# domain_agnostic_learning_with_disentangled_representations__e7ef2962.pdf

Domain Agnostic Learning with Disentangled Representations

Xingchao Peng 1 Zijun Huang 2 Ximeng Sun 1 Kate Saenko 1

Unsupervised model transfer has the potential to greatly improve the generalizability of deep models to novel domains. Yet the current literature assumes that the separation of target data into distinct domains is known as a priori. In this paper, we propose the task of Domain-Agnostic Learning (DAL): How to transfer knowledge from a labeled source domain to unlabeled data from arbitrary target domains? To tackle this problem, we devise a novel Deep Adversarial Disentangled Autoencoder (DADA) capable of disentangling domain-speciﬁc features from class identity. We demonstrate experimentally that when the target domain labels are unknown, DADA leads to stateof-the-art performance on several image classiﬁcation datasets.

1. Introduction

Supervised machine learning assumes that training and testing data are sampled i.i.d from the same distribution, while in practice, the training and testing data are typically collected from related domains but under different distributions, a phenomenon known as domain shift (Quionero-Candela et al., 2009). To avoid the cost of annotating each new test domain, Unsupervised Domain Adaptation (UDA) tackles domain shift by aligning the feature distribution of the source domain with that of the target domain, resulting in domain-invariant features. However, current methods assume that target samples have domain labels and therefore can be isolated into separate homogeneous domains. For many practical applications, this is an overly strong assumption. For example, a hand-written character recognition system could encounter characters written by different

1Computer Science Department, Boston University; 111 Cummington Mall, Boston, MA 02215, USA; email:xpeng@bu.edu 2Columbia Unversity and MADO AI Research; 116th St and Broadway, New York, NY 10027, USA; email:zijun.huang@columbia.edu. Correspondence to: Kate Saenko <saenko@bu.edu>.

Proceedings of the 36 th International Conference on Machine Learning, Long Beach, California, PMLR 97, 2019. Copyright 2019 by the author(s).

people, on different materials, and under different lighting conditions; an image recognition system applied to images scraped from the web must handle mixed-domain data (e.g. paintings, sketches, clipart) without their domain labels.

In this paper, we consider Domain-Agnostic Learning (DAL), a more difﬁcult but practical problem of knowledge transfer from one labeled source domain to multiple unlabeled target domains. The main challenges of domainagnostic learning are that: (1) the target data has mixed domains, which hampers the effectiveness of mainstream feature alignment methods (Long et al., 2015; Sun & Saenko, 2016; Saito et al., 2018), and (2) class-irrelevant information leads to negative transfer (Pan & Yang, 2010), especially when the target domain is highly heterogeneous.

Mainstream UDA methods align the source domain to the target domain by minimizing the Maximum Mean Discrepancy (Long et al., 2015; Tzeng et al., 2014), aligning highorder moments (Sun & Saenko, 2016; Zellinger et al., 2017), or adversarial training (Ganin & Lempitsky, 2015; Tzeng et al., 2017). However, these methods are designed for oneto-one domain alignment and do not account for multiple latent domains in the target. Multi-source domain adaptation (Peng et al., 2018; Xu et al., 2018; Mansour et al., 2009) considers adaptation between multiple sources and a single target domain and assumes domain labels on the source data. Continuous domain adaptation (Hoffman et al., 2014) aims to transfer knowledge to a continuously changing domain (e.g. cars in different decades), but in their scenario the target data are temporally related. Recently, domain generalization approaches (Li et al., 2018a; Carlucci et al., 2018b; Li et al., 2018b) have been introduced to adapt from multiple labeled source domains to an unseen target domain. All of the above models make a strong assumption that the target data are homogeneously sampled from the same distribution, unlike the scenario we consider here.

We postulate that a solution to domain-agnostic learning should not only learn invariance between source and target, but should also actively disentangle the class-speciﬁc features from the remaining information in the image. Deep neural networks are known to extract features in which multiple hidden factors are highly entangled (Bengio et al., 2013). Recent work attempts to disentangle features in the latent space of autoencoders with adversarial training (Cao et al.,

Domain Agnostic Learning with Disentangled Representations

2018; Liu et al., 2018b; Odena et al., 2017; Lee et al., 2018). However, the above models have limited capacity in transferring features learned from one domain to heterogeneous target domains. Liu et al. (2018a) proposes a framework that takes samples from multiple domains as input, and derives a domain-invariant latent feature space via adversarial training. This model is limited by two factors when applied to the DAL task. First, it only disentangles the embeddings into domain-invariant features and domain-speciﬁc features such as weather conditions, and discards the latter, but does not explicitly try to separate class-relevant features from class-irrelevant features like background. Second, there is no guarantee that the domain-invariant features are fully disentangled from the domain-speciﬁc features.

