Deep neural networks perform remarkably well when the training and the testing instances are drawn from the same distributions. However, they lack the capacity to generalize in the presence of adomain-shift  exhibiting alarming levels of dataset bias or domain bias . As a result, a drop in performance is observed at test time if the training data (acquired from a source domain) is insufficient to reliably characterize the test environment (the target
domain). This challenge arises in several Computer Vision tasks[32, 25, 18] where one is often confined to a limited array of available source datasets, which are practically inadequate to represent a wide range of target domains. This has motivated a line of Unsupervised Domain Adaptation (UDA) works that aim to generalize a model to an unlabeled target domain, in the presence of a labeled source domain.
In this work, we study UDA in the context of image recognition. Notably, a large body of UDA methods is inspired by the potential of deep CNN models to learn transferable representations . This has formed the basis of several UDA works that learn domain-agnostic feature representations [26, 44, 48] by aligning the marginal distributions of the source and the target domains in the latent feature space. Several other works learn domain-specific representations via independent domain transformations [47, 5, 32]
to a common latent space on which the classifier is learned. The latent space alignment of the two domains permits the reuse of the source classifier for the target domain. These methods however operate under the assumption of a shared label-set () between the two domains (closed-set). This restricts their real-world applicability where a target domain often contains additional unseen categories beyond those found in the source domain.
Recently, open-set DA [35, 39] has gained much attention, wherein the target domain is assumed to have unshared categories (), a.k.a category-shift. Target instances from the unshared categories are assigned a single unknown label  (see Fig. 1B). Open-set DA is more challenging, since a direct application of distribution alignment (e.g. as in closed-set DA [20, 44]) reduces the model’s performance due to the interference from the unshared categories (an effect known as negative-transfer ). The success of open-set DA relies not only on the alignment of shared classes, but also on the ability to mitigate negative-transfer. State-of-the-art methods such as  train a domain discriminator using the source and the target data to detect and reject target instances that are out of the source distribution, thereby minimizing the effect of negative-transfer.
In summary, the existing UDA methods assume access to a labeled source dataset to obliquely receive a task-specific supervision during adaptation. However, this assumption of co-existing source and target datasets poses a significant constraint in the modern world, where coping up with strict digital privacy and copyright laws is of prime importance . This is becoming increasingly evident in modern corporate dealings, especially in the medical and biometric industries, where a source organization (the model vendor) is often restricted to share its proprietary or sensitive data, alongside a pre-trained model to satisfy the client’s specific deployment requirements [7, 14]. Likewise, the client is prohibited to share private data to the model vendor . Certainly, the collection of existing open-set DA solutions is inadequate to address such scenarios.
Thus, there is a strong motivation to develop practical UDA algorithms which make no assumption about data-exchange between the vendor and the client. One solution is to design self-adaptive models that effectively capture the task-specific knowledge from the vendor’s source domain and transfer this knowledge to the client’s target domain. We call such models as inheritable models, referring to their ability to inherit and transfer knowledge across domains without accessing the source domain data. It is also essential to quantify the knowledge inheritability of such models. Given an array of inheritable models, this quantification will allow a client to flexibly choose the most suitable model for the client’s specific target domain.
Addressing these concerns, in this work we demonstrate how a vendor can develop an inheritable model, which can be effectively utilized by the client to perform unsupervised adaptation to the target domain, without any data-exchange. To summarize, our prime contributions are:
We propose a practical UDA scenario by relaxing the assumption of co-existing source and target domains, called as the vendor-client paradigm.
We propose inheritable models to realize vendor-client paradigm in practice and present an objective measure of inheritability, which is crucial for model selection.
We provide theoretical insights and extensive empirical evaluation to demonstrate state-of-the-art open-set DA performance using inheritable models.
2 Related Work
Closed-set DA. Assuming a shared label space (
), the central theme of these methods is to minimize the distribution discrepancy. Statistical measures such as MMD[51, 27, 28], CORAL  and adversarial feature matching techniques [10, 48, 46, 47, 40] are widely used. Recently, domain specific normalization techniques [23, 5, 4, 37] has started gaining attention. However, due to the shared label-set assumption these methods are highly prone to negative-transfer in the presence of new target categories.
