Open Set Domain Adaptation by Extreme Value Theory

Recently, deep learning techniques have drawn a lot of attention in both academia and industry, due to their astounding performance in fields such as computer vision and natural language processing [16, 31, 13, 35, 5, 38, 32, 1, 26, 10]. However, one major disadvantage of deep learning is that neural networks generally require a large amount of training data to converge to the right solution and generalize. When the training data are insufficient, the model performance is usually adversely affected. Sometimes even if the training data are sufficient, the domain gap, i.e. the difference between data distributions, between the source domain (the data we train model on) and the target domain (the desired target task) may still contribute to low generalizability. This is because in conventional machine learning tasks, we usually assume that the training data distribution is the same as the testing data distribution. However, in real world, testing data are uncontrollable, and thus the difference between the source and the target domain can be substantial, which results in the overfitting problem, that is, the model does not generalize well to the testing set.

In order to reduce the domain gap and better utilize the source domain knowledge, domain adaptation techniques have been proposed to resolve the issue. Domain adaptation assumes that the source domain has sufficient amount of labeled data to train a good model, while the desired target domain has insufficient amount of data to train the model. Note that in most domain adaptation tasks, the target domain does not have labeled data at all, which is also known as unsupervised domain adaptation. Domain adaptation methods leverage the knowledge from the source domain with sufficient labeled data to learn a model that works well in the target domain with insufficient or no labeled data. Typically, domain adaptation methods reduce the domain gap by diminishing the divergence between the label-rich source and the label-scarce target domain [14, 15, 11, 12, 36, 25, 34, 30, 21, 8, 7, 28]. A significant drawback of most of the existing works is that they assume the source label space and the target label space are identical, i.e. the target classes are assumed to have appeared during the training process and the training classes do not contain classes that are not in the target domain. This is also known as closed set domain adaptation (CSDA), which is infrequent in real-world scenarios since it is hard to guarantee that the target domain classes are the same as the source domain classes. Aligning the source and the target domain by brute force when their label spaces are different is extremely detrimental to the model’s generalizability, which is also known as the negative transfer phenomenon, because the CSDA methods would try to align the additional unknown classes as well during adaptation.

To handle the domain adaptation tasks without assuming identical label spaces, open set domain adaptation (OSDA) methods were proposed to first detect the irrelevant or unknown samples and then avoid adaptation on the unknown samples and perform domain adaptation only on the known classes [4, 29, 18, 2], which can be achieved by forcing the model to learn a clear boundary between known classes and unknown classes and a clear boundary within the known classes. After adaptation, the model is applied to the target samples as follows: either a target sample is classified as a class among the known classes, or rejected as an unknown class. However, all of the conventional OSDA methods employ a rejection threshold hyperparameter, where if a score or statistic for a sample is higher than the threshold, then the sample will be rejected as an unknown class and discarded during adaptation, and thus the model’s sensitivity is largely affected by this rejection threshold.

In our work, we handle the existing issue in OSDA by 1) utilizing an entropy-based instance-level reweighting strategy and 2) extreme value theory (EVT) which has proven to be useful in many classification tasks due to its ability to model extreme values [9, 23, 6, 37, 3]. We propose to use entropy of probability distribution of a sample to measure the likelihood it belongs to unknown classes. That is, the higher the entropy is, the more likely the sample belongs to the unknown classes, because the model is more uncertain regarding the prediction. We utilize the entropy values to construct an instance-level weight for domain adaptation, instead of setting a hard threshold. In this way, every sample is taken into account during the adaptation process, and a sample with high entropy should be focused less to avoid the negative transfer problem. In inference, we model the tail probability of the entropy distribution by fitting a generalized extreme value (GEV) distribution, and we use the cumulative distribution function (CDF) score to indicate if a sample belongs to unknown or known classes. Experimental results on three conventional domain adaptation datasets show outperformance over both state-of-the-art CSDA and OSDA benchmarks.

We claim the following key contributions. First, we model the tail of entropy distributions with EVT to detect and reject unknown classes. Second, the entropy-based instance-level weighting strategy avoids setting a hard threshold manually and thus is more robust and stable. Third, we have done extensive experiments on three conventional datasets in domain adaptation, which show that our model outperforms benchmarks by a significant margin.

The rest of the paper is organized as follows. In Section 2, we discuss the related literature and methods. In Section 3, we explain our OSDA method in details. In Section 4, we conduct experiments to validate the effectiveness of the proposed method and in Section 5, we conclude the paper by reiterating the main contributions.

