Unsupervised domain adaptation with imputation
Authors: Matthieu Kirchmeyer
Patrick Gallinari
Alain Rakotomamonjy
Amin Mantrach
Venue:  (2020)
Keywords: domain adaptation
imputation
missing data
advertising

Abstract: Motivated by practical applications, we consider unsupervised domain adaptation for classification problems, in the presence of missing data in the target domain. More precisely, we focus on the case where there is a domain shift between source and target domains, while some components of the target data are systematically absent. We propose a way to impute non-stochastic missing data for a classification task by leveraging supervision from a complete source domain through domain adaptation. We introduce a single model performing joint domain adaptation, imputation and classification which is shown to perform well under various representative divergence families (H-divergence, Optimal Transport). We perform experiments on two families of datasets: a classical digit classification benchmark commonly used in domain adaptation papers and real world digital advertising datasets, on which we evaluate our model’s classification performance in an unsupervised setting. We analyze its behavior showing the benefit of explicitly imputing non-stochastic missing data jointly with domain adaptation.

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UNSUPERVISED DOMAIN ADAPTATION WITH IMPUTATION
Anonymous authors Paper under double-blind review
ABSTRACT
Motivated by practical applications, we consider unsupervised domain adaptation for classification problems, the presence of missing data in the target domain. More precisely, we focus on the case where there is a domain shift between source and target domains, while some components in the target data are systematically absent. We propose a way to impute non-stochastic missing data for classi- fication task by leveraging supervision from a complete source domain through domain adaptation. We introduce single model performing joint domain adap- tation, imputation and classification which is shown to perform well under var- ious representative divergence families (H--divergence, Optimal Transport). We perform experiments on two families of datasets: a classical digit classification benchmark commonly used in domain adaptation papers and real world digital ad advertising datasets, on which we evaluate our model's classification performance in an unsupervised setting. We analyze its behavior showing the benefit of explic- itly imputing non-stochastic missing data jointly with domain adaptation.
INTRODUCTION
When dealing with machine learning applications in the real world, data usually come with several imperfections that make classical algorithms hardly deployable. One of these issues is that data are often incomplete. Typically, while capturing data coming from different locations with several sen- sors per location, a sensor may randomly fail or even may be just missing given location. Such a situation can also occur in disease diagnosis in multi-modal medical imaging where one of the modalities fails is not available; for example the positron emission tomography (PET) modality which reveals metabolic information for clinical tests requires ingesting radioactive tracer which poses health risks and is often missing @Cai et al. 2018). Similarly, in computational advertising ap- plications, information is missing for users who do not have a prior history on merchant's 's website while their global clicking behavior across websites may be known. Another common issue is that data used for training and deployment may differ in their generation process: data may be collected on different devices, background noise or compression schemes may affect differently training or deployment data, leading shift in data distribution. This has given rise to the important literature of Domain Adaptation (Pan & Yangl 2010) Kouw & Loog (201)). These two issues are usually inde- pendently addressed by developing models handling only the missing data or the domain adaptation problem.
In this paper, motivated by practical advertising applications, we consider unsupervised domain adaptation (i.e. labels are not available in the target domain) for classification when (1) part of input data missing in the target domain thus requiring some form of imputation, (2) there is no possible supervision in the target domain for imputation thus requiring indirect supervision from the source domain, and (3) there exists a domain shift berween the source and target distributions requiring domain adaptation. More precisely we consider this iilpptttioniimptaaiii stochastic missing data, i.c. when the same features are missing for all target samples. This contrasts with many imputation problems which take benefit of stochasticity in missing features.
setting for non-
We propose a model that handles unsupervised domain shift and missing data assuming non- stochastic missing data in the target domain. The model learns perform imputation for the target domain while aligning the distributions of the source and target domains in a latent space, thus going beyond the simple juxtaposition of a data imputation module followed by domain-invarian feature

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representation learning module. Imputation makes use of an indirect supervision from the complete source domain. This key property allows us to handle non-stochastic missing data, while satisfying the constraints related to adaptation and to the classification objective. The imputation process plays several roles in our glohal architecture as it provides us with information about the missing data for the target domain while contributing the domain-invariant loss and the reconstruction loss. Ex- tensive empirical evidence on handwritten digits and Click-Througee Through- Rate prediction (CTR) domain adaptation problems illustrate the benefit of the proposed model.
The original contributions are the following:
We introduce a new problem: joint unsupervised domain adaptation and imputation for classifi- cation motivated by practical applications:
We propose new model for handling the problem end-to-end. It learns to generate relevant missing information while aligning source and target distributions a latent space and to classify source instances;
We evaluate the model not only on academic benchmarks but also on challenging real world advertising data.
2
RELATED WORK
We review below typical related work for domain adaptation and data imputation.
2.1
UNSUPERVISED DOMAIN ADAPTATION (UDA)
A number of shallow learning methods approach Domain Adaptation by weighting individual obser- vations during training. These methods focus either on data importance-weijeee
(Cortes & Mohrij
2014 Zadrozny 2014)
class importance-weighhiin (Z. Lipton & Smola 2018). Recent deep learning methods try to align the distributions of the two domains, for example by embedding them in a joint latent space. There are two main directions for learning joint embeddings. One is based on adversarial training, making use of GAN extensions. The other one directly exploits explicit distance measures between distributions such as Wasserstein or Maximum Mean Discrepancy (MMD). For the former, the seminal work of Ganin & Lempitsky (2015) learns to map source and target domains onto a common embedding space, by optimizing double objective: on the one hand they minimize an approximation of the H-divergence between the source and target embeddings via adversarial training, on the other hand they learn to classify the source data embeddings. This influential work has been followed by several extensions and variants. ADDA (Tzeng et al.) (017)) advocates the use of two different mappings for the source and the target domains based on the argument that this is more suitable when the marginals are different in the two domains. Liu & Tuzel (2016) trains coupled generative adversarial network (CoGAN) for learning a joint distribution of multi-domain images, that can be used for UDA. Bousmalis al. (2017) use a generator map the source the target domain while training the classifier on the learned representations using source labels. CDAN (Long al. 2017) improves the domain discriminator by conditioning it classifier predictions.
A second family of approaches proposes metric based divergences such as MMD (Long et al. 2015) for measuring the loss between source and target representations. DeepJDOT (Damodaran Kel- lenberger 2018) makes use of an optimal transport formulation to align the joint distributions in latent space. In addition to feature alignment they perform label distribution alignment following Courty et al. (2017). All these works rely on the assumption of covariate shift and consider that full input data is available for both source and target domains. Our two models (ADV and OT) can be seen respectively as extensions of Ganin & Lempitsky (2015) and Damodaran & Kellenberger (2018) for the missing data problem.
