A Fair Generative Model Using Total Variation Distance
Authors: Soobin Um
Changho Suh
Venue: ICLR 2022 Submitted (2022)
Keywords: trustworthy AI
fairness
generative model
total variation distance

Abstract: We explore a fairness-related challenge that arises in generative models. The challenge is that biased training data with imbalanced representations of demographic groups may yield a high asymmetry in size of generated samples across distinct groups. We focus on practically-relevant scenarios wherein demographic labels are not available and therefore the design of a fair generative model is particularly challenging. In this paper, we propose an optimization framework that regulates such unfairness by employing one prominent statistical notion, total variation distance (TVD). We quantify the degree of unfairness via the TVD between the generated samples and balanced-yet-small reference samples. We take a variational optimization approach to faithfully implement the TVD-based measure. Experiments on benchmark real datasets demonstrate that the proposed framework can significantly improve the fairness performance while maintaining realistic sample quality for a wide range of the reference set size all the way down to 1% relative to training set.

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A FAIR GENERATIVE MODEL USING TOTAL VARIATION DISTANCE
Anonymous authors Paper under double-blind review
ABSTRACT
We explore a faimess-relatee challenge that arises in generative models. The chal- lenge is that biased training data with imbalanced representations of demographic groups may yield high asymmetry in size of generated samples across distinct groups. We focus on practically-relvaal scenarios wherein demographie labels are not available and therefore the design of fair generative model is particularly challenging. this paper, we propose an optimization framework that regulates the unfairness under such practical settings by employing one prominent statistical notion, total variation distance (TVD). We quantify the degree of unfairness via the TVD between the generated samples and balanced- salanced-yet-smaall yet-small reference samples. We take a variational optimization approach to faithfully implement the TVD-based measure. Experiments benchmark real datasets demonstrate that the proposed framework can significantly improve the fairness performance while maintaining realistic sample quality for wide range of the reference set size all the way down to 1% relative to training set.
INTRODUCTION
High-quality realistic samples synthesized thanks to recent advances in generative models (Brock) al. 2019 Goodfellow al., 2014, Karras al. 2019) have played a crucial role enrich training data for a widening array of applications such as face recognition. natural language processing, and medical imaging (Wang et al. 2019 Chang et al., 2018 Yi al. (019). One challenge concerning fairness arises when generative models are built upon biased training data that preserve unbalanced representations of demographic groups. Any existing bias in the dataset can readily he propagated to the learned model, thus producing generations that are biased towards certain demographics. The unbalanced generated samples may often yield undesirable performances against underrepresented groups for downstream applications. One natural way to ensure fair sample generation is to exploit demographic labels (if available) to build a fair generative model, e.g., via conditional GAN (Mirza) & Osindero 2014 Odena et al. 2017] MMyato & Koyamal 2018) which employs such labels to easily generate an arbitrary number of samples for minority groups In many practically-relevant scenarios, however, such labels are not often available.
To address the challenge, one pioneering work (Choi et al. 2020) develops a novel debiasing technique that employs the reweighting idea (Ren et al. 2018 Kamiran Calders 2012 Byrd & Lipton 2019) to put more weights to underrepresented samples, thereby promoting fair sample generation across demographic groups. One key feature of the technique is to identify the bias (reflected in the weights) via a small and unlabelled reference dataset. While it enjoys significant faimess performance for moderate sizes of the reference dataset, may provide marginal gain for more practically-rede relevann case of a small set size where the weight estimation is often inaccurate, as hinted by the meta-learning literature (Ren et al. 2018 Shu al. 2020). We also find such phenomenon in our experiments; see Table 2 for details.
On the other hand, one recent study (Roh et al. 2020) sheds lights on addressing the small set size issue. Roh et al. (2020) propose robust training approach by employing the Jensen-Shannow divergence (or equivalently mutual information (Majtey et al. 2005)) between poisoned training and clean reference samples. It then takes the divergence robust training. One key benefit of Roh et al, (2020)in light of the reweighting-base approaches (Ren) et al. 2018 Choi et al. 2020) is that the robustness performance is guaranteed even for small
regularization term in order promote

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size of the clean reference set down to 5% relative to the training set size. This implies that the divergence- based regularization approach makes a more efficient use of reference data for robustness, as compared to the reweighting technique.
Inspired by the key benefit featured in Roh et al. 2020), we address the small set issue by another well-known statistical measure, in particular, total variation distance (TVD). See Section 3.2 for details on the rationale behind the use of TVD. Similarly we introduce a reference dataset which is balanced and unlabelled. We then employ it to formulate the TVD between the generated and reference sample distributions, which can serve as quantifying the degree of unfairness. We then promote fair sample generation by adding the TVD into a conventional optimization (c.g.. GAN-based optimization (Goodfellow et al. [2014] Nowozin et al. Arjovsyy
Contribution:
[
al. 2017) Motivated by the variational optimization technique w.r.f. TVD (Villani 2009
Nowozin et al. 2016] Arjovsky et al. (0077), we translate the TVDD-regularization term into function optimization. We also conduct extensive experiments on three benchmark real datasets: CelebA (Liu al. 2015), UTKFace (Zhang et al. 2017), and FairFace (Karkkainen & Joo 202I). We demonstrate via simulation that the proposed framework can significantly boost up the fairness performance while offering high-quality realistic samples reflected in low FID. We also find that approach outperforms the state of the art (Choi et al., 2020), particularly being robust to the balanced reference set size: the significant improvements preserve for a wide range of the reference set size down to 1 1% relative to training data (more preferable in reality).
In addition to Choi et al. 2020). Tan al. (2020) propose a different way that promotes fair sample generation by smartly perturbing the input distribution of pre-trained generative model with the help of classifier for sensitive attributes. The key distinction w.r.t. ours is that it relies upon the additional classifier which requires the use of demographic labels to obtain. Yu jtt al.) (2020) employ demographic labels for minority groups to generate a wide variety of samples with improved data converge by harmonizing GAN and MLE ideas. A distinction w.r.t. ours is that it requires the knowledge on demographic labels. JJlal et al. (02T) consider a fair generative model yet in different context, image reconstruction. The goal of the task is to ensure fair sample generation of restored images from degraded versions. Since it relies upon the degraded images, not directly comparable to ours. Another line of fair generative modeling focuses on label bias,
Related works:
instead of representation bias (Xu et al. 2018 2019a Sattigeri et al. 2019 Jang et al. 2021 Kyono et al. 2021). The goal therein is to develop generative model such that the generated decision labels are statistically independent of the given demographic labels. Again, these are not directly comparable ours, as they require the use of demographic labels.
The variational optimization technique w.r.t. TVD that gives an inspiration to our work has originated from Villani (2003) 2009), wherein the author shows that the TVD can be expressed as function optimization in the context of transport theory. The technique was recently applied to the GAN context (Nowozin et al., 2016). The TVD has also served useful tool for quantifying various fairness measures in fair classifiers that pursue individual fairness (Dwork et al. 2012, Dwork & Ilvento 2018) and group fairness (Gordaliza et al. 2019 Wang et al. [020aa] Farokhi 2021).