To address the issues mentioned above, we propose a novel Deep Adversarial Disentangled Autoencoder (DADA), aiming to tackle domain-agnostic learning by disentangling the domain-invariant features from both domain-speciﬁc and class-irrelevant features simultaneously. First, in addition to domain disentanglement (Liu et al., 2018a; Cao et al., 2018; Lee et al., 2018), we employ class disentanglement to remove class-irrelevant features, as shown in Figure 1. The class disentanglement is trained in an adversarial fashion: a class identiﬁer is trained on the labeled source domain and the disentangler generates features to fool the class identiﬁer. To the best of our knowledge, we are the ﬁrst to show that class disentanglement boosts domain adaptation performance. Second, to enhance the disentanglement, we propose to minimize the mutual information between the disentangled features. We implement a neural network to estimate the mutual information between the disentangled feature distributions, inspired by a recently published theoretical work (Belghazi et al., 2018). Comprehensive experiments on standard image recognition datasets demonstrate that our derived disentangled representation achieves signiﬁcant improvements over the state-of-the-art methods on the task of domain-agnostic learning.

The main contributions of this paper are highlighted as follows: (1) we propose a novel learning paradigm of domainagnostic learning; 2) we develop an end-to-end Deep Adversarial Disentangled Autoencoder (DADA) which learns a better disentangled feature representation to tackle the task; and (3) We propose class disentanglement to remove classirrelevant features, and minimize the mutual information to enhance the disentanglement.

2. Related Work

Domain Adaptation Unsupervised domain adaptation (UDA) aims to transfer the knowledge learned from one or more labeled source domains to an unlabeled target domain. Various methods have been proposed, including discrepancybased UDA approaches (Long et al., 2017; Tzeng et al.,

2014; Ghifary et al., 2014; Peng & Saenko, 2018), adversarybased approaches (Liu & Tuzel, 2016; Tzeng et al., 2017; Liu et al., 2018a), and reconstruction-based approaches (Yi et al., 2017; Zhu et al., 2017; Hoffman et al., 2018; Kim et al., 2017). These models are typically designed to tackle single source to single target adaptation. Compared with single source adaptation, multi-source domain adaptation (MSDA) assumes that training data are collected from multiple sources. Originating from the theoretical analysis in (Ben-David et al., 2010; Mansour et al., 2009; Crammer et al., 2008), MSDA has been applied to many practical applications (Xu et al., 2018; Duan et al., 2012; Peng et al., 2018). Speciﬁcally, Ben-David et al. (2010) introduce an HΔH-divergence between the weighted combination of source domains and a target domain. We propose a new and more practical learning paradigm, not yet considered in the UDA literature, where labeled data come from a single source domain but the testing data contain multiple unknown domains.

Representation Disentanglement The goal of learning disentangled representations is to model the factors of data variation. Recent works (Mathieu et al., 2016; Makhzani et al., 2016; Liu et al., 2018a; Odena et al., 2017) aim at learning an interpretable representation using generative adversarial networks (GANs) (Goodfellow et al., 2014; Kingma et al., 2014) and variational autoencoders (VAEs) (Rezende et al., 2014; Kingma & Welling, 2013). In a fully supervised setting, Lee et al. (2018) proposes to disentangle the feature representation into a domain-invariant content space and a domain-speciﬁc attribute space, producing diverse outputs without paired training images. Another work (Odena et al., 2017) proposes an auxiliary classiﬁer GAN (AC-GAN) to achieve representation disentanglement. Despite promising performance, these methods focus on disentangling representation in a single domain. Liu et al. (2018a) introduces a uniﬁed feature disentangler to learn a domain-invariant representation from data across multiple domains. However, their model assumes that multiple source domains are available during training, which limits its practical application. In contrast, our model disentangles the representation based on one source domain and multiple unknown target domains, and proposes an improved approach to disentanglement that considers the class label and mutual information between features.