2.2 IMPUTATION
Data imputation is classical problem addressed by several methods (Little & Rubin 2002 Van Bu- uren 2018 Murray 2018). The usual setting is different from since considers reconstructing the whole missing data in the input space, while we consider 1) reconstruction a latent space and 2) partial reconstruction since are interested in the information relevant to the classification task
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only. Recent generative models like GANs (Goodfellow et al. 2014) VAEs (Kingma & Welling
2013 Rezende et al., 2214) have been adapted for data imputation in Yoon et al. (2018) and Mattei &
Frellsen (2119) respectively. GAIN (Yoon et al., 2018) is an extension of conditional GANs where
the generator takes as input an incomplete data and performs imputation while the discriminator is
trained to guess for each sample if each variable is original imputed. [Mattei & Frellsen (2019) suggests a method based on deep latent variable models and importance sampling that offers tighter likelihood bound compared to the standard VAE bound. Most approaches consider a supervised setting where 1) paired complete and incomplete data are available and 2) missingness corresponds to a stochastic process (e.g. a mask distribution for tabular data). 3) imputation is performed in the original feature space. Note that this is different from our setting where there is no direct su- pervision (supervision only provided indirectly through the source domain) and missingness non-stochastic which makes the problem harder since one cannot compute statistics on different incomplete samples. The general approach with generative models is to learn a distribution over imputed data which is similar to the one of plain data. This comes in many different instances and usually, generative training alone is not sufficient; additional loss terms are often used. In paired problems, i.e. when each missing datum is associated to plain version of the datum, these addi- tional terms consist of a reconstruction term imposed by a MSE contraint (Isola et al. (0016b). In unpaired problems a cycle-consistency loss is imposed in Zhu et al. (2017). Li et al. (2019); Pajot et al. (2119) are among the very few approaches addressing unsupervised imputation in which full instances are never directly used. Both extend the AmbientGAN (Bora et al. 2018 framework and consider stochastic missingness.
Our imputation problem is closer the ones addressed in some forms of inpainting or for multi- modality missing data. The former problem is addressed e.g. in Pathak et al. (2016) who proposes an mncodrrddecode model trained according to joint reconstruction and adversarial loss. The latter is addressed in Cai et al. (2018) who considers the case of multi-modality when one more modalities are systematically absent, but they do not consider adaptation. They propose to learn to reconstruct the missing modality distribution conditionally to the observed one. Both approaches are fully supervised. Ding et al. (2014) is the only paper we are aware of that considers imputation as we do. Their approach is based on low rank constraints and dictionary learning to guide the transfer between domains. We do not use this method as a baseline due to the complexity and running time of this method which relies on singular value decompositions and dictionnary learning.
PROBLEM DEFINITION
Let us denote respectively (æs, E R" x I and (IT, yr) E R x R. data from the source and target domains where x_ is an input, y- the associated label and n is the dimension of the input space. "_" holds for either source S or target T. The joint distribution on each domain is denoted respectively ps( X, Y) and pr (X Y). We consider that x= has two components, x_ (x-.. z-,). The problem we address Unsupervised Domain Adaptation (UDA) with missing features in the target domain. More precisely, we make the following hypotheses. Missingness: We assume that features are the same across domains and that source features 2ş = (xs,, xs,) are always available while in the target domain only FT; is available and 3r, systematically missing. For advertising applications for example, x would characterize the user browsing behaviour on merchant sites; x characterizes global user features aggregated over his navigation history, which are known for all users; _-, characterizes user history on a target merchant site. Source domain would consist of all users who already visited this merchant site and target domain of users who never visited this site. UDA: we assume that source labels ys are available whereas target labels yr are unknown. Covariate shift: we assume covariate shift as in most UDA papers e.g. Ganin & Lempitsky (2015).
ADAPTATION- MODEL
As in many generative approaches to UDA, the objective is to project source and target data onto a common latent space in which data distributions from the two domains match, and to learn clas- sifier on the source data that performs well on the target domain. The novelty of our approach is to offer solution to deal with datasets in which some information, FT,, is systematically missing in the target domain. Our model, denoted Adaptation it Imputat at ion, performs three opera- tions jointly: imputation of missing information for the target data, alignment of the distributions
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of source and target, and classification of source instances. The three operations performed in joint embedding space and all the model's components are trained together. The term imputation is used here in broad sense: our goal is not to recover the whole missing ZT2,, but to recover informa- tion from Iiy that will be useful for adaptation and for the target data classification objective. This is achieved via generative model, which for given datum in the target domain and conditionally on the available information 2T,, attempts to generate the required missing information. Because JT, is systematically missing for target data, there is no possible supervision in the target domain; instead we use distant supervision from the source data while transferring to the target domain. We consider two variants of the same model based on different divergence measures between source and target distributions: the Wasserstein distance and the H-divergence approximated through adversar- ial training. For simplicity we describe in the main text the adversarial version ADV and defer the Optimal Transport OT description to Appendix B We report the results obtained with both models in Section 5
4.1 TRAINING
Our model is composed of three different modules responsible for adaptation, imputation and clas- sification, that share parameters and are trained in parallel. For simplicity, we describe each compo- nent in turn, but it should be reminded that they all interact and that their parameters are all optimized according to the three objectives mentioned above. The interaction is discussed after the individual module descriptions. The model's components are illustrated in Figure (a).
Adaptation The latent space representations of source and target domains are denoted with a tilde notation: ãg = (Ts.. Ts.)) and äт = (ăT, TT,)). Referring to Figure | (a), _ه, = 91 (I-,). )) (Ø... denotes either Fs, or TT, ) is the mapping of the observed component æ=, onto the latent space and デ_ = h o g1 (z-,) is the second component's 's latent representation generated from x--- This generation mechanism will be described later. Adaptation aligns the distributions (Øs, Tsa) and (Tr) in the latent space. For the ADV model, alignment is performed via classical adversarial loss operating on the latent representations:
L (x) log Dj (3s) (x) log(1 D1 (TTr)
where (T) represents the probability that comes from the source rather than the target.
Imputation Imputation amounts at generating an encoding TT,, in the latent space, for the missing information in the target data, conditioned on the available information IT, Our objective here is to generate missing information which is relevant for the classification objective. Since we never have access to any target component .T. we learn to perform imputation based on the source data. More precisely, we learn to generate Ts from X through the generator h, T. = hog (I ). as depicted in Figure [ We want f to generate the missing information ãs, associated to the observed zss For that we perform two operations in parallel. First, we align the distribution of Ts, with the distribution of &s. = 92 (I.S). ), that is direct mapping of æs, onto the shared latent space, using an adversarial loss described below. The intuition is that both Φ1 and l2 are simple mappings operating respectively on æts and uss while h acts as a generator conditioned on rs for generating T5.- Moreover, we not only impose this distribution alignment, but would also like Ts, to represent missing information relative to æs, and associated the above alignment, in our case a MSE distance between ãs, and Gs., This MSE term guarantees that the imputed ãsz truly represents information present SSS.. Similar ideas combine distribution matching and MSE conditioning and have been used e.g. in [sola et al. (2016a) : Pathak et al. (2016). The learned mappings are used to perform imputation on the target data IT; h 91 (PT,).
specific 25, For that, we use reconstruction term in parallel to
The imputation loss has thus two components. The first is the adversarial term LADV responsible for aligning T.s and S. LADY = -Ezrpp(Xx)) log D2 (Ts,) + (x)n log(1 D2( )). The second is the reconstruction term LMSE = (Empp(X) 1 Ts, 1l. The total imputation loss is then:
Lg = AADV x LADY + AMSE X LMSE
(2)
where AADV, AMSE are hyperparameters. The two processes of imputation and adaptation influ- ence each other. Both are also influenced by the classification process described below. Its effect
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imputation is to foree the generated Σs, to contain information about 25, relevant for the clas- sification task. This information is transferred via adaptation to the target domain when generating .TZ
Classification The last component of the model is a classifier f. trained on the source domain mapping Vy for the classification task as classically done for UDA. The corresponding loss is:
La P
where Lpise is typically cross-entropy loss.