Open-set DA. ATI-  assigns a pseudo class label, or an unknown label, to each target instance based on its distance to each source cluster in the latent space. OSVM  uses a class-wise confidence threshold to classify target instances into the source classes, or reject them as unknown. OSBP  and STA  align the source and target features through adversarial feature matching. However, both OSBP and ATI-
are hyperparameter sensitive and are prone tonegative-transfer. In contrast, STA  learns a separate network to obtain instance-level weights for target samples to avoid negative-transfer and achieves state-of-the-art results. All these methods assume the co-existance of source and target data, while our method makes no such assumption and hence has a greater practical significance.
Domain Generalization. Methods such as [8, 21, 9, 22, 31, 16] largely rely on an arbitrary number of co-existing source domains with shared label sets, to generalize across unseen target domains. This renders them impractical when there is an inherent category-shift among the data available with each vendor. In contrast, we tackle the challenging open-set scenario by learning on a single source domain.
Data-free Knowledge Distillation (KD). In a typical KD setup , a student model is learned to match the teacher model’s output. Recently, DFKD  and ZSKD  demonstrated knowledge transfer to the student when the teacher’s training data is not available. Our work is partly inspired by their data-free ideology. However, our work differs from KD in two substantial ways; 1) by nature of the KD algorithm, it does not alleviate the problem of domain-shift, since any domain bias exhibited by the teacher will be passed on to the student, and 2) KD can only be performed for the task which the teacher is trained on, and is not designed for recognizing new (unknown) target categories in the absence of labeled data. Handling domain-shift and category-shift simultaneously is necessary for any open-set DA algorithm, which is not supported by these methods.
Our formulation of an inheritable model for open-set DA is much different from prior arts - not only is it robust to negative-transfer but also facilitates domain adaptation in the absence of data-exchange.
3 Unsupervised Open-Set Domain Adaptation
In this section, we formally define the vendor-client paradigm and inheritability in the context of unsupervised open-set domain adaptation (UODA).
Notation. Given an input space and output space , the source and target domains are characterized by the distributions and on respectively. Let , denote the marginal input distributions and denote the conditional output distribution of the two domains. Let denote the respective label sets for the classification tasks (). In the UODA problem, a labeled source dataset and an unlabeled target dataset are considered. The goal is to assign a label for each target instance , by predicting the class for those in shared classes (), and an ‘unknown’ label for those in unshared classes (). For simplicity, we denote the distributions of target-shared and target-unknown instances as and respectively. We denote the model trained on the source domain as (source predictor) and the model adapted to the target domain as (target predictor).
3.2 The vendor-client paradigm
The central focus of our work is to realize a practical DA paradigm which is fundamentally viable in the absence of the co-existance of the source and target domains. With this intent, we formalize our DA paradigm.
Definition 1 (vendor-client paradigm). Consider a vendor with access to a labeled source dataset and a client having unlabeled instances sampled from the target domain. In the vendor-client paradigm, the vendor learns a source predictor using to model the conditional , and shares to the client. Using and , the client learns a target predictor to model the conditional .
This paradigm satisfies the two important properties; 1) it does not assume data-exchange between the vendor and the client which is fundamental to cope up with the dynamically reforming digital privacy and copyright regulations and, 2) a single vendor model can be shared with multiple clients thereby minimizing the effort spent on source training. Thus, this paradigm has a greater practical significance than the traditional UDA setup where each adaptation step requires an additional supervision from the source data [24, 39]. Following this paradigm, our goal is to realize the conditions on which one can successfully learn a target predictor. To this end, we formalize the inheritability of task-specific knowledge of the source-trained model.
We define an inheritable model from the perspective of learning a predictor () for the target task. Intuitively, given a hypothesis class , an inheritable model should be sufficient (i.e. in the absence of source domain data) to learn a target predictor whose performance is close to that of the best predictor in .
