few-shot learning , and 3 ) weight transfer ( Scott et al. , 2018 ) . Deep metric learning methods are independent of the number of samples in each class of the target domain , denoted by k , meaning that they work for small and large k values . Few-shot learning methods focus on small k ( k ≤ 20 ) . Finally , weight transfer methods require a large k ( k ≥ 100 or k ≥ 1000 ) ( Scott et al. , 2018 ) . Figure A1 ( in Appendix ) presents this taxonomy . In drug response prediction , the target domain is small , which means a limited number of samples for each class is available , therefore , few-shot learning is more suitable for such a problem . Fewshot learning involves training a classifier to recognize new classes , provided only a small number of examples from each of these new classes in the training data ( Snell et al. , 2017 ) . Various methods have been proposed for few-shot learning ( Chen et al. , 2019 ; Scott et al. , 2018 ; Snell et al. , 2017 ; Vinyals et al. , 2016 ) . For example , Prototypical Networks ( ProtoNet ) ( Snell et al. , 2017 ) constructs prototypical representatives ( class means ) from source domain learned features and compares the Euclidean distance between the target domain learned features and these class representatives to assign labels to the target samples . 2.3 ADVERSARIAL TRANSFER LEARNING . Recent advances in adversarial learning leverage deep neural networks to learn transferable representation that disentangles domain-invariant and class-invariant features from different domains and matches them properly ( Peng et al. , 2019 ; Zhang et al. , 2019 ; Long et al. , 2018 ) . In this section , we first introduce the Generative Adversarial Networks ( GANs ) ( Goodfellow et al. , 2014 ) , and then introduce some of the existing works on adversarial transfer learning . 2.3.1 GENERATIVE ADVERSARIAL NETWORKS . GANs ( Goodfellow et al. , 2014 ) attempt to learn the distribution of the input data via a minimax framework where two networks are competing : a discriminator D and a generator G. The generator tries to create fake samples from a randomly sampled latent variable that fool the discriminator , while the discriminator tries to catch these fake samples and discriminate them from the real ones . Therefore , the generator wants to minimize its error , while the discriminator wants to maximize its accuracy : M G inM D axV ( G , D ) = ∑ x∼data log [ D ( x ) ] + ∑ z∼noise log [ 1−D ( G ( z ) ) ] ( 1 ) A majority of literature on adversarial transfer learning are for transductive transfer learning where the source domain is labeled while the target domain is unlabeled . 2.3.2 ADVERSARIAL TRANSDUCTIVE TRANSFER LEARNING . Transductive transfer learning , often referred to as domain adaptation , is the most common scenario in transfer learning . Various methods have been proposed for adversarial transductive transfer learning in different applications such as image segmentation ( Chen et al. , 2017 ; Tsai et al. , 2018 ) , image classification ( Tzeng et al. , 2017 ; Long et al. , 2018 ) , speech recognition ( Hosseini-Asl et al. , 2018 ) , domain adaptation under label-shift ( Azizzadenesheli et al. , 2019 ) , partial domain adaptation ( You et al. , 2019 ) , and multiple domain adaptation ( Schoenauer-Sebag et al. , 2019 ) . The idea of these methods is that features extracted from source and target samples should be similar enough to fool a global discriminator ( Tzeng et al. , 2017 ) and/or class-wise discriminators ( Chen et al. , 2017 ) .

Summary: The paper proposes an adversarial transfer learning network that can handle the adaptation of both the input space and the output space. The paper is motivated by the application of drug response prediction where the source domain is cell line data and the target domain is patient data. Patient data are usually scarce, hence motivating transferring the knowledge learned from the more widely available cell line data to improve the predictive performance based on the patient data.  The idea of making use of adversarial networks is to learn a representation of the data points that is invariant to whether the data points come from the source domain or the target domain. Experiments on real-world data over four drugs demonstrate the effectiveness of the proposed methods compared to other methods that are not specifically designed for this scenario.