Overall loss The overall loss function will be the weighted sum of the adaptation, imputation and classification losses:
L A x L1 + X x L2 + A x La
(4)
where \1, A2, A3 are hyperparameters and the final optimization problem is:
max L B. D1.
min
(5)
Interaction between the model's components Both mappings 91, 92 and generator h appear in the three terms the loss function in Equation 4 meaning that they should learn to perform three tasks simultaneously. !1 learns to map the ds; and Im components onto the latent space, the mappings being denoted respectively īs, and TT,- h learns to generate missing information Tr, from Tr. The formed __ is generated such that fulfills the classification objective. 92 its side should fulfill the imputation objective while preserving part of the information present in ISS- Note that model makes of unique mapping 9I for both source and target domains. Separate mappings could have been used for the two domains, but the proposed solution was found to be more robust and reduce the number of parameters during learning.
MAE
Dr
Clastfication
XY.
81
Classificaion
Xy.
Figure 1: Adaptation model: (a) training, (b) inference.
Implementation Let detail the implementation of this model. For adversarial training, discriminators D, (adaptation) and D2 (imputation) will be implemented by binary classifiers. D trained distinguish between source Ty and target Ter mappings while D, is trained to separate

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imputed T Fg generated from z from Ts, a direct embedding of ø92. We the gradient reversal trick in Ganin & Lempitsky (2013) for implementing the min-max condition and define two gradient adaptive update of the scale of the gradients in D1 and D2 and optimize 11, I/2 and La jointly as synthesized in A Algorithm| i the Appendix. In practise fix all hyperparameters but ÄMSE to 1, additional tuning could yield improved performance.
reversal networks D and D2. We
4.2 INFERENCE
At inference, given TT, we generate ãт = - ZT,) with ãτ, - (2TT, an embedding of ær,, and generated Tyy, encoding part of the missing information 2T; in æT, as illustrated in Figure] (b). We use for the latter the following mapping: žT₃- = h 9i (œT,) where is as above and is the generative mapping conditioned on ëT, Finally 2T used input the classifier f.
EXPERIMENTS
5.1 DATASETS AND EXPERIMENTAL SETTING
Datasets Experiments are performed on two types of datasets. The first one is a classical digits classification benchmark used in many domain adaptation studies which we will refer to tigits and transformed to fit our missing data setting. The second one corresponds to advertising datasets. (CTR) or Conversion
wants predict Elick-Through-- Rate (CR) given user behavior. This is one the problem that has initially motivated our adaptation- imputation framework. We
The task here is binary classification:
such datasets: ads -aagglaglll l is public kaggle datase while ads real has been gathered internally and corresponds to real advertising traffic. Further details
on datasets and preprocessing are presented in Sections 5.2 5.3 and in Appendix C
Baselines
We report results for the following models:
Full models: Source-Full is trained without adaptation on the full æs and tested full ær when the latter is available (digits). Adaptation Full adds adaptation to this model.
do the same but consid- ering full Vy while or is incomplete: Ir = (MT, 0), i.e. 2r, is set to 0.
Missing models: Source-Missing and edaptation-Missiin
Partial models: Source Source-Partial and Adaptati Paraatiaal is variant of the above setting where only the first component r-, for source and target are considered for adaptation and classification while the second ones r-, are simply ignored.
Imputation models: Adaptat inn InennnImmpttiiiio ion corresponds to our model.
Naive model: Na ive used for ads ads- maas-kaagle to provide reference loss value for this dataset. It predicts for all examples the mean CTR value computed using source training data only.
Claptation-Fuu is an upper bound of the performance of Adaptation-Imputaae since it uses full information while 27, is not available in practice. Adaptat Lon-Miss Miviissinn and Adaptation-tto Pn-oartiiiiaaa can be considered as lower bounds for our model since they only perform adaptation and no imputation.
Parameters and architecture of the neural networks used for the different models and experiments are presented in Appendix [ Hyperparameters are chosen using the Deep Embedded Validation estimator introduced in You et al. (2019) combined with heuristics and typical UDA values. Further
details are given in Appendix D.2.1
We present the results for digits and ads respectively Sections 5.2 ablation studies. Reported results mean value and standard deviation five different initial- izations; best results are indicated in bold.
5.3
Section 5.4 presents
5.2 DIGITS
Description For digits, consider the unsupervised adaptation between two datasets among MNIST (LeCun et al. (1998). USPS (Hull (1994)), SVHN (Netzer et al. (201T)) and MNIST-M
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(Ganin & Lempitsky (2013)). The direction MNIST SVHN is not considered as the task is difficult even for traditional UDA (Ganin & Lempitsky 2013). All tasks are 10-class classification problems. From the complete image datasets, we build datasets with missing input values.
Half digit missing In first series of experiments, horizontal bottom part. We report classification accuracy in Table for the different adaptation problems and models (ADV and OT). Removing half of the image leads to strong performance decrease for Source-Partinn Partial and Source -ic ssing with respect to the upper bounds pro- vided by Source-Fus 45 points. This is partially recovered when training with adaptation (Adaptation Pan--aa Partin ial, Adaptation -olcnn-Misinng for both ADV OT). But the gap is still important with respect to the upper bound, i.e. creases the performance: between 10 and 25 points of accuracy over Adaptation ss ing and 2 to 20 points over Adaptationn - Partial. This is very significant improvement which vali- dates the importance of the imputation component.
removed one half of each image, the
respectively between 10 and 20 points of accuracy, and between 15 and
In all cases, Adaptat delapatiio-Imnaeae oo- In-Imuttaiionn clearly in-
fection5.4)ww show that the simultaneous use of imputation and adaptation is required for reaching this level of performance. Imputation or adap- tation alone are well behind the jointly trained instance of the model. However, does not reach the upper bound performance of curacy points. Moreorever, Adaptat. in- -n-iooon----mmmm Imputat on beats the non-adapted Source-Fi Fulllllll baseline several datasets. Both the ADV and OT versions exhibit the same general behavior. In the reported results in [ ADV performance is higher than OT. This is because performance is models may reach
where the difference lies between 10 and 25
highly dependent on the NN architectures and we tuned our NNs for ADV. performance similar to ADV but we find that it requires models with an order of magnitude more parameters. To keep the comparison fair, we thus used the same NN models for both ADV and OT. Imputation models achieve their highest performance when the adaptation task between domains is complex (MNIST -> MNIST-M, SVHN - MNIST) illustrating the importance of imputation when transfer is difficult. In all experiments, the performance of --Partt rtiial model where "_" refers to Source or Adaptation ion, are usually higher than the --Missing model. Our understand- ing is that setting missing components to zero tends to increase distance between source and target distributions, compared to just ignoring them, making the classification and adaptation problems harder.
Table 1: Classification accuracy performance in % on digits for the two training criteria on the target domain test set. Standard deviation is in %.
MNIST
USPS
USPS
MNIST
SVHN > MNIST
MNIST
MNIST-M
Method
ADV
OT
ADV
OT
ADV
CT
ADV
OT
Source-Ful Full
71.5+2.7
74.2=2.7
58.1+1.1
18.3=14
Adaptation-Full
88.3+2.4
92.61
95.0=004
93.9=0.6
77.613.5
16.1
77.2+4.9
46.9=33
Mource-Missing
25.723.7
39.2=2.6
31.522.