Definition 2 (Inheritability criterion). Let be a hypothesis class, , and . A source predictor is termed inheritable relative to the hypothesis class , if a target predictor can be learned using an unlabeled target sample when given access to the parameters of , such that, with probability at least the target error of does not exceed that of the best predictor in by more than . Formally,
where, and is computed over the choice of sample . This definition suggests that an inheritable model is capable of reliably transferring the task-specific knowledge to the target domain in the absence of the source data, which is necessary for the vendor-client paradigm. Given this definition, a natural question is, how to quantify inheritability of a vendor model for the target task. In the next Section, we address this question by demonstrating the design of inheritable models for UODA.
How to design inheritable models? There can be several ways, depending upon the task-specific knowledge required by the client. For instance, in UODA, the client must effectively learn a classifier in the presence of both domain-shift and category-shift. Here, not only is the knowledge of class-separability essential, but also the ability to detect new target categories as unknown is vital to avoid negative-transfer. By effectively identifying such challenges, one can develop inheritable models for tasks that require vendor’s dataset. Here, we demonstrate UODA using an inheritable model.
4.1 Vendor trains an inheritable model
In UODA, the primary challenge is to tackle negative-transfer. This challenge arises due to the overconfidence issue  in deep models, where unknown target instances are confidently predicted into the shared classes, and thus get aligned with the source domain. Methods such as  tend to avoid negative-transfer by leveraging a domain discriminator to assign a low instance-level weight for potentially unknown target instances during adaptation. However, solutions such as a domain discriminator are infeasible in the absence of data-exchange between the vendor and the client. Thus, an inheritable model should have the ability to characterize the source distribution, which will facilitate the detection of unknown target instances during adaptation. Following this intuition, we design the architecture.
a) Architecture. As shown in Fig. 2A, the feature extractor comprises of a backbone CNN model and fully connected layers . The classifier contains two sub-modules, a source classifier with classes, and an auxiliary out-of-distribution (OOD) classifier with classes accounting for the ‘negative’ region not covered by the source distribution (Fig. 3C). The output for each input is obtained by concatenating the outputs of and (i.e. concatenating and ) followed by softmax activation. This equips the model with the ability to capture the class-separability knowledge (in ) and to detect OOD instances (via ). This setup is motivated by the fact that the overconfidence issue can be addressed by minimizing the classifier’s confidence for OOD instances . Accordingly, the confidence of is maximized for in-distribution (source) instances, and minimized for OOD instances (by maximizing the confidence of ).
b) Dataset preparation. To effectively learn OOD detection, we augment the source dataset with synthetically generated negative instances, i.e. , where and are the marginal latent space distribution and the conditional output distribution of the negative instances respectively. We use , to model the low source-density region as out-of-distribution (see Fig. 3C). To obtain , a possible approach explored by  could be to use a GAN framework to generate ‘boundary’ samples. However, this is computationally intensive and introduces additional parameters for training. Further, we require these negative samples to cover a large portion of the OOD region. This eliminates a direct use of linear interpolation techniques such as mixup [55, 50] which result in features generated within a restricted region (see Fig. 3A). Indeed, we propose an efficient way to generate OOD samples, which we call as the feature-splicing technique.
Feature-splicing. It is widely known that in deep CNNs, higher convolutional layers specialize in capturing class-discriminative properties . For instance,  assigns each filter in a high conv-layer with an object part, demonstrating that each filter learns a different class-specific
trait. As a result of this specificity, especially when a rectified activation function (e.g
. ReLU) is used, feature maps receive a high activation whenever the learnedclass-specific trait is observed in the input . Consequently, we argue that, by suppressing such high activations, we obtain features devoid of the properties specific to the source classes and hence would more accurately represent the OOD samples. Then, enforcing a low classifier confidence for these samples can mitigate the overconfidence issue.