2 PROBLEM FORMULATION
Setup: Fig. [ illustrates the problem setting for a fair generative model that we focus on herein. We consider challenging yet practically-relevant scenario wherein demographic information (or that we call sensitive attribute), say & E Z, is not available. Under this blind setting, the goal of the problem is to construct fair generative model that ensures the produced samples to have the same size across distinct demographics. We assume that there are two types of data given in the
(i) 1 (ii) reference data Drof := {x Jim1 Since we problem: (i) training data Doias := { bias)
(i)
consider the setting where training data is potentially biased, we use the word "bias" in the associated notations. Here maias denotes the number of training examples. Let Paiss be data distribution which
each training data [1( E X' is generated upon. In a biased scenario having female-vs-male sensitive attribute, e.g., z 0 (female) and = 1 (male), we may have Pbias 0) > Piias 1). As in Choi et al. (2020), we also employ a balanced yet small reference dataset for the purpose of promoting fair sample generation, which can be obtained via set of surefully-dssigne collection protocols employed in organizations like World Bank and biotech companies (Choi et al. 2020 23&me 2016: Hong 2016). Let Pref be the corresponding data distribution defined on X:
data
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generative model G
( fil
( 1 1i=
Figure 1: Part of fair generative model that intends to yield generated samples with the equal size over demographic groups. We employ training data ( / reference data {- (m. The entire structure of the proposed model will be illustrated in detail in Fig. Here Maias (or mief) denotes the number of training samples (or reference samples).
mais (potentially biased) and balanced
(Z = (Z 1). Since the balanced reference set is often challenging collect, typically the number of the reference samples is much smaller than that of training examples: mee < Mbias Denote by = G(w) E X' the generated sample fed by random noise input W. We assume that the generated samples have the same support X' as training and reference samples. Let Pe and Fw be distributions w.r.t. generated samples and the random noise input respectively.
As a fairness measure that will be employed for the purpose of evaluating our framework to be presented Section 3 we consider fairness discrepancy proposed by Choi al. (2020). quantifies how PG differs from Ire w.r.t. certain sensitive attribute, formally defined below.
fairmess
Definition (Fairness Discrepancy (Choi et al. 2020)). Fairness discrepancy between Fre and P w.E. sensitive attribute f31...., E|zil defined as:
F(Pret Pa) == (1)re(2) pa(2)ll2
(1)
where
Pref (2 = =11) P (Z 22)
Po 21) Pol2 = 22)
Pr)f
and pa(z):=
Pref (Z 2121)
Po = 2121)
Here & denotes the prediction of the sensitive attribute w.r.t. a generated sample, yielded by pre-trained classification model which we call attribute classifier as in Choi et al. (2020). The attribute classifier is employed only for the purpose of evaluation, and is trained based on another real dataset, e.g., like the one mentioned in Choi et al. (2020): the standard train and validation splits of CelebA (Liu et al. 2015). For faithful evaluation, we consider a vast number of generated samples (i.e., more than 10,000) well employ highly-accurate attribute classifiers, around 98% accuracy of gender classifier for instance.
As measure for the quality of generated samples that may compete with the fairness measure, we employ a well-known measure: Fréchet Inception Distance (FID) (Heusel et al. 2017). It defined as the Fréchet distance (Fréchet) 1957) (also known as the second-order Wasserstein distance (Wasserstein) 1969)) between real and generated samples approximated via the Gaussian distribution. The lower FID. the more realistic and diverse the generated samples are. For a more precise measure that reveals sample quality of each sensitive group, we consider FID computed within each demographic, called intra FID (Miyato & Koyama| 2018 Zhang et al.. 2019) Wang et al. 2020b). Computing intra FID requires the knowledge group identities of generated samples. Since demographic labels are not available in our context, we rely upon the attribute classifier (that we introduced above) for predicting demographie information of the generated samples.
GAN-based generative model: Our framework (to be presented soon) builds upon one powerful generative model: Generative Adversarial Network (GAN) (Goodfellow et al.) 2014). The GAN comprises two competing players: (i) discriminator D(-) that wishes to discriminate real samples against generated samples; and (ii) generator G(.) that intends fool the discriminator by producing
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realistic generated samples. In particular, consider general optimization framework (Tseng et al. 2021 which subsumes many GAN variants as special cases:
(Discriminator) max Epei [fD(D(X)) leea (fc(((())))))
D
(Generator) min -Ero [9G [(X))]
where fD. fa. and 9G indicate certain functions that vary depending
employed GAN approach.
For instance, the choice of (ft(t), (f(()) (c(t).GG(t)) = (t. -t, together with Lipschitz-1 condition on D leads to the prominent WGAN optimization (Arjovsky al. 2017). Another choice of
(JD(t), (() ga (()) (min -1 + 4,, min 4.0) yields a hinge-loss-based GAN (Lim)
& Yel 2017] Tran al. 2017). We adopt this base framework that will add fairness aspect
into in the next section.
3 PROPOSED FRAMEWORK
3.1 TVD-BASED APPROACH
One natural way to enforce a fairness constraint is to incorporate Yairness-regularizatie the base framework. However, since the base framework consists of two distinct optimizations, how add the regularization term is not clear. To gain some insights into this, we focus on one instance of GAN, which allows us express the two as only optimization and then relate the optimization to well-known statistical notion: total variation distance (TVD). To this end, we first consider following mappings: (fo(t), (a( (t) (t, t). Applying these into equation 2 gives:
into
min max Ep.... [(X) Iea [(X)].
We now employ the variational optimization technique presented in Villani 2003 2009); Nowozin et al. (2016); i Arrovsky et al.] (2017) to translate equation 3 into the TVD between Pbias and Fg- Details described in Theorem helow.
Theorem (Nowozin et al. (2016). The optimization in equation D()) [-1,
3 with the bounded constraint
is equivalent to:
min [V PP))
(4)
where
1 Σ TV Pc)
(ibias(2) Fo(x)].
Proof.
See appendix A
3.2 FATR GENERATIVE MODEL.
Now we have the TVD-based framework with the single optimization. So one natural way to impose fairness constraint is add proper regularization term on top of equation 4 Remember our framework employs the reference dataset containing balanced samples, reflected in Preef Hence, as the regularization term, we may consider distance measure between Ieee (target distribution) and Pa. since large distance penalizes the objective. To this end, we propose to use the same TVD as was used in equation
min (1 A) (iass Pa) + A TV ref, Pa)
where À E [0, 1] denotes normalized regularization factor that balances the sample quality against the faimess constraint. The rationale behind the use of TVD regularization is that it is robust to the size of dataset compared to a set of f f-divergences (Tseng et al., 2021 Moreover, it offers the best trade-off performances in fairness and sample quality compared other divergence measures: Jensen-Shannow Shannon divergence (Wong & You 1985). Kullback-Leible divergence (Kullback & Leibler
1951), Pearson diveereee (Pearson, 1900), and Wasserstein distance (Wasserstein 1969 We
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Diass
D(-)
G
ft
Dfair
Dfair (.)
Dref
Figure 2: The architecture of the proposed three-player optimization, reflected in equation
provide empirical evidence that demonstrates this performance benefit in Section 4.2 see Table for details.
One challenge that arises equation is that expressing the TVDs in terms of an optimization variable G is not that straightforward. For ease of implementation, we rely upon Theorem I Jagain, which shows the equivalence between the TVD-based optimization and the two-player game (equation 3). Since equation 5 includes one more TVD, we introduce the third player, who serves another discriminator trying to distinguish generated samples from the balanced reference samples. Based on this, we propose three-player game which is equivalent to equation 5 statement of the equivalence and its proof.
See Theorem
2 for the formal
Theorem 2. The optimization in equation S is equivalent to:
min max max (1 A) [x Ee [D(X)I + MIEx [Dtair()) Bp (Dair (X)I}.
Proof. Manipulating equation 6 we obtain:
min max max (1 X) (E [DXX] EF [D()]) + A( (Drair ( (X) Ep Drair (X))
[Dai1s 1
min (1 - A) Σ -P + A Σ ZEX
(Perr - Pa(x)
xEX
(7)
where the equality is because we assume the same support X' for all data samples. Under bounded discriminator functions D(-), Dtair (.) E [-1,
readily obtain the optimal discriminators as:
D* (x)) sign bins (x) Pa(x));
D (x) sign P ret (x) (=()))
Substituting these into equation] 7 we get equation
This completes the proof.