Agnostic Learning There are several prior studies of agnostic learning that are related to our work. Model-Agnostic Meta-Learning (MAML) (Finn et al., 2017) aims to train a model on a variety of learning tasks and solve a new task using only a few training examples. Different from MAML, our method mainly focuses on transferring knowledge to heterogeneous domains. Carlucci et al. (2018a) proposes a learning framework to seamlessly extend the knowledge from multiple source domain to an unseen target domain by

Domain Agnostic Learning with Disentangled Representations

class identifier

domain identifier

adversarial training

mutual information

reconstructor

class disentanglement

domain disentanglement

train on source train on source/target

Figure 1. Our DADA architecture learns to extract domain-invariant features of visual categories. In addition to domain disentanglement (blue lines), we employ class disentanglement (red lines) to remove class-irrelevant features, both trained adversarially. We further apply a mutual information minimizer to strengthen the disentanglement.

pixel-adaptation in an incremental architecture. Romijnders et al. (2018) introduces a domain agnostic normalization layer for adversarial UDA and improves the performance of deep models on an unseen domain. Though the results are promising, we argue that only normalizing the feature representation is not enough for domain-agnostic learning, and that extracting disentangled domain-invariant and domainspeciﬁc features is also important.

3. DADA: Deep Adversarial Disentangled Autoencoder

We deﬁne the domain-agnostic learning task as follows: Given a source domain Ds = {(xs i, ys i )}ns i=1 with ns labeled examples, the goal is to minimize risk on N target domains Dt = { D1, D2, ..., DN} without domain labels. We denote the target domains as Dt = {xt j}nt j=1 with nt unlabeled examples. Empirically, we want to minimize the target risk t (θ) = Pr(x,y) Dt [θ (x) = y], where θ (x) is the classiﬁer.

We propose to solve the task by learning domain-invariant features that are discriminative of the class. Figure 1 shows the proposed model. The feature generator G maps the input image to a feature vector f G, which has many highly entangled factors. The disentangler D is responsible for disentangling the features (f G) into domain-invariant features (fdi), domain-speciﬁc features (fds), and class-irrelevant features (fci). The feature reconstructor R aims to recover f G from either (fdi, fds) or (fdi, fci). D and R are implemented as the encoder and decoder in a Variational Autoencoder. A mutual information minimizer is applied between fdi and fci, as well as between fdi and fds, to enhance the disentanglement. Adversarial training via a domain identiﬁer aligns the source domain and the heterogeneous target domain in the fdi space. A class identiﬁer C is trained on the labeled source domain to predict the class distribution f C and to adversarially extract class-irrelevant features fci. We next

describe each component in detail.

Variational Autoencoders VAEs (Kingma & Welling, 2013) are a class of deep generative models that simultaneously train both a probabilistic encoder and decoder. The encoder is trained to generate latent vectors that roughly follow a Gaussian distribution. In our case, we learn each part of our disentangled representations by applying a VAE architecture with the following objective function:

Lvae = f G f G 2 F + KL(q(z|f G)||p(z)), (1)

where the ﬁrst term aims at recovering the original features extracted by G, and the second term calculates Kullback Leibler divergence which penalizes the deviation of latent features from the prior distribution p(zc) (as z N(0, I)). However, this property cannot guarantee that domain-invariant features are well disentangled from the domain-speciﬁc features or from class-irrelevant features, as the loss function in Equation 1 only aligns the latent features to a normal distribution.

Class Disentanglement To address the above problem, we employ class disentanglement to remove class-irrelevant features, such as background, in an adversarial way. First, we train the disentangler D and the K-way class identiﬁer C to correctly predict the labels, supervised by the crossentropy loss:

Lce = E(xs,ys) Ds

k=1 1[k = ys]log(C(f D)) (2)

where f D {fdi, fci}.

In the second step, we ﬁx the class identiﬁer and train the disentangler D to fool the class identiﬁer by generating classirrelevant features fci. This can be achieved by minimizing the negative entropy of the predicted class distribution:

j=1 log C(f j ci) 1

j=1 log C(f j ci) (3)

Domain Agnostic Learning with Disentangled Representations

where the ﬁrst term and the second term indicate minimizing the entropy on the source domain and on heterogeneous target, respectively. The above adversarial training process forces the corresponding disentangler to extract classirrelevant features.

Domain Disentanglement To tackle the domain agnostic learning task, disentangling class-irrelevant features is not enough, as it fails to align the source domain with the target. To achieve better alignment, we further propose to disentangle the learned features into domain-speciﬁc and domaininvariant and to thus align the source with the target domain in the domain-invariant latent space. This is achieved by exploiting adversarial domain classiﬁcation in the resulting latent space. Speciﬁcally, we leverage a domain identiﬁer DI, which takes the disentangled feature (fdi or fds ) as input and outputs the domain label lf (source or target). The objective function of the domain identiﬁer is as follows:

LDI = E[lf log P(lf)] + E(1 lf)[log P(1 lf)], (4)

Then the disentangler is trained to fool the domain identiﬁer DI to extract domain-invariant features.