Feature-splicing is performed by replacing the top- percentile activations, at a particular feature layer, with the corresponding activations pertaining to an instance belonging to a different class (see Fig. 3B). Formally,
where, for a source image belonging to class , and is the feature-splicing operator which replaces the top- percentile activations in the feature with the corresponding activations in as shown in Fig. 3B (see Suppl. for algorithm). This process results in a feature which is devoid of the class-specific traits, but lies near the source distribution. To label these negative instances, we perform a -means clustering and assign a unique negative class label to each cluster of samples. By training the auxiliary classifier to discriminate these samples into these negative classes, we mitigate the overconfidence issue as stated earlier. We found feature-splicing to be effective in practice. See Suppl. for other techniques that we explored.
c) Training procedure. We train the model in two steps. First, we pre-train using source data by employing the standard cross-entropy loss,
where, is the softmax activation function. Next, we freeze the backbone model , and generate negative instances by performing feature-splicing using source features at the last layer of . We then continue the training of the modules using supervision from both and ,
where, and , and the output of is obtained as described in Sec. 4.1a (and depicted in Fig. 2). The joint training of and , allows the model to capture the class-separability knowledge (in ) while characterizing the negative region (in ), which renders a superior knowledge inheritability. Once the inheritable model is trained, it is shared to the client for performing UODA.
4.2 Client adapts to the target domain
With a trained inheritable model () in hand, the first task is to measure the degree of domain-shift to determine the inheritability of the vendor’s model. This is followed by a selective adaptation procedure which encourages shared classes to align while avoiding negative-transfer.
a) Quantifying inheritability. In presence of a small domain-shift, most of the target-shared instances (pertaining to classes in ) will lie close to the high source-density regions in the latent space (e.g. Fig. 3E). Thus, one can rely on the class-separability knowledge of to predict target labels. However, this knowledge becomes less reliable with increasing domain-shift as the concentration of target-shared instances near the high density regions decreases (e.g. Fig. 3D). Thus, the inheritability of for the target task would decrease with increasing domain-shift. Moreover, target-unknown instances (pertaining to classes in ) are more likely to lie in the low source-density region than target-shared instances. With this intuition, we define an inheritability metric which satisfies,
We leverage the classifier confidence to realize an instance-level measure of inheritability as follows,
where is the softmax activation function. Note that although softmax is applied over the entire output of , is evaluated over those corresponding to (shaded in blue in Fig. 2). We hypothesize that this measure follows Eq. 5, since, the source instances (in the high density region) receive the highest confidence, followed by target-shared instances (some of which are away from the high density region), while the target-unknown instances receive the least confidence (many of which lie away from the high density regions). Extending the instance-level inheritability, we define a model inheritability over the entire target dataset as,
A higher arises from a smaller domain-shift implying a greater inheritability of task-specific knowledge (e.g. class-separability for UODA) to the target domain. Note that is a constant for a given triplet and the value of the denominator in Eq. 7 can be obtained from the vendor.
b) Adaptation procedure. For performing adaptation to the target domain, we learn a target-specific feature extractor as shown in Fig. 2B (similar in architecture to ). is initialized from the source feature extractor , and is gradually trained to selectively align the shared classes in the pre-classifier space (input to ) to avoid negative-transfer. The adaptation involves two processes - inherit (to acquire the class-separability knowledge) and tune (to avoid negative-transfer).
Inherit. As described in Sec. 4.2a, the class-separability knowledge of is reliable for target samples with high . Subsequently, we choose top- percentile target instances based on and obtain pseudo-labels using the source model, . Using the cross-entropy loss we enforce the target predictions to match the pseudo-labels for these instances, thereby inheriting the class-separability knowledge,
Tune. In the absence of label information, entropy minimization [27, 11] is popularly employed to move the features of unlabeled instances towards the high confidence regions. However, to avoid negative-transfer, instead of a direct application of entropy minimization, we use as a soft instance weight in our loss formulation. Target instances with higher are guided towards the high source density regions, while those with lower are pushed into the negative regions (see Fig. 3DE). This separation is a key to minimize the effect of negative-transfer.
On a coarse level, using the classifier we obtain the probability that an instance belongs to the shared classes as . Optimizing the following loss encourages a separation of shared and unknown classes,
To further encourage the alignment of shared classes on a fine level, we separately calculate probability vectors foras, , and for as, , and minimize the following loss,
where, is the Shannon’s entropy. The total loss selectively aligns the shared classes, while avoiding negative-transfer. Thus, the final adaptation loss is,
We now present a discussion on the success of this adaptation procedure from the theoretical perspective.