The optimization structure of the new discriminator Diair is the same as that of D, except that we read Pref instead Phias. The generator optimization has an additional term w.r.t. Drair accordingly. The translated three-player game can then be implemented, e.g., via parameterization of three neural networks. We then employ a three-way alternating gradient descent (Goodfellow et al. 2014) for the parameterized neural networks. This procedure is formally presented in Algorithm
Remark (Implementing bounded functions via hinge loss). Among multitude of practices for implementing bounded functions D(.). (-air() [-1,1], we take an approximated approach that offers empirical benefits: the use of hinge loss (Lim & Ye 2017 Tran et 2017). As expressed in Steps] 7 and 12 in Algorithm | we apply the hinge loss both and Drair so that the discriminators attempt to constrain themselves within the interval [-1, 1]. We found via extensive experiments that this choice enables more stabilized training, thereby offering greater performances relative to a direct and simple approach: employing tanh activations in D and Diair Actually this lange-loss-base approximation inspired by Nguyen et al. (2009); Arrovsky et al. (2017): Tan et al, (2019) which explore in depth the equivalence between TVD and linge-loss-basee optimization.
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Algorithm 1 Three-player optimization for the TVD-based fair generative model
1: Input: Training data Daias = (ii mi reference data Dref = (s >== noise input distribu-
tion Pw. and several hyperparameters: X; the numbers of discriminator steps & and I; and the number of iterations T
2: Initialize: ((w; 0) (generator), (zx; Φ) (discriminator), and (aii v/ (fairness discriminator)
3: for T steps do
4: for k steps do (Loop for training D(z;)))
5: Sample minibatch of mg noise inputs {w.)....,
..... w((s)) from Pw
6: Sample minibatch of mg training data points { (1) (1mn)) bias Update (x:; Φ) by ascending its stochastic gradient:
from Daias at random bias
7:
min {0, -1 D( bias' 6)} - min -1 -D)
MB
8:
end for
9:
for steps do (Loop for training Dtair (z; 4))
10:
Sample minibatch of mss, noise inputs {w(11) ...., w (memn)) from Pw
11:
Sample minibatch of mm, reference data points {- ...., ref
(m
from Dref at random
12:
Update (2; () by ascending its stochastic gradient:
[min {0, -1 + Dtair ( x/) + min {0, (0,-1- Diair (G(w (0) }
MBir
13:
end for
14:
Sample minibatch of mB. noise inputs (w(1),
( from Pw
15:
Update G(w:; 0) by descending its stochastic gradient:
mBa
V
1-
([G(W();));)))
Dtair (G(w (G(w));)):))
MBG
mBc
end for
Remark 2 (Three-way way battles). Fig. 2 iillustrates the entire architecture of the translated three-level optimization. Here we interesting three- way battles. The first is well-known battle between the generator G and the 1st discriminator D. Remember D = { (x) - Pa(x)} }. So one can interpret D* as the strength of distinguishing real (potentially biased) samples against generated samples. On the other hand, the generator intends to fool D, thus promoting realistic samples. The second battle in between the generator and the 2nd discriminator Dtair- The same interpretation can be made from (z) = sign (z))(()) Po(x)) (the ability to distinguish balanced reference samples against the generated samples). This way, the generator G is encouraged produce balanced yet less realistic (due to the small-sized reference set) samples, thus pitting the 1st discriminator against the 2nd discriminator indirectly. The last battle is in between the 1st and 2nd discriminators. This tension is directly controlled by the fairness luning knob X; see corresponding tradeoff curves presented in Fig. 4 in appendix E.4 turns out the three-way tradeoff relationships established via our TVD-based framework are greatly balanced. thus achieving significant performances both in fairness and sample quality. This is empirically demonstrated in Section 4.2 see Tables anddd for details.
4 EXPERIMENTS
We conduct experiments three benchmark real datasets: CelebA (Liu et al., 2015). UTK- Face (Zhang et al.] (017), and FairFace (Karkkainen & Joo (02T). We implement our algorithm in PyTorch (Paszke al. 2019) and all experiments performed servers with TITAN RTX and

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Quadro RTX 8000 GPUs. For our algorithm, all the simulation results (to be reported) are the ones averaged over five trials with distinct seeds.
4.1 SETUP
Datasets: Our construction of Daias and Dief respects the method described in Choi et al. (022)) Only for the purpose of data construction, have an access sensitive attributes 2, as control the ratio of demographic group sizes. For CelebA, we consider two scenarios depending on the number of focused attributes: (i) CelebA-single (gender); (ii) CelebA-multi (two attributes: gender and hair color). Training data Dbias is constructed to have 9 ratio (female vs. male) samples where miias 67507. We take balanced samples for Dier (1 : ratio). For CelebA-multi, we have four groups: (i) (female. non- non-black); (ii) (male, non-black); (iii) (female, black); (iv) (male, black). For Daias, we take 85 ratio samples (non-black hair vs. black hair) where mbias = 60000. For UTKFace dataset, we consider a race attribute: white vs. non-white. We take 9 1 ratio biased samples with Whias As 10000. For FairFace dataset, we consider another type of race categorized as white vs. black. We also take the 9 : 1 ratio biased samples yet with Maias 2 20000. A wide range of the reference set size is taken into consideration. We focus mainly on two sizes: (i) 10% (Mref 0.1mpias); (ii) 25% (Meef 0.25mbies). To demonstrate the robustness of our proposed approach to the reference set size, we also consider small sizes of the reference set down to 1%. See appendix B. for more details.
Baselines: We consider three baselines. The first baseline, say Baseline I, is a non-fair algorithm building upon the base framework deseribed in equation [ It is trained on the aggregated dataset Daias Dree. The second baseline, say Baseline II, is the same non-fair algorithm yet trained only with small balanced reference Drof- The last is the state of the art, Choi al. (2020). For all three
baselines, we employ the hinge loss optimization (Lim & Ye 2017 Tran et al. 2017): choosing the min (0,
mapping functions in equation 2 as (fo(t), fc((), gC (t)
t). min -1 -1- t).
Atrribute classifiers: As mentioned in Section 2 (near Definition D we employ attribute classifiers, only for the purpose of evaluating our twin measures: (i) fairness discrepancy (defined in equation []: (ii) intra FID. We introduce four different attribute classifiers for predicting senstive attributes in the following scenarios: (i) gender for CelebA-single; (ii) gender and hair-color for CelebA-mulie (iii) white-vs-non-we white race for UTKKaace; (iv) white-vs-black race for FairFace. For all the classifiers, we use a variant of R (He et al. 2016). CelebA and FairFace classifiers are trained over the standard train and validation splits of CelebA (Liu et al. 2015) and FairFace (Karkkainen & Joo 202T), respectively. For training UTKFace classifier, we use 1 : 1 splits of UTKFace (Zhang al. 2017) dataset. We found that our evaluation is sensitive the performances of the attribute classifiers; see appendix C 1 for a detailed discussion.
Hyperparameter search: For implementation of all three baselines (Baselines I, Baseline II, and Choi ctt al. (2020)) and the proposed framework, we all employ the BigGAN architecture (Brock et al. 2019) In other words, we parameterize G, D, and Drair with the neural-net architecture introduced in Brock et al.] (2019). We leave details in appendix [.22] We also provide a complexity analysis of our algorithm with a comparison to the state of the (Choi et al. 2020 see appendix D for details.