Mutual Information Minimization To better disentangle the features, we minimize the mutual information between domain-invariant and domain-speciﬁc features (fdi, fds), as well as domain-invariant and class-irrelevant features (fdi, fci):

I(Dx; Dfdi) =

X Z log d PXZ d PX PZ d PXZ, (5)

where x {fds, fci}, PXZ is the joint probability distribution of (Dx, Dfdi), and PX =

Z d PXZ and PZ =

X d PXZ are the marginals. Despite being a pivotal measure across different domains, the mutual information is only tractable for discrete variables, or for a limited family of problems where the probability distributions are unknown (Belghazi et al., 2018). The computation incurs a complexity of O(n2), which is undesirable for deep CNNs. Is this paper, we adopt the Mutual Information Neural Estimator (MINE) (Belghazi et al., 2018)

I(X; Z)n = sup θ Θ EP(n) XZ[Tθ] log(EP(n) X P(n) Z [e Tθ]). (6)

which provides unbiased estimation of mutual information on n i.i.d samples by leveraging a neural network Tθ.

Practically, MINE (6) can be computed as I(X; Z) = Pn XZ(x, z)T(x, z, θ) - log( Pn X(x)Pn Z(z)e T (x,z,θ)). Additionally, to avoid computing the integrals, we leverage Monte-Carlo integration:

I(X, Z) = 1

i=1 T(x, z, θ) log( 1

i=1 e T (x,z ,θ)) (7)

Algorithm 1 Learning algorithm for DADA

Input: source labeled datasets {(xs i, ys i )}ns i=1; heterogeneous target dataset {xt j}nt j=1; feature extractor G; disentangler D; category identiﬁer C, domain identiﬁer DI, mutual information estimator M, and reconstructor R. Output: well-trained feature extractor ˆG, well-trained disentangler ˆD, and class identiﬁer ˆC. 1: while not converged do 2: Sample mini-batch from {(xs i, ys i )}ns i=1 and {xt j}nt j=1; 3: Class Disentanglement: 4: for 1:iter do 5: Update G, D, C by Eq.2; 6: Update D by Eq.3; 7: end for 8: Domain Disentanglement: 9: Update D and DI by Eq.4; 10: Mutual Information Minimization: 11: Calculate mutual information between the disentangled feature pair (fdi, fds), as well as (fdi,fci) with M; 12: Update D, M by Eq.7; 13: Reconstruction: 14: Reconstruct f G by (fdi,fci) and (fdi, fds) with R; 15: Update D, R by Eq.1 16: end while 17: return ˆG = G; ˆC = C; ˆD = D.

where (x, z) are sampled from the joint distribution and z

is sampled from the marginal distribution. We implement a neural network to perform the Monte-Carlo integration deﬁned in Equation 7.

Ring-style Normalization Conventional batch normalization (Ioffe & Szegedy, 2015) diminishes internal covariate shift by subtracting the batch mean and dividing by the batch standard deviation. Despite promising results on domain adaptation, batch normalization alone is not enough to guarantee that the embedded features are well normalized in the scenario of heterogeneous domains. The target data are sampled from multiple domains and their embedded features are scattered irregularly in the latent space. Zheng et al. (2018) proposes a ring-style norm constraint to maintain a balance between the angular classiﬁcation margins of multiple classes. Its objective is as follows:

i=1 (||T(xi)||2 R)2 (8)

where R is the learned norm value. However, ring loss is not robust and may cause mode collapse if the learned R is small. Instead, we incorporate the ring loss into a Geman-Mc Clure model and minimize the following loss function:

LGM ring = n i=1(||T(xi)||2 R)2

2nβ + n i=1(||T(xi)||2 R)2 (9)

where β is the scale factor of the Geman-Mc Clure model.

Domain Agnostic Learning with Disentangled Representations

skt rel qdr pnt inf clp

airplane clock axe ball bicycle bird strawberry flower pizza

up sy sv mm mt

computer monitor headphones projector bike mouse (a) Digit-Five (b) Office-Caltech10 (c) Domain Net

Figure 2. We demonstrate the effectiveness of DADA on three dataset: Digit-Five, Ofﬁce-Caltech10 (Gong et al., 2012) and Domain Net (Peng et al., 2018) dataset. The Digit-Five dataset includes: MNIST (mt), MNIST-M (mm), SVHN (sv), Synthetic (syn), and USPS (up). The Ofﬁce-Caltech10 dataset contains: Amazon (A), Caltech (C), DSLR (D), and Webcam (W). The Domain Net dataset includes: clipart (clp), infograph (inf), painting (pnt), quickdraw (qdr), real (rel), and sktech (skt).