4.3 Theoretical Insights
We defined the inheritability criterion in Eq. 1 for transferring the task-specific knowledge to the target domain. To show that the knowledge of class-separability is indeed inheritable, it is sufficient to demonstrate that the inheritability criterion holds for the shared classes. Extending Theorem 3 in , we obtain the following result.
Result 1. Let be a hypothesis class of VC dimension . Let be a labeled sample set of points drawn from . If be the empirical minimizer of on , and be the optimal hypothesis for , then for any , we have with probability of at least (over the choice of samples),
See Supplementary for the derivation of this result. Essentially, using labeled target-shared instances, one can train a predictor (here, ) which satisfies Eq. 12. However, in a completely unsupervised setting, the only way to obtain target labels is to exploit the knowledge of the vendor’s model. This is precisely what the pseudo-labeling process achieves. Using an inheritable model (), we pseudo-label the top- percentile target instances with high precision and enforce . In doing so, we condition the target model to satisfy Eq. 12, which is the inheritability criterion for shared categories (given unlabeled instances and source model ). Thus, the knowledge of class-separability is transferred to the target model during the adaptation process.
Note that, with increasing number of labeled target instances (increasing ), the last term in Eq. 12 decreases. In our formulation, this is achieved by enforcing , which can be regarded as a way to self-supervise the target model. In Sec. 5 we verify that, during adaptation the precision of target predictions improves over time. This self-supervision with an increasing number of correct labels is, in effect, similar to having a larger sample size in Eq. 12. Thus, adaptation tightens the bound in Eq. 12 (see Suppl.).
In this section, we evaluate the performance of unsupervised open-set domain adaptation using inheritable models.
|STA ||89.50.6||92.10.5||93.71.5||96.1 0.4||97.50.2||96.50.5||99.50.2||99.60.1||89.10.5||93.50.8||87.90.9||87.40.6||92.9||94.1|
5.1 Experimental Details
a) Datasets. Office-31  consists of 31 categories of images in three different domains: Amazon (A), Webcam (W) and DSLR (D). Office-Home  is a more challenging dataset containing 65 classes from four domains: Real World (Re), Art (Ar), Clipart (Cl) and Product (Pr). VisDA  comprises of 12 categories of images from two domains: Real (R), Synthetic (S). The label sets , are in line with  and  for all our comparisons. See Suppl. for sample images and further details.
We implement the framework in PyTorch and use ResNet-50 (till the last pooling layer) as the backbone models and for Office-31 and Office-Home, and VGG-16  for VisDA. For inheritable model training, we use a batch size of ( source and negative instances each), and use the hyperparameters and . During adaptation, we use a batch size of 32 and set the hyperparameter . We normalize the instance weights with the weight of each batch , i.e. . During inference, an unknown label is assigned if is one of the negative classes, otherwise, a shared class label is predicted. See Supplementary for more details.
c) Metrics. In line with , we compute the open-set accuracy (OS) by averaging the class-wise target accuracy for classes (considering target-unknown as a single class). Likewise, the shared accuracy (OS*) is computed as the class-wise average of target-shared classes ().
a) State-of-the-art comparison. In Tables 1-3, we compare against the state-of-the-art UODA method STA . The results for other methods are taken from . Particularly, in Table 1, we report the mean and std. deviation of OS and OS* over 3 separate runs. Due to space constraints, we report only OS in Table 2. It is evident that adaptation using an inheritable model outperforms prior arts that assume access to both vendor’s data (source domain) and client’s data (target domain) simultaneously. The superior performance of our method over STA is described as follows. STA learns a domain-agnostic feature extractor by aligning the two domains using an adversarial discriminator. This restricts the model’s flexibility to capture the diversity in the target domain, owing to the need to generalize across two domains, on top of the added training difficulties of the adversarial process. In contrast, we employ a target-specific feature extractor () which allows the target predictor to effectively tune to the target domain, while inheriting the class-separability knowledge. Thus, inheritable models offer an effective solution for UODA in practice.
b) Hyperparameter sensitivity. In Fig. 4, we plot the adaptation performance (OS) on a range of hyperparameter values used to train the vendor’s model (, ). A low sensitivity to these hyperparameters highlights the reliability of the inheritable model. In Fig. 5C, we plot the adaptation performance (OS) on a range of values for on Office-31. Specifically, denotes the ablation where is not enforced. Clearly, the performance improves on increasing which corroborates the benefit of inheriting class-separability knowledge during adaptation.