4.2 RESULTS
Table [ provides performance comparison with the three baselines on CelebA dataset. Notice for all the considered settings that our approach exhibits better (or comparable) performances than the state of the art (Choi al., 2020) both in faimess ("Fairness discrepancy") and sample quality ("Intra FID"). The lower, the better for all the measures. The performance gaps are more apparent in the small reference set size. Notice in the last row w.r.t. CelebA-single in Table [ that the fairness performance exhibits slight degradation with an increase in the reference set size. See appendix C22 for an in-depth discussion on this counter-intuitive adverse effect of the increased reference set size. Due to space limitation, we leave in appendix E. experimental results conducted on the other two datasets: UTKFaae and FairFace. The performance trends are similar to those in CelebA.
Fig. 3 visualizes generated samples CelebA-single with the 10% reference set size. The top figure corresponds to ahoho et al.) (2020). while the bottom is due to the proposed algorithm. For each figure, faces above the yellow lines are female samples, while the rest are male samples. Here the gender is
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Table I: Performance comparison on CelebA dataset. CelebA-single indicates the scenario in which a single attribute (gender) is employed. CelebA refers to the case considering two attributes: gender and hair color. Bascline I is a non-fair fair algorithm building upon the base framework with the hinge loss (Lim & Ye, 2017; Tran et al. 2017), and trained with the aggregated data Diias U Dref- Baseline II is the same non-fair algorithm yet trained only with the small yet balanced reference dataset Dref- Choi et al. is the state of the art (Choi al. 2020). "Intra FID" refers to Fréchet Inception Distance (Heusel et al. 2017) computed within each group (Miyato & Koyama 2018 8 Zhang et al. 2019). and we provide results for minority groups herein; see appendix [.22 for complete results. The lower intra FID, the more realistic and diverse samples. "Faireess" is fairness discrepancy introduced by Choi al. (2020): equation for the definition. The lower, the fairer. The reference set size indicates a ratio relative to training data.
CelebA-sing
CelebA-muli
Reference set size
10%
25%
10%
25%
Intra FID
12.73 + 0.053
12.00 + 0.069
10.83 + 0.046
9.76 = 0.067
Baseline I
Fairness
0.554 + 0.002
0.495 = 0.001
0.245 = 0.002
0.224 + 0.002
Intra FID
32.31 + 0.109
23.81 0.118
29.66 0.088
21.92 + 0.056
Baseline
Fairness
0.115 + 0.002
0.093 = 0.002
0.136 0.001
0.107 = 0.001
Intra FID
25.74 + 0.079
20.68 = 0.076
16.27 0.042
13.68 = 0.062
Choi et al.
Fairness
0.104 + 0.002
0.065 + 0.002
0.090 = 0.001
0.063 = 0.002
Intra FID
14.29 + 1.354
11.34 + 1.288
12.93 0.631
12.07 = 0.299
Proposed
Fairness
0.057 + 0.012
0.069 + 0.015
0.080 = 0.006
0.073 = 0.002
Figure 3: (Top) Generated samples by Choi et al. (2020) trained on CelebA-singlt with 10% reference set size. Faces above the yellow line female (57 pictures), while the rest male (43). Intra FID values are around 21.07 (female) and 25.74 (male); (Bottom) Generated samples by the proposed approach under the same setting. We obtain 54 females and 46 males, yet producing more realistic sample images, reflected in a much lower intra FID values, around 9.51 (female) and 14.29 (male).
predicted via the attribute classifier. While both approaches yield well-balanced samples (57 43 for Choi et al. (2020), and 54/ : 46 for ours; see Table for more precise performance comparison), our algorithm produces more realistic sample images. This is reflected in lower intra FID values, around 9.51 (female group) and 14.29 (male group). On the other hand, Choi et al. (020) offers intra FID values of around 21.07 and 25. 25.74 for female and male groups, respectively. See Table 17 (in appendix [ for the values of intra FID. In appendix F we also provide generated samples for UTCe and FairFace datasets.
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Table 2: Robustness of the proposed approach to the reference set size down to 1%. This evaluated on CelebA-single. All the other settings and baselines are the same those in Table [ Our algorithm offers more robust performances both in fairness and intra FID.
Reference size
5%
2.5%
1%
Intra FID
13.54 + 0.074
13.79 + 0.072
15.89 + 0.094
Baseline
Fairness
0.559 + 0.001
0.566 + 0.002
0.576 = 0.002
Intra FID
40.07 + 0.062
67.70 + 0.112
92.34 + 0.131
Baseline II
Fairness
0.120 + 0.003
0.150 + 0.003
0,455 + 0.002
Intra FID
32.30 + 0.049
25.81 + 0.043
30.28 + 0.085
Choi et al.
Fairness
0.043 + 0.002
0,274 + 0.002
0.355 = 0.002
Intra FID
23.42 + 1.312
24.53 + 1.157
30.93 = 2.196
Proposed
Fairness
0.048 + 0.012
0.119 + 0.011
0.166 = 0.011
Table demonsstates the robustness of our algorithm to the reference set size. Notice even for the 1% reference set size, our algorithm offers still respectable performances both in fairness and sample quality. On the other hand. Choi et al. (2020) suffers from performance degradation starting from 2.5%. Refer to appendix
E.2 for intra FIDs w.r.t. the female group.
Table @ooeeddemnsttee demonstrates the rationale behind the use of TVD-based regularization. Observe that among the considered regularization methods, our TVD-based approach offers the best (or the second best) performances both in fairness and sample quality. It also yields the smallest discrepancy between intra FIDs of different groups. Another noticeable observation is that our divergence- based regularization approach outperforms Choi et al. (2020) for variety of other divergence measures not limited to TVD; also see Table for detailed comparison. For implementing other measures, e.g., JSD, we replace the TVD regularization term in equation [ with the considered measure (e.g., JSD) while maintaining the first term in the objective function. We also conduct more extensive experiments which take different divergence measures even for the first term in the objective function in equation 5 Even in such cases, we obtain similar results which exhibit good performances when employing TVD for fairness regularization. See appendix EE.3 for the experimental results.
Table 3: Performance comparison with other fairness regularizers on CelebA-single with the 10% reference set size. "JSD-based" refers to regularization method based on Saasen-Shannon divergence implemented via Goodfellow et al. (2014). "KL.D-based" is the one built upon Kullback-Leible divergence (Nowozin al. (016)) "x" "bsed"" represents the one implementing Pearson-x diver- gence (Mao et al. 2017). "WD-based" refers to a regularization with Wasserstein distance (Gulrajani al. 2017). "Female" (or "Male") refers intra FID for female (or male) group. For each measure, we mark the best result in bold and the second-best with underline.
JSD-baased
KL.D-based
x bassdd
WDD-based
TVD-bbaed
Female
12.80 + 1.499
15.24 + 0.371
16.01 + 1.601
16.51 + 1.244
9.51 + 1.069
Male
17.83 + 1.173
22.47 + 0.331
25.25 + 1.877
24.54 + 2.731
14.29 + 1.354
Fairness
0.087 + 0.012
0.077 + 0.019
0.058 + 0.019
0.047 + 0.033
0.057 0.012
CONCLUSION
We introduced TVD-based optimization framework for fair generative model that well tradeoffs the fairness performance (quantified as fairesss discrepancy) against sample quality (reflected in intra FID). Inspired by the equivalence between the TVD and function optimization, we also developed an equivalent three-player optimization which can readily be implemented via neural-net parameteri- zation. Our algorithm offers better performances than the state of the art both in fairness and intra FID, exhibiting more significant performances particularly for rractin scenarios where the access to balanced dataset is limited. One future work of interest is to push forward for more challenging scenarios where the reference dataset is not available.

