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Register a new userHow does the Combined Risk Affect the Performance of Unsupervised Domain Adaptation Approaches?
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Zhen Fang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Unsupervised domain adaptation (UDA) aims to train a target classifier with labeled samples from the source domain and unlabeled samples from the target domain. Classical UDA learning bounds show that target risk is upper bounded by three terms: source risk, distribution discrepancy, and combined risk. Based on the assumption that the combined risk is a small fixed value, methods based on this bound train a target classifier by only minimizing estimators of the source risk and the distribution discrepancy. However, the combined risk may increase when minimizing both estimators, which makes the target risk uncontrollable. Hence the target classifier cannot achieve ideal performance if we fail to control the combined risk. To control the combined risk, the key challenge takes root in the unavailability of the labeled samples in the target domain. To address this key challenge, we propose a method named E-MixNet. E-MixNet employs enhanced mixup, a generic vicinal distribution, on the labeled source samples and pseudo-labeled target samples to calculate a proxy of the combined risk. Experiments show that the proxy can effectively curb the increase of the combined risk when minimizing the source risk and distribution discrepancy. Furthermore, we show that if the proxy of the combined risk is added into loss functions of four representative UDA methods, their performance is also improved.
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Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard Empirical Risk Minimization (ERM), and little is understood about how much MAML improves over ERM in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the condition number of the tasks loss function. Specifically, we prove that in order for MAML to achieve substantial gain over ERM, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights also apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.
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