c) Openness (). In Fig. 5A, we report the OS accuracy on varying levels of Openness  . Our method performs well for a wide range of Openness, owing to the ability to effectively mitigate negative-transfer.
d) Domain discrepancy. As discussed in , the empirical domain discrepancy can be approximated using the Proxy -distance where is the generalization error of a domain discriminator. We compute the PAD value at the pre-classifier space for both target-shared and target-unknown instances in Fig. 6B following the procedure laid out in . The PAD value evaluated for target-shared instances using our model is much lower than a source-trained ResNet-50 model, while that for target-unknown is higher than a source-trained ResNet-50 model. This suggests that adaptation aligns the source and the target-shared distributions, while separating out the target-unknown instances.
a) Model inheritability (). Following the intuition in Sec. 4.2a, we evaluate the model inheritability () for the tasks DW and AW on Office-31. In Fig. 6C we observe that for the target W, an inheritable model trained on the source D exhibits a higher value than that trained on the source A. Consequently, the adaptation task DW achieves a better performance than AW, suggesting that a vendor model with a higher model inheritability is a better candidate to perform adaptation to a given target domain. Thus, given an array of inheritable vendor models, a client can reliably choose the most suitable model for the target domain by measuring . The ability to choose a vendor model without requiring the vendor’s source data enables the application of the vendor-client paradigm in practice.
b) Instance-level inheritability (). In Fig. 5D, we show the histogram of values plotted separately for target-shared and target-unknown instances, for the task AD in Office-31 dataset. This empirically validates our intuition that the classifier confidence of an inheritable model follows the inequality in Eq. 5, at least for the extent of domain-shift in the available standard datasets.
c) Reliability of . Due to the mitigation of overconfidence issue, we find the classifier confidence to be a good candidate for selecting target sample for pseudo-labeling. In Fig. 5B, we plot the prediction accuracy of the top- percentile target instances based on target predictor confidence (
). Particularly, the plot for epoch-shows the pseudo-labeling precision, since the target predictor is initialized with the parameters of the source predictor. It can be seen that the top-15 percentile samples are predicted with a precision close to 1. As adaptation proceeds, improves the prediction performance of the target model, which can be seen as a rise in the plot in Fig. 5B. Therefore, the bound in Eq. 12 is tightened during adaptation. This verifies our intuition in Sec. 4.3
d) Qualitative results. In Fig. 6A we plot the t-SNE  embeddings of the last hidden layer (pre-classifier) features of a target predictor trained using STA  and our method, on the task AD. Clearly, our method performs equally well in spite of the unavailability of source data during adaptation, suggesting that inheritable models can indeed facilitate adaptation in the absence of a source dataset.
e) Training time analysis. We show the benefit of using inheritable models, over a source dataset. Consider a vendor with a labeled source domain A, and two clients with the target domains D and W respectively. Using the state-of-the-art method STA  (which requires labeled source dataset), the time spent by each client for adaptation using source data is 575s on an average (1150s in total). In contrast, our method (a single vendor model is shared with both the clients) results in 250s of vendor’s source training time (feature-splicing: 77s, -means: 66s, training: 154s), and an average of 69s for adaptation by each client (138s in total). Thus, inheritable models provide a much more efficient pipeline by reducing the cost on source training in the case of multiple clients (STA: 1150s, ours: 435s). See Supplementary for experiment details.
In this paper we introduced a practical vendor-client paradigm, and proposed inheritable models to address open-set DA in the absence of co-existing source and target domains. Further, we presented an objective way to measure inheritability which enables the selection of a suitable source model for a given target domain without the need to access source data. Through extensive empirical evaluation, we demonstrated state-of-the-art open-set DA performance using inheritable models. As a future work, inheritable models can be extended to problems involving multiple vendors and multiple clients.
Acknowledgements. This work is supported by a Wipro PhD Fellowship (Jogendra) and a grant from Uchhatar Avishkar Yojana (UAY, IISC_010), MHRD, Govt. of India.
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