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ETHICS STATEMENT
One defining feature our proposed framework to offer fair sample generation of demographic groups while maintaining realistic high quality generated samples. Hence, is expected play crucial role to enrich well-balanced training data for a widening array of downstream applications, thereby ensuring great performances even for underrepresented groups which often suffer from degraded performances due to biased data.
One disadvantage of our approach requires the use of the balanced reference set. So it may not be directly applicable to more challenging scenarios where gathering such non-biased samples are very limited. Another flip side is that our framework builds upon the adversarial training approach which often incurs training instabilityy Hence, we believe one promising future direction is to push the boundary towards such challenging settings while addressing the training stability issue.
REPRODUCIBILITY STATEMENT
To ensure the reproducibility of experiments. we provide a thorough description regarding our three benchmark real datasets: CelebA (Liu et al. 2015), UTKFace (Zhang et al. (017). and Fair- Face Karkkainenn& & Joo (202T), along with data construction methods in Section[4. and appendix[B.] All the hyperparameter settings w.r.t. the three real datasets presented in Appendix [B.2] We also provide the average running time of our algorithm together with specific computer configuration details in Appendix [ Lastly, provide the codes in the supplementary material.
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A
APPENDIX: PROOF OF THEOREM 1
Theorem
Nowozin et al. (016)). The optimization in equation with the bounded constraint
D(-) E [-1,]] equivalent to:
min TV(Fbias: Pc)
where
[V( bias: PG)
P (2) - Pa(x))
2
Proof. We first manipulate equation 3
min max E [(X)] - Epg [D())]
G
min
Σ
bias (z) D'(x)
=Ex
where the equality is because assume the same support X' for training and generated samples. Under the bounded constraint D)-) E 11,, the optimal D maximizing the above summation
becomes (Nowozin al. 2016
(* sign D (bia( - }.
Substituting this into equation g we obtain:
min
(z) Po(c))
FEX
min
- min (I Pa)
where the first equality is due to the optimal D This completes the proof.
B APPENDIX: IMPLEMENTATION DETAILS
We first present Milas (the number samples for training set) and myef (w.r.t. reference set) employed in variety of considered scenarios. Next we provide details on the model architectures (together with hyperparameters) employed for (G(-), D(-), Drair()) (in our framework) well as for attribute classifiers.
B. THE NUMBER OF SAMPLES FOR TRAINING AND REFERENCE SETS
Tables and 5 show maias and myef employed for our experiments. Notice that maias (or m,ef) in UTKFace and FairFace is much smaller than that of CelebA. As expected, this leads the overall
performance degradation of UTKFace and FairFace, as reported in appendix E. see Tables, 15 16 and therein.
Table 4: Number of samples used CclebA. CelebA-single indicates the scenario in which a single
attribute (gender) is employed. CelebA-multi refers to the case considering two attributes: gender and hair color. For CelebA-single, we consider 9 remale-vs-male samples for training set. For CelebA-multi, consider 85 15 non-black-hair black-hair samples. The reference size indicates ratio relative to training set.
CelebA-single
CelebA-multt
Reference set size
1%
2.5%
5%
10%
25%
10%
25%
Mbias
67, 507
67, 507
67, 507
67,507 507
67, 507
60, 000
60, 000
Mref
674
1, 686
3, 3,374
6, 750
16, 876
6, 000
15, 000
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Table 5: Number of samples used in UTKEaaee and FairFace. All the settings the same those in T For UTKFace, we consider 9 white-vs-non-whitg samples for training set. For FairFace, we consider ratio white-vs-black samples.
UTKFace
FairFace
Reference set size
10%
25%
10%
25%
Mibass
8, 486
7, 865
17, 397
16, 123
848
1, 1,966
1.7
4, 032
B.2 ARCHITECTURES AND HYPERPARAMETER CONFIGURATIONS
We employ attribute classifiers, only for the purpose evaluating our twin measures: (i) fairness discrepancy (defined in equation I); (ii) intra FID. We introduce four different attribute classifiers for predicting sensitive attributes in the following scenarios: (i) gender for CelebA-single; (ii) gender and hair-color for CelebA-multi; (iii) white-vs-non- -ontteiteeeeeeeee race for UTKFaae; (iv) white-vs-blasd race for FairFace. For all the attribute classifiers, we use a modified version of ResNet18 (He et al. 2016); see Table for architectural details. We train the classifiers for CelebA and FairFace scenarios with the standard train and validation splits of CelebA (Liu et al. 2015) and FairFace (Karkkainen Joo 2021), respectively. UTKFace (Zhang al. 2017) does not provide such standard dataset splits, so we mamually divide the full UTKFace dataset into 8 1: ratio of train/valid/test splits and use them for training the attribute classifier for FTKe We the same hyperparameters for training all of the classifiers. We use batch size 64 and adam optimizer with the learning rate 0.001 and (B1, (0.9, 0.999). We also employ early stopping.
We adopt the BigGAN (Book et al. 2019) architecture for implementing all the baselines (Baselines I. II, and Choi et al. (020)) and the proposed framework. See Table for architectural details. For Diair employed in our framework, we use the same architecture as D. Tables 8 p and TO exhibit hyperparameters used for our approach. Tables [1 and
a exhiibit hyperparmteer used for experiments with other regularizations. For implementing JSD>based regularization, we rely upon the original GAN with non-saturating loss (Goodfellow al.) 2014). For Kullback-Leibler divergence, we employ the loss function proposed in f-GAN (Nowozin et al.
2016). Least Squares GAN loss (Mao et al. 2017) is employed for implementation Pearson-x" divergence. For implementing 2017) is employed.
Wasserstein distance, WGAN-GP (Gradient Penalty) (Gulrajani al.
For all the experimental results, was chosen as the one that yields the lowest FID among all the candidates respecting good fairness performance, e.g., fairness discrepancy
0.1 on CelebA
dataset. For a batch size, we considered the following candidates {8, 16, 32, 64, 128, 256). We controlled the learning rates for G and 1 among (5 10- 10-4 20--1 10-1) respectively. For the number of D-step per G-step, we considered number among (2, 3, 4).
1, 4. 10-4) and (2. 10 1, 4.
Table 6: A modified ResNet18 architecture for attribute classifiers.
Name
Component
Conv
x 7 conv, 64 filters, stride
Residual Block
3 max pool, stride 2
3 x 3 conv, 128 filters
Residual Block
x 2
3 x 3 conv, 128 filters
3 x conv, 256 filters
Residual Block
x 2
3 x 3 conv, 256 filters
3 x 3 conv, 512 filters 3 x 3 conv, 512 filters
Residual Block
x
x 7 average pool stride 1, fully-connected, softmax
Output Layer
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Table BigGAN architecture for generator and discriminator, Here ch represents the channel width multiplier: ch = 64 for 64 x 64 images of our interest. "ResBlock up" means a Generator Residual Block where the input passed through a ReLU activation and then upsampled, followed by two 3 x 3 convolutional layers with another ReLU activation in between. "ResBlock down" refers to Discriminator Residual Block which the input is passed through two x convolutional layers with ReLU activation in between, and then downsampled. Upsampling is implemented via nearest neighbor interpolation, and downsampling is via average pooling. "ResBlock up/down n + mi
refers to ResBlock with input channels and m output channels.
