We propose Adversarial Inductive Transfer Learning (AITL), a method for addressing discrepancies in input and output spaces between source and target domains. AITL utilizes adversarial domain adaptation and multi-task learning to address these discrepancies. Our motivating application is pharmacogenomics where the goal is to predict drug response in patients using their genomic information. The challenge is that clinical data (i.e. patients) with drug response outcome is very limited, creating a need for transfer learning to bridge the gap between large pre-clinical pharmacogenomics datasets (e.g. cancer cell lines) and clinical datasets. Discrepancies exist between 1) the genomic data of pre-clinical and clinical datasets (the input space), and 2) the different measures of the drug response (the output space). To the best of our knowledge, AITL is the first adversarial inductive transfer learning method to address both input and output discrepancies. Experimental results indicate that AITL outperforms state-of-the-art pharmacogenomics and transfer learning baselines and may guide precision oncology more accurately. 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; , 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 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. To our surprise, ProtoNet and ADDA could not outperform the method of (Geeleher et al., 2014) and MOLI baselines. For ProtoNet, this may be due to the depth of the backbone network. A recent study has shown that a deeper backbone improves ProtoNet performance drastically in image classification Chen et al. (2019) . However, in pharmacogenomics, employing a deep backbone is not realistic because of the much smaller sample size compared to an image classification application. Another limitation for ProtoNet is the imbalanced number of training examples in different classes in pharmacogenomics datasets. Specifically, the number of examples per class in the training episodes is limited to the number of samples of the minority class as ProtoNet requires the same number of examples from each class. For ADDA, this lower performance may be due to the lack of end-to-end training of the classifier along with the global discriminator of this method. The reason is that end-to-end training of the classifier along with the discriminators improved the performance of the second adversarial baseline in AUROC and AUPR compared to ADDA. Moreover, the method of ) also showed a relatively better performance in AUPR compared to the method of (Geeleher et al., 2014) and MOLI. In pharmacogenomics, patient datasets are small or not publicly available due to privacy and/or data sharing issues. We believe including more patient samples and more drugs will increase generalization capability. In addition, recent studies in pharmacogenomics have shown that using multiple genomic data types (known as multi-omics in genomics) works better than using only gene expression . In this work, we did not consider such data due to the lack of patient samples with multi-omics and drug response data publicly available; however, in principle, AITL also works with such data. Last but not least, we used pharmacogenomics as our motivating application for this new problem of transfer learning, but we believe that AITL can also be employed in other applications. For example, in slow progressing cancers such as prostate cancer, large patient datasets with gene expression and short-term clinical data (source domain) are available, however, patient datasets with long-term clinical data (target domain) are small. AITL may be beneficial to learn a model to predict these long-term clinical labels using the source domain and its short-term clinical labels (Sharifi-Noghabi et al., 2019a) . Moreover, AITL can also be applied to the diagnosis of rare cancers with a small sample size. Gene expression data of prevalent cancers with a large sample size, such as breast cancer, may be beneficial to learn a model to diagnose these rare cancers. In this paper, we introduced a new problem in transfer learning motivated by applications in pharmacogenomics. Unlike domain adaptation that only requires adaptation in the input space, this new problem requires adaptation in both the input and output spaces. To address this problem, we proposed AITL, an Adversarial Inductive Transfer Learning method which, to the best of our knowledge, is the first method that addresses the discrepancies in both the input and output spaces. AITL uses a feature extractor to learn features for target and source samples. Then, to address the discrepancy in the output space, AITL utilizes these features as input of a multi-task subnetwork that makes predictions for the target samples and assign cross-domain labels to the source samples. Finally, to address the input space discrepancy, AITL employs global and class-wise discriminators for learning domain-invariant features. In our motivating application, pharmacogenomics, AITL adapts the gene expression data obtained from cell lines and patients in the input space, and also adapts different measures of the drug response between cell lines and patients in the output space. In addition, AITL can also be applied to other applications such as rare cancer diagnosis or predicting long-term clinical labels for slow progressing cancers. We evaluated AITL on four different drugs and compared it against state-of-the-art baselines from three categories in terms of AUROC and AUPR. The empirical results indicated that AITL achieved a significantly better performance compared to the baselines showing the benefits of addressing the discrepancies in both the input and output spaces. We conclude that AITL may be beneficial in pharmacogenomics, a crucial task in precision oncology. For future research directions, we believe that the TCGA dataset consisting of gene expression data of more than 12,000 patients (without drug response outcome) can be incorporated in an unsupervised transfer learning setting to learn better domain-invariant features between cell lines and cancer patients. In addition, we did not explore the impact of the chemical structures of the studied drugs in the prediction performance. We believe incorporating this input with transfer learning in the genomic level can lead to a better performance. Currently, AITL borrows information between the input domains indirectly via its multi-task subnetwork and assignment of cross-domain labels. An interesting future direction can be to exchange this information between domains in a more explicit way. Moreover, we also did not perform theoretical analysis on this new problem of transfer learning and we leave it for future work. Finally, we did not distinguish between different losses in the multi-task subnetwork, however, in reality patients are more important than cell lines, and considering a higher weight for the corresponding loss in the cost function can improve the prediction performance.
A novel method of inductive transfer learning that employs adversarial learning and multi-task learning to address the discrepancy in input and output space
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