14.4=1. 1.1
Adaplation-Min Missinn
48.414.8
60.916.3
67.5
65.315.2
47.115.7
37.516.2
34.7+2.5
20.2
Source-Partie
52.919.7
54.311.6
44.611.9
19.1
Adaptation-Pait Partial
71.5+3.2
64.0#5.0
80.0=1.4
72.0=1.8
45,5+119
47.9+1.8
29.4=1.6
26.8
Adaptation-mmuttaii Imputation
75.211.5
66.8113
81.5 0.8
7..5=2.7
54.121.4
49,211.5
58.5
29.2=1.4
Missing patch size In second group of experiments on digits, we analyze the evolution of the performance of the models with respect to the size of the missing in- formation in the target domain. For that,
digits SVHN >> MNIST ADV models
ADV Adaptation Partial
Adaptation
ADV copptationIImutatae
Accuracy on Test Target
60
we vary the size of the missing patch re- moving a percentage of the image p with E (30%, 40%, 50% 60%, 70%} on SVHN
50
40
- MNIST for ADV models, keeping the same hyperparameters as the ones used for
30
p = 50%. We report the mean val- ues over five runs in Figure 2 We notice innttatiioniiaa that Adaptation-IIputatt ion constantly
20
10
0.30
0.35
0.40
0.45
0.50
055
0.60
0.65
070
beats the other baselines regardless of the miss- ing patch size. The figure exhibits borderline cases when the size of the missing patch be-
Missing patch size
Figure 2: Missing patch size study

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comes very small (< 30%) very large (> 65%). When the missing patch is too small most of the information for predicting the target label is already available thus simple models perform already well; while when it becomes too big, too few information is available guarantee efficient reconstructions from the non-missing patch.
5.3 ADS
Description We performed second series of tests on two advertising datasets: ads kaggle and ads-real. The ads datasets correspond to binary classification problems: the task is to predict the probability that a user exposed to an ad from target partner (e.g. Booking) on a publisher (e.g. NY Times) will click (ads Bads-kaggle, or make purchase (ads-real) conditioned on the user history. A row in the dataset corresponds a display i.e. an ad opportunity of a click or purchase for given (user, partner) pair at given time on a given publisher site. The source domain is composed of users who already had interactions with target partner. The target domain composed of users with no history target partner. We consider all partners in a given traffic. For the two domains, r-, features correspond to aggregated user features on all the partners, while x-, corresponds to user target partner specific interaction which is known for the source domain but unknown for the target domain. Note that besides missingness, there is also an adaptation problem since statistics for new
(e.g. in terms of frequency of partner's website visits) as seen in Appendix [ In real datasets, traffic in the source domain is usually abundant while scarce in the target domain. Statistics for each dataset are provided in Table S in the Appendix; exact preprocessing used is provided in Appendix C
are usually different from those of known
Results For this group of experiments, we report the results only for ADV models since the trend has been observed to be similar on digits for both ADV and OT. For ads datasets, missing features do not exist, so we do not report the --Full models' results on these datasets. The classes being imbalanced, accuracy is not relevant here (CE) between the predicted values and the true labels on the target domain which is considered as the most reliable metric estimate revenue, Note that given the test set size of ads -kaglle an improvement of 0.001 in logloss is considered as practically significant (Wang el al. 2017). For the ads problem and for large user bases, small improvement in prediction accuracy can lead to large increase in company's ' revenue. For all experiments, we report in Table CE on target test for ads-kaggle l and ads-real.
report another performance measure, cross-entropy
is that A first observation is signif- edaptatiion-mpptatioon icantly better than the baselines both datasets (Table [] For ads-kaggle it improves by 2.3% the best adaptation model (Adaptation-ae (iterttiiooMssssng)) while for ads ads-real the improvement reaches 6.3% over the best second which happens to be Source-Partial. A second observation is that for any model, adaptation consistently improves over the same model without adaptation. The only exception the --Partial setting in ads-real. A third observation is that the missing component indeed contains relevant infor- mation: CE performance on source data (not reported Table 2 shows that Source-Mis Mirrcc--issiing which exploits the x-, component is consistently higher than Source-Partise not exploit this component, leading to relative gains of the former over the latter of 5.6% on ads ads-kaggle and 8.2% on ads-real exploit this information.
Table 2: CE ads for ADV models
Dataset
ads daaa-kaggle
ada-real
Naive
0.403
Souree-Missing
0.545=0.019
0.663+0.011
Source-Partial
0.40620.00046
0.622=00.0488
Adaptation-Miss Mistionn---iinng
0.397=0.0057
0.660:0.025
Adaptation- Partial
0.403=0.0030
0.634=0.0082
Adaptation- Imputation
Adaptation-Impputation
0.389:0.0144
0.583=0.013
which does
on is able to generate and to
5.4 ABLATION ANALYSIS
We analyze now the role and importance of the different components of model, and compare with the results from Tables and We perform experimentation on the public datasets, cii digits and Figure
and ads -kaggle and report results in Table and
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Importance of adaptation We compare the performance of the model with and without the adap-
tation term L1 in Equation 4 When removing adaptation, inference is performed as before, by feeding Σт (Øn, ITr)) to the classifer f. This means that only rely on the imputation and classification losses to learn the parameters of the model. Results appear on the top of 3 For all datasets, the adaptation component considerably increases the performance, from 10 30 points for digits and by significant 0.009 CE value on ada-aaasaae kaggle.
Imputation mechanism Imputation, cf. Equation combines adversarial training (ADV) and conditioning on the input datum via the MSE loss (MSE). The objective is to learn from 2 Ts, = (Trs) and generate missing information in S T.s h()s;) ADV aligns the distributions of J.s, and Fs while MSE can be thought performing some form of regression. For given partial information I there are possibly several potential Øs; and thus Ts,- ADV allows to focus on specific mode of Tgg. while MSE will favour mean value of the distribution. Results Table 3 second group of rows, show that for digits combining the two influences (MSE and ADV) leads to improved results compared to using separately each loss. MSE alone already provides good performance, while using only ADV is clearly below. For this classification task, identifying the most simple regression (LMSE). Note that reconstruction an ill posed problem since the task is inherently ambiguous different digits may be reconstructed from one half of an image. We performed tests with a stochastic input component in order to recover different modes, but the performance was broadly similar. Achieving diversity with Conditional GANs remains an open research topic (Yang et al. 2019).
relevant mode improves the performance
For the ads-kaggle dataset, the perfor- mance of MSE and MSE ADV are similar. This is analyzed deeper in an additional se- ries of experiments with several weighted com-
ads-kaggle ADV Adaptation-mpuuttion weighting study
La Lass
La Lav + Aunz Laus
binations of MSE, and ADV. Results are pro-
0.55
vided in Table 3 third group of rows, for both digits and ads -asgga and are plotted for ads-kaggle e in Figure 3 For digits, this confirms that the equal weights selected for our experiments are indeed generally a good choice reducing the burden of hyperparame- ter selection, while for ads-kaggle e perfor- mance could be slightly improved with other weightings. One can see on Figure Y that ADV induces a high variance in the results (left part of x-axis) while MSE stabilizes the performance (right part of x-axis). The former allows for bet- ter maximum performance but with high variance: performance ranges from 0.35 to 0.7 on the target domain. A small contribution from MSE (here AMSE = 0.005) stabilizes the results.