G
D (or Drair)
x 1 x 2ch Noise
64 x 64 x 3 Image
Linear x 1 16ch 1 x 16ch
ResBlock down 1ch 2ch Non-Local Block (64 x 64)
ResBlock up 16ch + 16ch
ResBlock up 16ch + 8ch
ResBlock down 2ch + 4ch
ResBlock up Sch 4ch
ResBlock down 4ch 8ch
ResBlock up 4ch 2ch
ResBlock down 8ch 16ch
Non-Local Block (64 64)
ResBlock down 16ch 16ch
ResBlock up 4ch + 2ch
ResBlock 16ch + 16ch
BN, ReLU, 3 x Conv 1ch - 3
ReLU, Global sum pooling
Tanh
Linear
For the second discriminator w.r.t fairness, we swept the learning rate through { 1104,22 10 4. 10 and the number of D-step per G-step through {1, 2, 33. For Choi et al. 2020), we found for UTKFace and FairFace that simple 3 or 5-layer CNN classifier better estimates example weights than the ResNet-based architecture used in Choi et al. (2020). All baseline performances are measured using the same approach in Choi al. (2020): average 10 independent evaluation sets of 10,000 samples each drawn from the corresponding baseline model.
Table 8: Hyperparameters used for CelebA experiments. We the same betas for (G, D, Drair).
CelebA-single
CelebA-multi
Reference set size
10%
25%
10%
25%
0.9
0.85
0.9
0.925
Batch size (D & G)
16
8
16
16
Batch size (Dtar)
8
16
Learning rate (G)
5e-5
5e-5
5e-5
5e-5
Learning rate (D D
2e-4
2e-4
2c-4
2e-4
(B1, (2)) (for Adam optimizer)
(0, 0.999
(0, 0.999)
(0, 0.999) 2
(0, (.,9.9
D steps per G step
2
2
Draie steps per G step
1
1
C APPENDIX: ADDITIONAL DISCUSSIONS
We first investigate the evaluation sensitivity w.t.. the attribute classifiers that we employ for performance evaluation. Next, discuss the impact of the reference set size on the fairness performance in our framework. Lastly, we explore connection between our interested setting and transfer learning framework.
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Table 9: Hyperparameters used for CelebA experiments with small reference set sizes. We share
(B1, 52) = (0.9.9 for (G, D, Drair).
CelebA-single
Reference set size
1%
2.5%
5%
X
0.9
0.9
0.9
Batch size (D & G)
8
16
16
Batch size (Dair)
4
8
Learning rate (G)
5e-5
5e-5
5e-5
Learning rate (D & Diair)
2e-4
2e-4
2e-4
(B1, (2) (for Adam optimizer)
(0, 0.999)
(0, 0.999) 2
(0, (.,999
D steps per G step
2
Dairr steps per G step
1
Table 10: Hyperparameters used for UTKFace and FairFace experiments. We employ the same betas
for (G, D, Drir).
UTKFace
FairFace
Reference set size
10%
25%
10%
25%
0.9
0.8
0.9
0.85
Batch size (D & G)
16
16
16
16
Batch size (Dfir)
8
8
Learning rate (G)
5e-5
5e-5
5e-5
5e-5
Learning rate (D D
2e-4
2e-4
2c-4
2e-4
(81, .22) (for Adam optimizer)
(0, 0.999)
(0, 0.999)
(0, 0.999) 2
(0, (0,0.999)
D steps per G step
2
Diair steps per G step
1
1
Table 11: Hyperparameters used for experiments with other faimesss regularizers. We employ the same betas for (G, D, D "JSD-based" refers to regularization method based on Jensen-Shannon divergence (Wong You 1985) implemented via Goodfellow et al. (2014). "KLD-based" is the one built upon Kullback Leibler divergence (Kullback & Leibler 1951 1951 Nowozin et al. 2016 2_
based" represents the one implementing Pearson-x" divergence (Pearson 1900 Mao al. 2017 7
"WD-based" refers to regularization with Wasserstein distance (Wasserstein 1969 Gulrajani et al.
2017.
JSD-based
KLD-based
--based
WD-based
0.985
0.925
0.9
0.975
Batch size (D & G)
16
16
16
16
Batch size (Dair)
8
Learning rate (G)
5e-5
5e-5
5e-5
le-4
Learning rate (D & Dfai) (81, 32) (for Adam optimizer)
2c-4
2e-4
2e-4
le-4
(0, 0.999)
(0, 0.999)
(0, 0.999)
(0,0.9)
D steps per G step
2
2
Diair steps per G step
1
1
7
C.I EVALUATION SENSITIVITY W.R.T. ATTRIBUTE CLASSIFIERS
As mentioned in Sections and 4.1 we rely upon the attribute classifier for evaluating our two performance measures, fairness discrepancy (see Definition inn Section and intra FID. One natural question then to ask how sensitive the evaluation is to the choice of the attribute classifier. We address this question by investigating gap between performances measured with two differently- accurate classifiers. We found that fairness discrepancy varies significantly depending on the accuracy of the attribute classifier. This is in contrast with intra FID which is not much affected with the choice
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Table 12: Hyperparameters used for experiments with other fairness regularizers. "JSD-JSD" indicates the case where both base optimization (the first term in equation 5 and regularization are based on Jensen-Shannon divergence (Wong You, 1985 "x²-x" 2" refers the one that implements Pearson-x" divergence (Pearson 1900) for base optimization well as for regularization. "WD-WD" represents the one that employs Wasserstein distance (Wasserstein, 1969) both for base optimization and regularization.
JSD-JSD
x²-x²
WD-WD
A
0.99
0.75
0.975
Batch size (D G))
16
Batch size (Drair)
8
8
16
Learning rate (G)
5e-5
5e-5
lc-4
Learning rate (D & Dtair)
2e-4
2e-4
le-4
(81, (32) (for Adam optimizer)
(0, 0.999)
(0, 0.999)
(0.0.9)
D steps per G step
2
Dtair steps per G step
of the attribute classifier. For instance, 10% accuracy of the attribute classifier yields around 25% deviations in faimess discrepancy, while exhibiting marginal deviations in intra FID values less than 1 %.
C.2 IMPACT OF REFERENCE SET SIZE ON FAIRNESS PERFORMANCE
Our framework heavily depends reference data in regulating unfaimess, and the size of the reference data indeed affects our performance of fairness. If a given reference dataset is too small well-represent the underlying reference distribution, the measured TVD (via such small-sized reference set) would then be inaccurate, degrading the fairness performance accordingly.
On the other hand, such degradation the faimess regularization, we rely upon GAN framework that often yields model focused on learning only specific part of representations in given dataset, rather than covering all the representations inside (Metz et al.) 2016; Arjovsky et al. 2017). Due to this property, with larger reference set augmented with vast amount representations, our models (generator and fairness discriminator) can be more encouraged toward learning such augmented (yet less relevant to representations w.r.t. demographic groups) representations and therefore less focused on respecting balanced representations of demographic groups, degrading the fairness performance accordingly. This phenomenon is well exhibited our experiments; see the last rows in Tables and 15 for instance.
oceur with a large reference dataset. For implementing
C.3 RELATION TRANSFER LEARNING
Our problem setting can be interpreted as a transfer learning framework, where we wish to exploit the knowledge learned from large training dataset Dolas augment learning on a small reference dataset Dref- We explore such connection herein with basic transfer learning technique, fine-tuning. Employing only one discriminator, we first train our models on Doias until convergence, and then fine-tune the models on Dref- Table compares the performance of the fine-tuning method with all the other approaches, evaluated on CelebA-single with 10% reference set. Notice that the fine-tuning method well-balances between Baseline I and II, yet still inferior than the proposed approach both in fairness and sample quality.