Existing works on CSDA typically try to diminish the domain gap by minimizing a statistical divergence between two domains for adaptation or by an adversarial approach. MCD [28] utilize two task-specific classifiers to detect the target domain samples which are far from the source domain by maximizing the two classifiers’ inconsistency regarding predictions. Based on the mean teacher model [33] that is originally proposed for semi-supervised learning tasks, the self-ensemble network [7] is proposed to calculate the exponentially moving average of the student model weights and it assigns the weights to the teacher model to reduce the domain gap. There are also a plethora of works on adversarial learning to reduce domain gap. DANN [8] reduces the domain gap by introducing a domain discriminator during the training process to discriminate between domains where the domain discriminator is optimized by a specially designed gradient reversal layer. ADDA [34] incorporates adversarial training to reduce the domain gap by the discriminator to distinguish across domains. The soft labeling method [14] utilizes a soft cross-entropy loss function to optimize for the domain invariance and thus aligning the source and target domains. WDGRL [30] is proposed to minimize the Wasserstein distance across domains adversarially for learning domain invariance. CADA [20] aligns the joint distribution for labels and features across two domains by exploring classifier predictions for adversarial domain adaptation. Our proposed method differs from these prior works in that we focus on the practical OSDA setting while these prior works assume an identical label space across domains, and thus they cannot recognize the unknown classes samples included during domain adaptation. Our method is able to detect the unknown classes by instance-level weights based on entropy to avoid negative transfer.

There are also several existing works on OSDA to address the issue of unknown classes. STA [19] is proposed to develop a coarse-to-fine progressive separation method for unknown and known classes. OSBP [29] forces the generator to either match target samples with source known classes or ignore them in adaptation as unknown samples by adversarial training. Based on the work of SE [7] in CSDA, [18] modifies the adaptation loss and then aligns the target domain with the source domain to address the unknown classes using weights calculated by entropy values. By factorization and joint separation, D-FRODA [2] represents the source and target classes with a shared embedding space for domain adaptation. ATI [4] is also proposed to detect the target samples that potentially belong to the known classes by learning a mapping from the source domain to the target domain. We see the difference between our proposed work and the prior works in the utilization of a hard threshold to recognize and reject the unknown samples, and thus the model accuracy largely depends on how the threshold is set. The proposed method utilizes entropy to indicate the likelihood of unknown classes and it constructs a soft instance-level weight. We further fit an EVT model on the tail of the entropy distribution to detect unknown classes. Therefore, by avoiding manual thresholding and introducing EVT to detect unknown classes, the proposed method is more robust and suitable in the OSDA setting, which is also validated in the experimental results.

In this section, $K$ denotes the number of known classes; $x^{s},x^{t}$ denote a source, target sample, respectively; $y^{s}$ denotes a source label; $X^{s},X^{t}$ denote the source, target sample distribution, respectively; $D^{s},D^{t}$ denote the source, target domain, respectively; $g$ denotes a feature extractor; $clf$ denotes a $K$-way classifier to classify samples into one of the $K$ known classes; and $clf^{d}$ denotes the binary domain classifier to classify samples into source or target domains.

Even though all samples in the source domain are labeled, in one loss component we assume a split of known classes to $S$ (the classes of interest) and $C$ (the irrelevant classes), where $S\cap C=\phi,S\cup C=\{1,2,...,K\}$, and we treat the classes in $C$ as unknown. To this end, we denote by $X^{s}_{U}$ as the sample distribution of the samples corresponding to the classes in $C$ (unknown-class distribution). This is a known concept, e.g. [18, 29].

We evaluate ADAGEV on three conventional benchmark datasets in domain adaptation: Digits, Office-31 [27] and VisDA [24]. In the experiments, the source domain samples are labeled and the target domain samples are not labeled, and the task is to either classify target samples into one of the known classes or reject as unknown. We use the conventional OSDA metrics OS and OS* as performance measures, which denote the mean accuracy for all $K+1$ classes (all known classes and the additional unknown class) and the mean accuracy for the $K$ known classes, respectively. The hyperparameters are set as $\lambda_{d}=0.5,\lambda_{e}=1,\lambda_{c}=1$ (discussed later). The benchmark state-of-the-art methods are discussed in Section 2, and the accuracies are obtained from the corresponding papers except [18], which only reported the OS accuracy. To complete the comparison for OS*, we ran the source code of [18] and after finetuning we are able to achieve a slightly better performance for OS than the original paper, and both the OS and OS* accuracies are reported in our experiments. We discuss the network architectures for each experiment in the following subsections. For a fair comparison, the same network architecture is used in ADAGEV as in the benchmark algorithms (which all use the same architecture). The stopping criteria are also discussed in the following subsections.

We propose an open set domain adaptation method which models the tail of the entropy distributions using EVT and utilizes an instance-level reweighting strategy to detect and reject unknown samples. Experiments show that the method achieves the new state-of-the-art performance by beating the existing benchmarks by a large margin for three conventional domain adaptation datasets.