Test Tatget Loss
0.50
0.45
0.40
0.35
0.002
0.004
Interpo ation coeffic
Figure 3: ADV-MSE weighting ads kaggle
Table 3: Accuracy on digits and CE ads aals-kaggt kaggle for ADV Adaptat Imputation
Datasel
digits
ada-kagg-e
Adaptation direction
MNIST > USPS
USPS - MNIST
SVHN - MNIST
MNIST MNIST-M
Known - New
La
64.221.8
$1.3=2.5
44.5a14
24.1=2.6
0,410=0.0020
+ La
75.2#1.5
81.5+0.8
54.0=14
58.5#1.6
1.401=00011
LASE LADV
719:3.7
814=1.2
32.5+3.7
56.5+2.8
0.400=0.0014
28. 28.6+3.22
39.4=5.2
28.8+3.8
30.0=3.7
0.469=0.11
LADY + LUSE
75.2+1.5
81.5+0.8
54.0:144
58.5#1.6
0.401
0.1.x LADV + Larse
73.412.7
81.3:0.8
53.0:2.0
56.212.6
0.0011
LADV + 0.001 x LisEE
37.312.5
31.2+3..8
45.0422.
50.0134
0.440:00.1
LADV 0.005 LusE
47,8+3.7
49.6+5.8
46.0=2.6
50.6+2.2
0.388:4.015
LADV + 0.01 LuSE
53.642.4
57.0=3.6
43.4+1.1
51.0=2.5
0.397=0.0046
Lanv + LusS
68.2144.2
50.3:6.8
$4.0=2.1
51.5#3.6
0.402=0.0044
LADV + LuSE
75.2+1.5
81.5+0.8
54.0=14
58.5+116
0..01
6 CONCLUSION
We have proposed a new model to solve unsupervised adaptation problems in the presence of non- stochastic noise in the target domain, by using distant supervision from complete source domain

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through domain adaptation and imputing missing values on the target domain in latent space. This method uses only labelled source instances and leads to important gains on classical adaptation benchmarks over baseline models for two representative families of divergences (optimal transport, adversarial training). We have demonstrated on real world advertising datasets that these meth- ods can be used for problems with missing features in advertising. Potential follow-ups include: extending this method to semi or fully supervised setting on the target domain; considering simul- taneously domain and target shift which frequently occurs in real world problems while still being an open problem; introducing increased diversity in the generation process.
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A
PSEUDO-CODE
Input: N: number of epochs, k: batch size, try initial learning rate
Initialize parameters of 91, 92, D1, D2. f. h
while Repochs N do
Sample {as', "es" Jys)isigh from ps
Sample {- Jısjs from pr
Decay learning rate and update gradient scale at each batch
Compute L L1 + L2 + Ls performing joint adaptation, imputation, classification
Update D,, D2 by ascending L through Gradient Reversal Layer
Update f. 92, by descending L
end
Algorithm 1: Training procedure for ADV Adaptation-IImputttionn
B OT FORMULATION
We present here in more details Adaptat inpieaatiiinnmnnn IetoonImputatiiii using Optimal Transport diver- gence metric. The formulation is slightly different compared to ADV models.
B.I FORMULATION OF THE IMPUTATION OT MODEL
We replace the H-divergence approximation given by the discriminators Dj and D2 by the Wasser- stein distance between source and target instances (D1) 1 and true and imputed feature representations (D2), following the original ideas Shen et al. (2018); Damodaran Kellenberger (2018). In prac- tice, compute the Wasserstein distance using its primal form by finding joint coupling matrix y, using linear programming approach (Peyré et 2019).
Adaptation In Damodaran Kellenberger 2018): Courty al. (017)) the optimal transportation problem is formulated on the joint (X, Y)) distributions. Similarly to Shen et al. (2018), in our case, we focus on plan that acts only on the feature space without taking care the labels. This leads to the following optimization problem:
L
Σ (1 - TT., 11 || 11 71 f-m-
min
(6)
where Yi is the alignment value between source instance and target instance j.
Imputation For the imputation part, we keep the reconstruction MSE component in Equation and derive the distribution matching loss as:
Lor min Σ Ts.. Es2, 12 f.72.9
37
where Y2. is the alignment value between source instance and j. The final imputation loss is:
=== X Lor + AMSE x LMSE
(8)
Classification
The classification term in Equation 3 is unchanged.
B.2 IMPLEMENTATION
The optimization problem in Equation 5 is solved two stages following an alternate optimization strategy:
we fix all parameters but 7i and 7/2 and find the joint coupling matrices 7 and 7/2 using EMD
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we fix Y and "/2 and solve min go..h. L
In practice, we first minimize L3 for couple of epochs (taken to be 10 for digits) then minimize L1 + L2 Lg in the remaining epochs.
Learning rate and parameters are explained further in Section D
C DATASET DESCRIPTION
C.1 DIGITS
Table 4: Statistics on di git datasets
SVHN
MNTSTMM
Train
7438
60k
73257
60k
Test
1860
10k
26032 x 32
10k
28
28 28
28
Channels
3
S
8
4
5 8
4
5
8
2
0
1
0
/
10
2
Pre-processing We scale all images to be 32 x 32 and we normalize the input in [-1,1] 1]. When adaptation involves a domain with three channels (SVHN MNIST-M) and a domain with a single channel, we simply triplicate the channel of the latter domain. As in Damodaran & Kellenberger (2018) we use balanced source batches which proves to increase performance especially when the source dataset is imbalanced (e.g. SVHN and USPS datasets) while the target dataset (usually MNIST derived) balanced. Scaling the input images enables us to use the same architecture across datasets. In practise the embedding size is 2048 after preprocessing. For missing versions, we set pixel values to zero in given patch. Figure 4 shows MNIST-M digits with varying missing patch size.
Figure 4: missing-features MNIST-M
The di digita i datasets are provided with a predefined train / test split. We report accuracy results the target test set and use the source The number of instances in each dataset is reported in Table We run each model five times with a different seed for initialization (using Xavier Uniform initialization) and report mean and standard deviations in Table II
Evaluation
validation set (Section 1.2.1
Infrastructure Experiments are run using a Tesla V100-SXM2 GPU machine with 32GB RAM. Code is written in Py Torch https::/pytorch. org/ (Paszke et al. 2017).
C.2 ADS
Preprocessing Table lists various statistics on the traffic for the two ads datasets; we describe this paragraph how datasets are processed.
ads-kaggle The Criteo Kaggle dataset is reference dataset for CTR prediction and groups one week log data. The objective is to model the probability that a user will click on given ad given his navigation context: (onteet))) Positives refer displays which are clicked
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and negatives to displays not clicked. For each datum, there are 13 continuous and 26 categorical features. We divide the traffic into two domains using feature number 30; for a given value for this categorical feature, all instances have a single missing numeric feature (feature number 5). We then construct an artificial dataset simulating transfer between known and new users. We process the original Criteo Kaggle dataset have equal number of source and target data. We then perform train/ / test split on this dataset keeping 20% of data for testing. We used in our experiments the continuous features; show the benefit of modelling additional missing features, we extend the missing features list to features I, 5, 6, 7, 11 and 12 by setting them to zero on the target domain. After these operations, features are missing and 7 are non-missing. Preprocessing consists in normalizing continuous features using log transform.