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Table 13: Performance comparison with fine-tuning method on CelebA-single with 10% reference set. Baseline I is a non-fai fair algorithm building upon the base framework with the hinge loss (Lim) & Ye 2017: Tran et al. 2017). and trained with the aggregated data Dias Dref. Baseline same non-fair algorithm yet trained only with the small yet balanced reference dataset Dref- Choi al. is the state of the art (Choi al. 2020p. "Female" (or "Male") refers to intra FID for female (or male) group. The lower intra FID, the more realistic and diverse samples. "Fairness" is fairness discrepancy introduced by Choi et al. (2020); see equation I for the definition. The lower, the fairer.
the
Female
Male
Fairness
Baseline
12.73 0.053
8.37 + 0.057
0.554 0.002
Baseline II
32.31 0.109
26.18 = 0.049
0.115 + 0.002
Choi et al.
25.74 + 0.079
21.07 + 0.064
0.104 + 0.002
Fine-tuning
19.79 + 0.451
13.40 = 0.514
0.147 = 0.008
Proposed
14.29 + 1.354
9.51 + 1.069
0.057 = 0.012
D APPENDIX: COMPLEXITY ANALYSIS
We also offer complexity analysis of our approach while making a comparison to Choi et al. (022)) As performance measures, we consider the total number of parameters well as the running time measured under Pytorch on Xeon Silver 4210R CPU and TITAN RTX GPU. Table I4 presents the interested measures (together with fairness and intra FID performances) for one certain scenario: CelebA-single with 10% reference set size. While our approach provides better intra FID and faimess performances, it comes at cost of an increased complexity, around 16.7% and 40% for the running time and model complexity, respectively.
Table 14: Performance comparison on CelebA-single with 10% reference set size. Choi et al. (0220) corresponds to the state of the art. "Intra FID" refers to Fréchet Inception Distance (Heusel et al.) 2017) computed within each group (Miyato & Koyama| 2018 Zhang et al. 2019), and we provide results for minority group herein. The lower intra FID, the more realistic and diverse samples. "Fairness" is fairness discrepancy introduced by Choi et al. (2020). The lower, the fairer.
Intra FID
Fairness
Running Time (s)
# of parameters
Choi et al.
25.74 + 0.079
0.104 + 0.002
42, 417.24
577, 028 71, 120, 773
Proposed
14.29 1.354
0.057 = 0.012
49, 497.7277
E APPENDIX: ADDITIONAL RESULTS
We first provide performance comparison with the three baselines (Baseline I, Baseline II, and Choi et al. (2020)) on UTKFaae and FairFace datasets. Next present the complete results on CelebA dataset, where intra FID values for all demographics are included. We then compare fairness regularization performances with distinct base optimizations. Lastly, we provide tradeoff curves that illustrate the tension between fairness and sample quality in our framework.
E.1 PERFORMANCES ON UTKFACE AND FAIRFACE
Tables 15 and 16 concern UTKFaae and FairFace datasets. One significant distinction w.r.t. CelebA is that training and reference set sizes are much smaller, around 7 times. Hence, expected, the overall performances are worse than those on CelebA dataset. Even in this small data regime, we observe the same trends the performance benefits of ours relative to the baselines.
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Table 15: Performance comparison UTKFace dataset where attribute is considered: white vs. non-white. Baseline is a non-fair algorithm building upon the base framework with the hinge loss (Lim & Yel 2017] Tran al. 2017), and trained with the aggregated data Diias DDef- Baseline is the same non-fair algorithm yet trained only with the small yet balanced reference dataset Dref- Choi al. is the state of the art (Choi al., 2020). "White" (or "Non-white") refers to intra FID (Miyato & Koyama 2018 Zhang et al. 2019) for white (or non non-white) group. The lower intra FID, the more realistic and diverse samples for that group. "Fairness" fairness discrepancy introduced by Choi et al. (2020); see equation for the definition. The lower, the fairer. The reference
set size indicates ratio relative training data.
Reference set size
10%
25%
White
15.37 + 0.053
14.17 0.047
Baseline
Non-white
19.89 + 0.119
18.86 + 0.117
Fairness
0,453 = 0.002
0,400 0.003
White
77.83 + 0.136
36.78 0.070
Baseline II
Non-white
83.51 + 0.071
35.73 + 0.077
Fairnsss
0.010 + 0.003
0.007 = 0.003
White
28.07 + 0.068
33.95 0.081
Choi et al.
Non-white
36.43 + 0.231
40.06 + 0.138
Fairness
0.285 + 0.003
0,123 + 0.003
White
23.64 + 3.153
16.69 = 0.913
Proposed
Non-white
27.24 +: 4.125
19.20 2.285
Fairness
0.091 + 0.022
0,131 + 0.021
Table 16: Performance comparison on FairFace dataset. All settings and baselines are the same as those in Table 15 except for different types of demographics: white vs. black.
Reference set size
10%
25%
White
25.38 +: 0.084
23.68 + 0.109
Baseline
Black
25.76 0.068
22.96 + 0.047
Fairness
0.434
0.002
0.386 + 0.003
White
77.45 + 104
48.02 + 0.117
Baseline
Black
83.76 0.118
45.20 + 0.055
Fairness
0.105 0.002
0.009 + 0.002
White
33.20 + 0.059
36.56 + 0.106
Choi et al.
Black
33.33 0.076
36.37 + 0.082
Fairness
0.317 0.002
0.142 + 0.002
White
30.73 +: 2.210
28.67 + 2,330
Proposed
Black
31.16 + 2.158
34.07 + 3.140
Fairness
0.044 0.019
0.106 + 0.023
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E.2 COMPLETE RESULTS ON CELEBA
Tables 17 to 19 exhibit the complete results w.r.t. CelebA experiments, where intra FID values for all associated groups provided. Observe that in all considered settings, our approach offers better (or comparable) sample quality than the state of the art (Choi et al. 2020) for all demographics, reflected in low intra FID values.
Table 17: Complete results on CelebA-single in which single attribute (gender) is employed. Baseline is non-fair algorithm building upon the base framework with the hinge loss (Lim &
Ye 2017: TTan et al., 2017), and trained with the aggregated data Diias U Drer- Baseline 11 is the fair algorithm yet trained only with the small yet balanced reference dataset Dref- Choi
ct al. 2020) is the state of the art. "Female" (or "Male") refers to intra FID (Miyato & Koyama
2018 Zhang et al. 2019) for female (or male) group. The lower intra FID, the more realistic and diverse samples for that group. "Fairness" is fairness discrepancy introduced by Choi et al. (2020); ; see equation]
[ for the definition. The lower, the fairer. The reference set size indicates a ratio relative to training data.
Reference set size
10%
25%
Female
8.37 + 0.057
7.32 + 0.047 12.00 = 0.069
Baseline
Male
12.73 0.053
Fairness
0.554 0.002
0.495 + 0.001
Female
26.18 + 0.049
17.66 + 0.084
Baseline
Male
32.31 + 0.109
23.81 = 0.118
Fairness
0.115 0.002
0.093 + 0.002
Female
21.07 0.064
21.33 + 0.059
Choi et al.
Male
25.74 + 0.079
20.68 + 0.076
Fairness
0.104 0.002
0.065 + 0.002
Female
9.51 1.069
7.45 + 1.351
Proposed
Male
14.29 + 1.354
11.34 - 1.288
Fairness
0.057 0.012
0.069 + 0.015
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Table 18: Complete results on CelebA-multe experiments where two attributes are considered: gender and hair color. All the settings and basclines the same those in [7ble[7]]ett here we consider intra FID values for four groups: (i) female with non-black hair; (ii) male with non-black hair; (iii) female with black-hair; (iv) male with black hair.