Optimization Our model is trained in an end-to-end fashion. We train the class and domain disentanglement component, MINE and the reconstruction component iteratively with Stochasitc Gradient Descent (Kiefer et al., 1952) or Adam (Kingma & Ba, 2014) optimizer. We employ the popular neural networks (e.g. Le Net, Alex Net, or Res Net) as our feature generator G. The detailed training procedure is presented in Algorithm 1.

4. Experiments

We compare the DADA model to state-of-the-art domain adaptation algorithms on the following tasks: digit classiﬁcation (MNIST, SVHN, USPS, MNIST-M, Synthetic Digits) and image recognition (Ofﬁce-Caltech10 (Gong et al., 2012), Domain Net (Peng et al., 2018)). Sample images of these datasets can be seen in Figure 2. Table 6 (suppementary material) shows the detailed number of images we use in our experiments. In the main paper, we only report major results; more implementation details are provided in the supplementary material. All of our experiments are implemented in the Py Torch1 platform.

4.1. Experiments on Digit Recognition

Digit-Five This dataset is a collection of ﬁve benchmarks for digit recognition, namely MNIST (Le Cun et al., 1998), Synthetic Digits (Ganin & Lempitsky, 2015), MNISTM (Ganin & Lempitsky, 2015), SVHN, and USPS. In our experiments, we take turns setting one domain as the source domain and the rest as the mixed target domain (discarding both the class and the domain labels), leading to ﬁve transfer tasks. To explore the effectiveness of each component in our model, we propose four different ablations, i.e. model I: with class disentanglement; model II: I + domain disentanglement; model III: II + ring loss; model IV: III + reconstruction loss. The detailed architecture of our model can be seen in Table 5 (supplementary material).

1http://pytorch.org

We compare our model to state-of-the-art baselines: Deep Adaptation Network (DAN) (Long et al., 2015), Domain Adversarial Neural Network (DANN) (Ganin & Lempitsky, 2015), Adversarial Discriminative Domain Adaptation (ADDA) (Tzeng et al., 2017), Maximum Classiﬁer Discrepancy (MCD) (Saito et al., 2018), and Uniﬁed Feature Disentangler Network (UFDN) (Liu et al., 2018a). Speciﬁcally, DAN applies MMD loss (Gretton et al., 2007) to align the source domain with the target domain in reproducing kernel Hilbert space. DANN and ADDA align the source domain with target domain by adversarial loss. MCD is a domain adaptation framework which incorporates two classiﬁers. UFDN employs a variational autoencoder (Kingma & Welling, 2013) to disentangle domain-invariant representations. When conducting the baseline experiments, we utilize the code provided by the authors and keep the original experimental settings.

Results and Analysis The experimental results on the Digit-Five dataset are shown in Table 1. From these, we can make the following observations. (1) Model IV achieves 62.3% average accuracy, signiﬁcantly outperforming other baselines on most of the domain-agnostic tasks. (2) The results of model I and II demonstrate the effectiveness of class disentanglement and domain disentanglement. Without minimizing the mutual information between disentangled features, UFDN performs poorly on this task. (3) In model III, the ring loss boost the performance by three percent, demonstrating that feature normalization is essential in domain-agnostic learning.

To dive deeper into the disentangled features, we plot in Figure 3(a)-3(d) the t-SNE embeddings of the feature representations learned on the sv mm,mt,up,sy task with sourceonly features, UFDN features, MCD features, and DADA features, respectively. We observe that the features derived by our model are more separated between classes than UFDN and MCD features.

Domain Agnostic Learning with Disentangled Representations

Table 1. Accuracy on Digit-Five dataset with domain agnostic learning protocol. DADA achieves 62.3% accuracy, signiﬁcantly outperforming other baselines. We incrementally add each component to our model, aiming to study their effectiveness on the ﬁnal results. (model I: with class disentanglement; model II: I + domain disentanglement; model III: II + ring loss; model IV: III + reconstruction loss. mt, up, sv, sy, mm are abbreviations for MNIST, USPS, SVHN, Synthetic Digits, MNIST-M.)