ads-real The data collected in this dataset is similar ads ads-kaggle. We filter out non-clicks and the final task is to model the sale probability for a clicked ad: p(Sale)Click = 1, Conlexi). Positives refer clicked ads which lead to a sale; negatives to clicked ads which did not lead to a sale. We use one week of sampled logs as a training set, and use the following day data as the test set. This train test definition is used so as better correlate with the performance of a model used online. We use typical features in production models on this dataset and focus on a sample of continuous features aggregated across user timelines describing the clicking and purchase behavior of a user. In comparison to ads-kagg can User-centric i.e. describe the global activity of the user (number of clicks, displays, sales done globally across partners) or User-partner features i.e. describing the history of the user on the given partner (number of clicks, sales... on the partner). The latter are missing for new users. Counts aggregated across varying windows of time and categories of partner catalog. We bucketize these count features using log transforms and consider these as categorical features by one-hot encoding the different buckets based on the vocabulary file. After processing the final input size is 596 with 29 features used. 12 features are missing and 17 are non-missing.
more continuous features are used. The count features
Table 5: Statistics ads datasets
Dataset
acs kaggle
ads real
Domain
Source
Target
Source
Target
Split
Train
Test
Train
Test
Train
Test
Train
Test
Positive
246 872
61 841
92 333
22 943
X
X
X
X
Negative
699 621
174 783
854 160
213 681
X
X
X
X
Total
946 493
236 624
946 493
236 624
24 465
756
3 760 233
819 073
147 358
P(Y)
0.2608
0.2613
0.0976
0.0970
X
X
X
X
Evaluation On both datasets the train and test sets are fixed. We run each model five times with different seed for initialization (using Xavier Uniform initialization) and report mean and standard deviations in Table
Infrastructure For ads real, models are trained using internal large-scale distributed infras- tructure. For ads ads-kaggles we keep the same setting and code as in digits.
D IMPLEMENTATION DETAILS
D.1 NEURAL NET ARCHITECTURE
D. DIGITS
We experiment with the ADV and OT versions of our imputation model. For ADV models, the DANN model description in Ganin & Lempitsky (2015); for OT we use the DeepJDOT model description in Damodaran & Kellenberger (2018). Both models can be considered as simplified instances of our corresponding ADV and OT imputation models when no imputation is performed.
Performance of the adaptation models is highly dependent the NN architectures used for adap- tation and classification. In order to perform fair comparisons and since our goal to evaluate the potential of joint
we selected these architectures through pre-
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liminary tests and them for both the ADV and OT models. The two models are described below and illustrated in Figure
Feature extractors 91 and 92 consists of three convolutional layers with 5 x kernel and 64 filters interleaved with max pooling layers with stride of and 2 kernel. The final layer has 128 filters. We use batch norm on convolutional layers and ReLU as an activation after max pooling. As in Damodaran & Kellenberger (2018) we find that adding sigmoid activation layer as final activation is helpful.
Classifier f consists of two fully connected layers with 100 neurons with batch norm and ReLU activation followed by the final softmax layer. We add Dropout as an activation for the first layer of the classifier.
Discriminator Dj and D2 is a single layer NN with 100 neurons, batch norm and ReLU followed by the final softmax layer. USPS + MNIST and MNIST + USPS dataset we use stronger discriminator network which consists of two fully connected layers with 512 neurons.
Generator h consists of two fully connected layers with 512 neurons, batch norm and ReLU activation. This architecture is used for ADV and OT imputation models. In practice using wider and deeper networks increases classification performance with the more complicated classifica- tion tasks (SVHN - MNIST, MNIST - MNIST-M); in these cases we add an additional fully connected network with 512 neurons. The final activation function is sigmoid.
We the same architecture described above for full, missing and partial models guarantee fair comparison. As a side note, the input to the imputation model's classifier is twice bigger as in the standard adaptation models.
Comv 5x5 64
mat-pool 2x2 2x2 BelU
Conv SKS IN
max-pool 2x2 2x2 BeLU
Cony 5K5
BN Sigmoid
BN RsLl Dropout
fc 100 BN
fc 10 Softmax
BN
fc 100 ReLU
fc Softmax
GRL
Figure 5: Base architecture for the ADV DANN model
D.1.2 ADS
We experiment with ADV models only. As input data is numeric and low dimensional, architectures are simpler than in di digits.
ads-kaggle Our feature extractor is three layered NN with 128 neurons and with final sigmoid activation. The classifier is taken be single layered NN with 128 neurons and a final softmax layer. Activations are taken to be ReLUs. The domain discriminator taken to a two layered NN with 128 neurons and final softmax layer. Finally the reconstructor is taken to be two-layered NN with 256 neurons and final sigmoid activation.
ads-real Input features after processing are fed directly into the feature extractors 91, 92 con- sisting of two fully connected layers with 128 neurons. The classifier and discriminator is taken to be single-layered NN with 25 neurons. The reconstructor is taken to be two-layered NN with 128 neurons. Inner activations are taken to be ReLUS and the final activation of the feature extractor is taken to be a sigmoid.
D.2 NETWORK PARAMETERS
D.2.1
HYPERPARAMETER TUNING
Tuning byperparameters for UDA is tricky as we do not have access to the label in the target distribu- tion and thus cannot choose parameters minimizing the target risk validation set. Several papers
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set inperpaarametes through reverse cross- venssdaniiitionn (Ganin & Lempitsky 2015). Other approaches developed for model selection are based on risk surrogates obtained by estimating an approximation of the risk value the source based on the similarity of source and target distributions (without the labels). In the experiments, we used a recent estimator, Deep Embedded Validation (DEV) (You et al., (219) for tuning the initial learning rate; X and Xor in OT. For other parameters, heuristics and typical hyperparameter values from UDA papers (such as batch size) without further tuning. We use cross entropy link function on the source validation set; this value provides proxy for the target test risk. Using parameters from the original paper, this estimator helps select parameter ranges which perform reasonably well. We keep the estimator unchanged for the full and missing adaptation models. In the imputation case the discriminator used for computing importance sampling weights discriminates between [īs, [s2] and [TT,, TTa, (cf. D1 Figure I
used
D.2.2 DIGITS
We find that the results are highly dependent on the NN architecture and the training parameter setting. In order to evaluate the gain obtained with Adaptat ieiiiinnmmmn Imputation, we use the same NN architecture for all models (ADV and OT) but fine tune the learning rates for each model using the DEV estimator (other parameters do not have significant impact on the classification performance).
ADV We use an adaptive approach as in Ganin & Lempitsky (0155) for decaying the learning rate Ir and updating the gradient's scale s between 0 and for the domain discriminators. We
2
choose the decay values used in Ganin & Lempitsky (2015) ie, s 1 exp(-10 p) 1 and
Ir.
Ir = (1 10 x p)0.75 where is ratio of current batches processed over the total number of batches to be processed without further tuning. We tune the initial learning rate Ir;, chosen in the range {10-2, 10-2.5 10-3, 10-3.5 10 following Section D.2.1 In practise we take lr; = 10-2 for Adaptat i
ADV Adaptat on on- Imputation Adaptation-Fin 10-5.5 for ADV Adaptat -iiiinnMMinng.... We use Adam (Kingma & Ba 2014) as the optimizer with momentum parameters B1 0.8 and B2 = 0.999 and use the same decay strategy and initial learning rate for all components (feature extractor, classifier, reconstructor). Batch size is chosen to be 128; we see in practise that initializing the adaptation models with source model with smaller batch size (such as 32) can be beneficial.
a and lr;
оT We choose parameter A1 = Aor 0.1 in Equations and g after tuning in the range {10-1,10 10 2, 10 }) using DEV; the goal is indeed to down weight the contribution of align- ment through Wasserstein distance which should be scaled compared to the classification term. Following [amodarran & Kellenberger (2018), batch size is taken be 500 and use EMD) as Optimal Transport metric. We initialize adaptation models with a source model in the first 10 epochs and divide the initial learning rate by two as adaptation starts for non-imputation models. For Adaptat
ion we follow a decaying strategy on the learning rate and on the adaptation weight as explained in the next item, We choose Ir; in the range (10-2, 10 2.5 10 10-3, 10 10-3.1 10=4J. }. In practise we fix lr; = 10 for all models.