Models mt mm,sv,sy,up mm mt,sv,sy,up sv mt,mm,sy,up sy mt,mm,sv,up up mt,mm,sv,sy Avg Source Only 20.5 1.2 53.5 0.9 62.9 0.3 77.9 0.4 22.6 0.4 47.5 DAN (Long et al., 2015) 21.7 1.0 55.3 0.7 63.2 0.5 79.3 0.2 40.2 0.4 51.9 DANN (Ganin & Lempitsky, 2015) 22.8 1.1 45.2 0.6 61.8 0.2 79.3 0.3 38.7 0.6 49.6 ADDA (Tzeng et al., 2017) 23.4 1.3 54.8 0.8 63.5 0.4 79.6 0.3 43.5 0.5 52.9 UFDN (Liu et al., 2018a) 20.2 1.5 41.6 0.7 64.5 0.4 60.7 0.3 44.6 0.2 46.3 MCD (Saito et al., 2018) 28.7 1.3 43.8 0.8 75.1 0.3 78.9 0.3 55.3 0.4 56.4 DADA+class (I) 28.9 1.2 50.1 0.9 65.4 0.2 79.8 0.1 50.4 0.3 54.9 DADA+domain (II) 34.1 1.7 57.1 0.4 71.3 0.4 82.5 0.3 45.4 0.4 57.5 DADA+ring (III) 35.3 1.5 57.5 0.6 80.1 0.3 82.9 0.2 46.2 0.3 60.4 DADA+rec (IV) 39.4 1.4 61.1 0.7 80.1 0.4 83.7 0.2 47.2 0.4 62.3

(a) Source Features

(b) UFDN Features

(c) MCD Features

(d) DADA Features

Figure 3. Feature visualization: t-SNE plot of source features, UFDN (Liu et al., 2018a) features, MCD (Saito et al., 2018) features and DADA features on agnostic target domain in sv mm,mt,up,sy setting. We use different markers and different colors to denote different categories. (Best viewed in color.)

4.2. Experiments on Ofﬁce-Caltech10

Ofﬁce-Caltech10 (Gong et al., 2012) This dataset includes 10 common categories shared by Ofﬁce-31 (Saenko et al.,

2010) and Caltech-256 datasets (Grifﬁn et al., 2007). It contains four domains: Caltech (C), which are sampled from Caltech-256 dataset, Amazon (A), which contains images collected from amazon.com, Webcam (W) and DSLR (D), which are images taken by web camera and DSLR camera under ofﬁce environment. In our experiments, we take turns to set one domain as the source domain and the rest as the heterogeneous target domain, leading to four DAL tasks.

In our experiments, we leverage two popular networks, Alex Net (Krizhevsky et al., 2012) and Res Net (He et al., 2016), as the backbone of the feature generator G. Both the networks are pre-trained on Image Net (Deng et al., 2009). Other components are randomly initialized with normal distribution. In the optimization procedure, we set the learning rate of randomly initialized parameters ten times of the pretrained parameters. The architecture of other components can be seen in Table 7 (supplementary material).

In addition to the baselines mentioned in Section 4.1, we add

three baselines: Residual Transfer Network (RTN) (Long et al., 2016), Joint Adaptation Network (JAN) (Long et al., 2017) and Self Ensembling (French et al., 2018). Speciﬁcally, RTN employs residual layer (He et al., 2016) for better knowledge transfer, based on DAN (Long et al., 2015). JAN leverages a joint MMD-loss layer to align the features in two consecutive layers. SE applies self-ensembling learning based on a teacher-student model and was the winner of the Visual Domain Adaptation Challenge 2. We do not apply these methods in digit recognition because the Le Net-based model (Le Cun et al., 1989) is too simple to add a residual or joint training layer. We also omit ADDA and UFDN baselines as these models fail to converge while training on Ofﬁce-Caltech10 under the domain-agnostic setup.

Results The experimental results on Ofﬁce-Caltech10 dataset are shown in Table 2. For fair comparison, we utilize the same backbone as the baselines and separately show the results. From these results, we make the following observations. (1) Our model achieves 89.8% accuracy with an Alex Net backbone (Krizhevsky et al., 2012) and 92.9% accuracy with a Res Net backbone, outperforming the cor-

2http://ai.bu.edu/visda-2017/

Domain Agnostic Learning with Disentangled Representations

Table 2. Accuracy on Ofﬁce-Caltech10 dataset with DAL protocal. The methods in the above table are based on Alex Net backbone and the methods below are based on the Res Net backbone. For both backbones, our model outperforms other baselines.

Method A C,D,W C A,D,W D A,C,W W A,C,D Average Alex Net (Krizhevsky et al., 2012) 83.1 0.2 88.9 0.4 86.7 0.4 82.2 0.3 85.2 DAN (Long et al., 2015) 82.5 0.3 86.2 0.4 75.7 0.5 80.4 0.2 81.2 RTN (Long et al., 2016) 85.2 0.4 89.8 0.3 81.7 0.3 83.7 0.4 85.1 JAN (Long et al., 2017) 83.5 0.3 88.5 0.2 80.1 0.3 85.9 0.4 84.5 DANN (Ganin & Lempitsky, 2015) 85.9 0.4 90.5 0.3 88.6 0.4 90.4 0.2 88.9 DADA (Ours) 86.3 0.3 91.7 0.4 89.9 0.3 91.3 0.3 89.8 Res Net (He et al., 2016) 90.5 0.3 94.3 0.2 88.7 0.4 82.5 0.3 89.0 SE (French et al., 2018) 90.3 0.4 94.7 0.4 88.5 0.3 85.3 0.4 89.7 MCD (Saito et al., 2018) 91.7 0.4 95.3 0.3 89.5 0.2 84.3 0.2 90.2 DANN (Ganin & Lempitsky, 2015) 91.5 0.4 94.3 0.4 90.5 0.3 86.3 0.3 90.6 DADA (Ours) 92.0 0.4 95.1 0.3 91.3 0.4 93.1 0.3 92.9

(a) A-Distance

(b) Training loss for C A,D,W

(c) MCD confusion matrix

(d) DADA confusion matrix

Figure 4. Empirical analysis: (a)A-Distance of Res Net, MCD and DADA features on two different tasks; (b) training errors and accuracy on C A,D,W task. (c)-(d) confusion matrices of MCD, and DADA models on W A,C,D task.

responding baselines on most shifts. (2) The adversarial method (DANN) works better than the feature alignment methods (DAN, RTN, JAN). More interestingly, negative transfer (Pan & Yang, 2010) occurs for feature alignment methods. This is somewhat expected, as these models align the entangled features directly, including the class-irrelevant features. (3) From the Res Net results, we observe limited improvements for the baselines from the source-only model, especially for boosting-based SE method. This phenomenon suggests that the boosting procedure works poorly when the target domain is heterogeneously distributed.

To better analyze the error modes, we plot the confusion matrices for MCD (84.3% accuracy) and DADA (93.1% accuracy) on W A,C,D task in Figure 4(c)-4(d). The ﬁgures illustrate MCD mainly confuses calculator vs. keyboard , backpack vs. headphones , while DADA is able to distinguish them with disentangled features.

A-Distance Ben-David et al. (2010) suggests A-distance as a measure of domain discrepancy. Following Long et al. (2015), we calculate the approximate A-distance ˆd A = 2 (1 2 ) for W A,C,D and D A,C,W tasks, where is the generalization error of a two-sample classiﬁer (kernel SVM) trained on the binary problem to distinguish input samples between the source and target domains. Fig-

ure 4(a) displays ˆd A for the two tasks with raw Res Net features, MCD features, and DADA features, respectively. We observe that the ˆd A for both MCD features and DADA features are smaller than Res Net features, and the ˆd A on DADA features is smaller than ˆd A on MCD features, which is in consistent with the quantitative results, demonstrating the effectiveness of our disentangled features.

Convergence Analysis As DADA involves multiple losses and a complex learning procedure including adversarial learning and disentanglement, we analyze the convergence performance for the C A,D,W task, as showed in Figure 4(b) (lines are smoothed for easier analysis). We plot the cross-entropy loss on the source domain, ring loss deﬁned by Equation 9, mutual information deﬁned by Equation 7, and the accuracy in the ﬁgure. Figure 4(b) illustrates that the training losses gradually converge and the accuracy become steady after about 20 epochs of training.

4.3. Experiments on the Domain Net dataset

Domain Net3 (Peng et al., 2018) This dataset contains approximately 0.6 million images distributed among 345 categories. It contains six distinct domains: Clipart (clp), a

3http://ai.bu.edu/M3SDA/

Domain Agnostic Learning with Disentangled Representations

Table 3. Accuracy on the Domain Net dataset (Peng et al., 2018) dataset with DAL protocol. The upper table shows the results based on Alex Net (Krizhevsky et al., 2012) backbone and the below are the results of Res Net (He et al., 2016) backbone. For both setting, our model outperforms other baselines.