Imputation parameters In practice we can define a weight for each term in Equation 2 and Further studies are conducted in Section 5.4] weightings in Equation 2 in digits experiments we choose L2 = LMSE + LADV for ADV and OT to reduce the burden of additional feature tuning. For ADV model, we fix parameters in Equation 4 to 1. In the OT model, we vary X between 0 and 0.1 and X2 between 0 and following the same schedule as the gradient scale update for ADV models. Although necessary to achieve good mean values, this proves reduce significantly the variance.
D.2.3 ADS
We use an adaptive strategy for updating the gradient scale and the learning rate with the same parameters as in the digits dataset. Optimizer is taken to be Adam. Batch size is taken to be big so that target batches include sufficient positive instances.
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Under review as a conference paper at ICLR 2020
ads-kaggle The initial learning rate is chosen in the range (10-4, 10 1105,110-00 10006 10-7) using DEV and fixed to be 10-6 for all models. Batch size is taken to be 500 and we initialize models with simple classification loss for five epochs. We models for 50 epochs after which we notice that models reach plateau. We find that adding a weighted MSE term allows to achieve higher stability (as measured by variance) further studied in Section 5.4 In similar fashion to Pathak et al. (2016). we tune this weight in the range {1, 11,10-1 10 7.5 7..5%
10 10-3, 5 x 10-s, 10033, We find that 0.005 offers the best compromise between mean loss and variance. Moreover on this dataset we use a faster decaying strategy for the discriminator's s D2 and the reconstructor's s h learning rate, lr;
Ir
achieve higher stability in the training curves while the feature extractor 91. and D1's learning rate are unchanged.
(1 + x p)0.75
ads-real The initial learning rate chosen in the range {10-4, 10-5, 1,00-,10-5 10-6) and fixed to be 10-6 for all models. The learning rate is decayed with the same parameters as digits for all models. We run models for ten epochs which provides a good trade-off between learning time and classification performance. Batch size is taken to be 500. We choose L2 LMSE LADV without further tuning; this simple weight achieves already good results.
E VISUALIZATION OF FEATURES' DISTRIBUTION ON ADS-KAGGLE
The goal this section is to visualize the domain shift existing in ads- kaggle pre-adaptation to show that the problem comprises both domain shift and an imputation problem. Table 0 re- ports mean and standard deviation on each feature's value over the domain and Figure 6 plots the histogram of the normalized distributions for better visualization. The y-axis corresponds to real counts. We see that feature 5 is missing on the target domain and that distribu- tions different in shape, mean and variance on each domain.
normalized and
Table 6: Mean and standard deviation for each feature on ads ads-kaggle
Dataset
ads kaggle
Domain
Source
Target
feature I
0.80+2.21
4.4 x 110- 10.04
feature 2
9.16+13.04
9.01=13.42
feature 3
4.40#6.32
3.44#6..9
feature
2.58+3.27
0.94+2.31
feature S
61.09+37.67
0.0+0.0
feature 6
11.26:112.44
0.090 .9
feature 7
4.10#16.23
0.003410.13
feature 8
5.1244.50
1.91
feature 9
14.32+11.57
3.273+5.36
feature 10
0.046#4.22
1.35 x10 $+0.0037
feature 11
1.08+2.11
4.25 x10 4+0.029
feature 12
0.083+10.78
6.68 =10001
feature 13
2.74+3.59
1.21
F EMBEDDING VISUALIZATION ON DIGITS
this section we visualize the embeddings learned by the various models on digits by projecting the embeddings in 2D space using t-SNE (the original embedding size being 2048). Figure rep- resents the embeddings learned for ADV models on MNIST + MNIST-M. Figures 8 and represent these embeddings for OT models respectively MNIST + MNIST-M and MNIST USPS.
On these figures, we see that imputation models generate feature representations that overlap better between source and target examples per class than the adaptation counterparts (although Adaptation-Patt ial does a good job at overlapping feature representations). This corre- lates with the accuracy performance on the and partial adaptation networks perform badly compared to the full adaptation counterparts which justifies the use of imputation model when confronted to missing data.
Moreover we notice, as expected, that missing
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Under review as a conference paper at ICLR 2020
(a)
(b)
Figure 6: Features' normalized distribution for each input dimension (features 12): (a) Source domain (blue), (b) Target domain (red)
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Under review as a conference paper at ICLR 2020
(a)
(d)
(f)
(h)
Figure 7: Embeddings for MNIST + MNIST-M dataset on batch, for source missing (ace 14.4%) (a) (b); ADV missing (ace 32.6%) (c) (d): ADV partial (ace 27. 27.0%) (e) (f) ADV with imputation (acc 56.3%); (g) (h) and ADV full (ace 74.2%) (i) (). (a) (c) (e) (g) (i) represent the target (blue) and source (red) clusters, (b) (d) (1) (h) (i) represent the classes source and target instances.
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Under review as a conference paper at ICLR 2020
(a)
(b)
(d)
(f)
(h)
Figure 8: Embeddings for MNIST + MNIST-M dataset on batch, for source missing (ace 14.5%) (a) (b); OT missing (ace 18.8%) (c) (d); OT partial (ace 27.75%) (e) (f); OT with imputation (acc 28.6%) (g) (h) and OT full (ace 45.9%) ()). (a) (c) (e) (g) (i) represent the target (blue) and source (red) clusters, (b) (d) (f) (h) (j) represent the classes on source and target instances.
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Under review as a conference paper at ICLR 2020
(a)
(f)
V
(h)
Figure 9: Embeddings for MNIST USPS dataset on batch. for source missing (ace 25.0%) (a) (b); OT missing (ace 58.0%) (c) (d); OT partial (acc 62.42% (e) (f); OT with imputation (acc 65.2%) (g) (h) and or full (ace 91.5%) (i) ()). (a) (c) (e) (g) represent the target (blue) and source (red) clusters, (b) (d) (f) (h) (i) represent the classes on source and target instances.
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Reviews:
[{"review_id": "ryxFdPLRYH", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "*Summary.* The paper presents and addresses the problem of performing domain adaptation when the target domain is systematically (i.e., not the result of a stochastic process) missing subsets of the data. The issue is motivated by applications where one modality of data becomes unavailable in the target domain (e.g., when deciding which ads to serve to new users, the predictor may have access to behavior across other websites but not on a specific merchant's website). The proposed method learns to map source and target data to a latent space where the representations for the source and target are aligned, the missing components of the target can be inferred, and classification can be performed successfully. These are achieved by adversarial/optimal transport loss on source and target features, a mean-squared error and adversarial loss on latent generation/imputation, and a cross entropy loss on source label prediction, respectively. Experiments are performed on digits and click-through rate (CTR) prediction and include a thorough set of baselines/oracles for comparison.\n\n*Review.* While the problem statement is novel, I am unconvinced that the advertising experiment includes both a domain adaptation and imputation problem. I describe this in detail below. For this reason, I am giving the paper a weak reject.\n\n*Questions that impacted rating.*\n1. Ads experiment: From my understanding, the source domain is the traffic of users who have interacted with (clicked through to?) a specific partner and the target domain is the traffic of the users who have not interacted with that specific partner. The data that needs to be imputed is the click through rate for target users with that specific partner. In this case, it is not obvious to me why there is a domain shift between these two groups of users. This would imply that the traffic of source users and target users is different for other partners. I don't see why this would need to be true. Could the authors provide an explanation as to why this is the case (e.g., by showing that CTRs differ with other (partner, publisher) pairs between source and target). From my understanding, Table 5 only shows CTR averaged across all users in each domain, but does not show that the CTRs differ between source and target users for contexts/(partner, publisher) pairs (i.e., the results in table 5 could be due to the fact that the prior distribution over context is different for source and target users).\n\n*Additional notes. Immaterial to rating.*\n1. I personally felt that the motivation for UDA vs imputation in the first paragraph was a bit muddled. I think sticking to one example would make the motivation more clear to the reader. E.g., explain the prediction problem for medical imaging (which I assume is disease diagnosis, but it is not stated explicitly), describe how some medical imaging may be missing for certain patients (imputation), then explain that there may be noise across different medical imaging systems (UDA), then list the other applications where this arises with citations (e.g., These phenomena have also been documented in advertising applications [1], ...).\n2. I was surprised by the difference between Adaptation-Partial and the other two train/test conditions in Figure 2 when p=30%. Out of curiosity, do the authors have an explanation for this discrepancy? I would have predicted that, if most of the information necessary for prediction was available in the remaining 70% of the image that the performance of these cases would be very similar.  I think it would be helpful to see the accuracy on the source domain and the labeled target domain to better understand that result.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "Ske7FfJTFB", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The submission describes an approach for unsupervised domain adaptation in a setting where some parts of the target data are missing.\n\nBoth UDA approaches as well as data completion approaches have a sizable research history, as laid out in the related work section (Section 5). The novelty here comes from the properties that a) domain adaptation and data imputation are handled in a joint manner, b) the missing data in the target domain is non-stochastic, and c) imputation is performed in a latent space. This maps to a fairly specific, but realistic enough set of real-world problems; the authors give an image recognition as well as an advertising prediction related problem as experimental examples.\n\nThe submission is overall well written and easy to understand. I'd rate the novelty as medium (smart combination of existing methods), but the exemplary experimental evaluation elevates it to more than a systems paper.\n\nThe method is described clearly in Section 3, and the joint training makes sense. I notice that not all hyperparameters ({lambda_adv, lambda_mse}, {lambda_1, lambda_2, lambda_3}) are truly needed. lambda_adv and lambda_1 could be canonically set to 1 for such a loss minimization problem, so why are the extraneous parameters included?\n\nIn addition to Section 3, the experimental evaluation on two very different data sets in Section 4 is highly detailed and describes the insights clearly, both qualitatively and quantitatively. I'm happy that mean standard deviations are reported on an acceptable experiment sample set size.\nRegarding the different approaches: I'm wondering whether the higher performance of the ADV approach over OT (or the parameter hunger of OT over ADV) is only due to the tuning of the network architectures, or whether this is due to the approximations described in B.1.\nThe ablation study in Section 4.4 is interesting w.r.t. the trade-off it shows between stable, consistent, \"average\" results from an MSE loss term, vs. high-variance (and on average better) results when a choice of mode is forced using an adversarial loss term.\n\nMinor comments:\n- In Table 2, I am not sure what the first row ('Naive') refers to. As far as I can tell, it is not referenced in the text.\n- I would move Section 5 (related work) to right after the introduction, as is common in conference papers and makes for smoother reading.\n- Section 5.2: type \"impainting\" -> \"inpainting\"\n- Appendix, section 'Pre-processing': It seems to me that there is a clear assumption made that the target set is balanced, since training happens with a balanced source set. Is this realistic in practical scenarios? There is work on DA with unequal class distributions between domains.\n\nIn summary, I can clearly recommend this submission for publication.", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}, {"review_id": "HJlx9WDWcS", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposed to address a compound problem where missing data and distribution shift are both at play.  The paper goes on to describe some heuristic methods that resemble the gradient reversal methods due to Ganin et al for handling both problems. \n\nThe novel part of the paper over DANNs is the joint, end-to-end training of latent representations for missing data,  While it is sloppy with terminology, the paper is overall reasonably easy to follow although it might mislea a novice reader and sufficient details are provided to replicate their results.  \n\nThe major problem here is the problem appears to be underspecified, and its not clear under what conditions if any the proposed methods are valid. Moreover it’s not clear to what extent the experimental results should ameliorate these concerns. \n\nIf the data is not missing at random then there is presumably confounding. The authors dance around this topic, just asserting that they are handling non-stochastic missing data but do not say precisely what is assumed about the relationship between the observed and missing data. \n\nIn short the paper addresses an under-specified problem with a heuristic technique based upon domain-adversarial nets which have recently been shown have a number of fundamental flaws. It's never made clear under what assumptions this proposed procedure is valid and the paper misrepresents the prior work on lable shift, including the theoretically sound work, e.g.:\n\n\"we assume covariate shift as in most UDA papers e.g. Ben-David et al. (2010); Ganin & Lempitsky (2015).”\n>>>  Ben-David 2010 is not about covariate shift ….\n\nSome minor thoughts:\n\n“some components of the target data are systematically absent”\n>>> \tNot clear what “component” means at this point\n\n“We propose a way to impute non-stochastic missing data”\n>>> \tWhat does this mean? Is non-stochastic, not missing at random? What is the pattern of missing-ness conditioned on? What assumption, if any, is made? \n\n“This key property allows us to handle non-stochastic missing data,” \n>>> \tagain what precisely does this mean?\n\n“Consider that x has two components (x_1, x_2)…”\n>>>\tsloppy  notation:\n\t“Source features” x_s = (x_S1, x_S2) are always available \n\n\nI read the author's reply but do not believe that the responses are satisfactory. The authors do not address the primary concerns clearly and do not point to specific improvements in the draft that might cause me to change my mind.\n\n", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper addresses the problem of performing unsupervised domain adaptation when some target domain data is missing is a potentially non-stochastic way. The proposed solution consists of applying a version of domain adversarial learning for adaptation together with an MSE based imputation loss learned using complete source data. The method is evaluated on both the standard digit recognition datasets and a real-world advertising dataset. 

The reviewers had mixed recommendations for this work, with two recommending weak reject and one recommending acceptance. The key positive point from R3 who recommended acceptance was that this work addresses a new problem statement which may be of practical importance. The other two reviewers expressed concerns over the contribution of the work and the validity of the problem setting. Namely, both R2 and R4 had significant confusion over the problem specification and/or under what conditions the proposed setting is valid. 

It is a difficult decision for this paper as there is a core disagreement between the reviewers. All reviewers seem to agree that the proposed solution is a combination of prior methods in a new way to address the specific problem setting of this work.  However, the reviewers differ in precisely whether they determine the proposed problem setting to be valid and justified. Due to this discrepancy, the AC does not recommend acceptance at this time. If the core contribution is to be an application of existing techniques to a new problem statement than that should be clarified and motivated further. 

Decision: Reject