Models clp inf,pnt qdr,rel,skt inf clp,pnt, qdr,rel,skt pnt clp,inf, qdr,rel,skt qdr clp,inf, pnt,rel,skt rel clp,inf, pnt,qdr,skt skt clp,inf, pnt,qdr,rel Avg

Alex Net (Krizhevsky et al., 2012) 22.5 0.4 15.3 0.2 21.2 0.3 6.0 0.2 17.2 0.3 21.8 0.3 17.3 DAN (Long et al., 2015) 23.7 0.3 14.9 0.4 22.7 0.2 7.6 0.3 19.4 0.4 23.4 0.5 18.6 RTN (Long et al., 2016) 21.4 0.3 14.2 0.3 21.0 0.4 7.7 0.2 17.8 0.3 20.8 0.4 17.2 JAN (Long et al., 2017) 21.1 0.4 16.5 0.2 21.6 0.3 9.9 0.1 15.4 0.2 22.5 0.3 17.8 DANN (Ganin & Lempitsky, 2015) 24.1 0.2 15.2 0.4 24.5 0.3 8.2 0.4 18.0 0.3 24.1 0.4 19.1 DADA (Ours) 23.9 0.4 17.9 0.4 25.4 0.5 9.4 0.2 20.5 0.3 25.2 0.4 20.4 Res Net101 (He et al., 2016) 25.6 0.2 16.8 0.3 25.8 0.4 9.2 0.2 20.6 0.5 22.3 0.1 20.1 SE (French et al., 2018) 21.3 0.2 8.5 0.1 14.5 0.2 13.8 0.4 16.0 0.4 19.7 0.2 15.6 MCD (Saito et al., 2018) 25.1 0.3 19.1 0.4 27.0 0.3 10.4 0.3 20.2 0.2 22.5 0.4 20.7 DADA (Ours) 26.1 0.4 20.0 0.3 26.5 0.4 12.9 0.4 20.7 0.4 22.8 0.2 21.5

Table 4. One-to-one (o-o) vs. one-to-many alignment (o-m). We only show the source domain in the table, the remaining ﬁve domains set as the target domain.

Source clp inf pnt qdr rel skt Avg DAN (o-o) 25.2 14.9 24.1 7.8 20.4 25.2 19.6 DAN (o-m) 23.7 14.9 22.7 7.6 19.4 23.4 18.6 JAN (o-o) 24.2 18.1 23.2 7.8 15.8 23.8 18.8 JAN (o-m) 21.1 16.5 21.6 9.9 15.4 22.5 17.8

collection of clipart images; Infograph (inf), infographic images with speciﬁc object; Painting (pnt), artistic depictions of object in the form of paintings; Quickdraw (qdr), drawings from the worldwide players of game Quick Draw! 4; Real (rel, photos and real world images; and Sketch (skt), sketches of speciﬁc objects. It is very large-scale and includes rich informative vision cues across different domains, providing a good testbed for DAL. Sample images can be seen from Figure 2. Following Section 4.2, we take turns to set one domain as the source domain and the rest as the heterogeneous target domain, leading to six DAL tasks.

Results The experimental results on Domain Net (Peng et al., 2018) are shown in Table 3. The results shows our model achieves 21.5% accuracy with a Res Net backbone. Note that this dataset contains about 0.6 million images, and so a one percent accuracy improvement is not a trivial achievement. Our model gets comparable results with the bestperforming baseline when the source domain is pnt, or qdr and outperforms other baselines for the rest of the tasks. From the experimental results, we make two interesting observations. (1) In DAL, the SE model (French et al., 2018) performs poorly when the number of categories is large, which is in consistent with results in (Peng et al., 2018). (2) The adversarial alignment method (DANN) performs better than feature alignment methods in DAL, a similar trend to that in Section 4.2.

4https://quickdraw.withgoogle.com/data

One-to-one vs. one-to-many alignment In the DAL task, the UDA models are performing one-to-many alignment as the target data have no domain labels. However, traditional feature alignment methods such as DAN and JAN are designed for one-to-one alignment. To investigate the effectiveness of domain labels, we design a controlled experiment for DAN and JAN. First, we provide the domain labels and perform one-to-one unsupervised domain adaptation. Then we take away the domain labels and perform one-tomany domain-agnostic learning. The results are shown in Table 4. We observe the one-to-one alignment does indeed outperform one-to-many alignment, even though the models in one-to-many alignment have seen more data. These results further demonstrate that DAL is a more challenging task and that traditional feature alignment methods need to be re-thought for this problem.

5. Conclusion

In this paper, we ﬁrst propose a novel domain agnostic learning (DAL) schema and demonstrate the importance of DAL in practical scenarios. Towards tackling DAL task, we have proposed a novel Deep Adversarial Disentangled Autoencoders (DADA) to disentangle domain-invariant features in the latent space. We have proposed to leveraging class disentanglement and mutual information minimizer to enhance the feature disentanglement. Empirically, we demonstrate that the ring-loss-style normalization boosts the performance of DADA in DAL task. An extensive empirical evaluation on DAL benchmarks demonstrate the efﬁcacy of the proposed model against several state-of-the-art domain adaptation algorithms.

6. Acknowledgement

This work was partially supported by NSF and Honda Research Institute.

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