Reference set size
10%
25%
Female w/ non-black hair
9.25 + 0.040
7.74 = 0.082
Male non- non-black hair Female w/ black hair
12.70 0.090
11.61 = 0.065
Baseline I
8.93 + 0.049
8.14 + 0.043
Male black hair
10.83 0.046
9.76 + 0.067
Fairness
0.245 0.002
0.224 + 0.002
Female w/ non-black hair
26.96 + 0.065
19.22 = 0.087
Male non- bon-black hair
35.35 0.116
25.73 + 0.131
Baseline II
Female w/ black hair
24.51 = 0.085
17.15 - 0.078
Male w/ black hair
29.66 + 0.088
21.92 = 0.056
Fairness
0.136 = 0.001
0.107 = 0.001
Female w/ non-blan non-black hair
15.86 + 0.048
13.11 = 0.032
Male non-black hair
18.78 0.058
14.78 = 0.058
Choi et al.
Female w/ black hair
16.88 + 0.047
12.85 + 0.039
Male black hair
16.27 0.042
13.68 0.062
Fairness
0.090 + 0.001
0.063 + 0.002
Female w/ non-black hair
9.14 0.733
8.84 + 0.457
Male non-black hair
11.93 0.656
11.82 = 0.451
Proposed
Female w/ black hair
11.01 - 0.390
9.75 = 0.435
Male black hair
12.93 + 0.631
12.07 = 0.299
Fairness
0.080 = 0.006
0.073 = 0.002
Table 19: Complete results CelebA-single with the reference set size down to 1%. All the other settings and baselines are the same as those in Table 17
Reference set size
5%
2.5%
1%
Female
8.25 + 0.039
8.09 + 0.064
8.31 + 0.057
Baseline I
Male
13.54 + 0.074
13.79 + 0.072
15.89 + 0.094
Fairness
0.559 + 0.001
0.566 0.002
0.576 + 0.002
Female
33.56 0.036
52.46 + 0.070
83.46 + 0.100
Baseline II
Male
40.07 = 0.062
67.70 = 0.112
92.34 + 0.131
Faimess
0.120 + 0.003
0.018 + 0.003
0.455 + 0.002
Female
25.51 0.044
16.94 0.046
21.49 + 0.057
Choi et al.
Male
32.30 + 0.049
25.81 + 0.043
30.28 + 0.085
Faimess
0.043 + 0.002
0.274 0.002
0.355 + 0.002
Female
15.04 0.635
17.03 1.174
21.88 + 1,946
Proposed
Male
23.42 + 1.312
24.53 + 1.157
30.93 + 2.196
Faimess
0.048 + 0.012
1119
0.166 + 0.011
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E.3 REGULARIZATION WITH DIFFERENT BASE OPTIMIZATIONS
Table 20 compares regularization performances with different divergence measures for the first term in equation 5 Even in this comparison, we observe that our TVD-based approach still prominent among the considered methods, yielding well-balanced performances of fairness and sample quality, We do include the performance regarding Kullback-Leibe divergence, where we failed to get meaningful results due to numerical problem. This is also reported in other works (Song & Ermon 2020 which relies upon the same implementation (Nowozin 2016).
Table 20: Performance comparison with other fairness regularizations on CelcbA-single with the 10% reference set size. "ISD-ISD" indicates the case where both base optimization (the first term in equation 5) and regularization are based on Jensen-Shannen Shannon divergence (Wong & You 1985 Goodfellow al. 2014). "x²-x2" refers to the one that implements Pearson-x" divergence (Pearson 1900; Mao et al., 2017) for base optimization as well as for regularization. "WD-WD"" represents the that employs Wasserstein distance (Wasserstein. 1969 Gulrajani al. (017) both for base optimization and regularization. "Female" (or "Male") refers to intra FID for female (or male) group.
For each measure, mark the best result in bold and the sacond-best with underline.
JSD-JSD
x²-x²
WD-WD
TVD-TVD
Female
11.02 +: 1.521
26.68 + 1.496
15.80 + 1.049
9.51 + 1.069
Male
15.33 + 1.661
40.35
2.605
21.86 + 0.782
14.29
1.354
Fairness
0.107 = 0.015
0.054 + 0.012
0.037 = 0.014
0.057 = 0.012
E.4 FAIRNESS-QUALIT TRADEOFF CURVES
Fig. visualizes tradeoff relationship between sample quality and fairesss in our framework. Despite slight fluctuations, one can readily see that as lambda increases, fairness performance improves (smaller fairness discrepancy) at the expense of the degraded sample quality, reflected in larger intra FID. This validates the role of À as a tuning knob for controlling fairness.
Female
0.6
Male
Fairness discrepancy
0.5
0.4
0.3
0.2
0.1
6
8
10
12
14
16
18
20
Intra FID
Figure 4: chirness-quality tradeoff curves evaluated on CelebA-single with 10% reference set. Each point is obtained with a particular the tuning knob in our framework. Blue dot points indicate performances for female group, and green dots are for male group.
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F APPENDIX: ADDITIONAL GENERATED SAMPLES
We provide generated samples obtained from many scenarios under the three real datasets, not included in the main paper due space constraint. Unlike the main paper, we also present samples generated from Baseline and Baseline II. Remember that Baseline is non-fair algorithm building
upon the base framework (equation in Section 2 with the hinge loss (Lim & Ye 2017 Tran et 2017), while being trained with the aggregated dataset Diias U Baseline II is the same non-fair algorithm yet trained only with Dref. We leave all the samples from below.
(a) Baseline I (84 : 16)
(b) Baseline II (56 44)
Choi et al. (56 44)
(d) proposed (56 : 44)
Figure 5: Generated samples trained on CelebA-single with 25% reference set size. Faces above the yellow line female, while the rest are male.
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(a) Baseline (44 28 17 : 11)
(b) Baseline II (31 13 29 27)
Choi et al. (31 19 24 26)
(d) proposed (31 28 20 21)
Figure 6: Generated samples trained on CelebA-multi with 10% reference set size. Faces above the red line are samples without black hair, while the rest are black hair.
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Baseline (40: 27 17 16)
(b) Baseline II (26 18 33 23)
(c) Choi et al. (30 22 25 23)
(d) proposed (31 : 27 20 : 22)
Figure 7: Generated samples trained on CelebA-multi with 25% reference set size. Faces above the red line are samples without black hair, while the rest are black hair.
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(a) Baseline (79 21)
(b) Baseline 11 (53 47)
(c) Choi et al. (60 : 40)
(d) proposed (60 40)
Figure 8: Generated samples trained on UTKFace with 10% reference set size. Faces above the yellow line are white, while the rest are non-white.
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(a) Baseline I (79 : 21)
(b) Baseline I1 (51 49)
(c) Choi et al. (60 40)
(d) proposed (59 41)
Figure 9: Generated samples trained on UTKFace with 25% reference set size. Faces above the yellow line are white, while the rest are non-white.
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(a) Baseline I (85 : 15)
(b) Baseline II (41 59)
Choi et al. (62 38)
(d) proposed (61 39)
Figure 10: Generated samples trained on FairFace with 10% reference set size. Faces above the yellow line white, while the rest are black.
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Baseline (77 23)
(b) Baseline II (46 : 54)
Choi et al. (60 : 40)
(d) proposed (56 44)
Figure 11: Generated samples trained on FairFace with 25% reference set size. Faces above the yellow line are white, while the rest are black.
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(a) Baseline I (91 9)
(b) Baseline II (62 38)
(c) Choi et al. (55 45)
(d) proposed (55 45)
Figure 12: Generated samples trained on CelebA-single with 5% reference set size. Faces above the yellow line female, while the are male.
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(a) Baseline (11 99)
(b) Baseline II (61 39)
Choi et al. (67 33)
(d) proposed (37 : 43)
Figure 13: Generated samples trained on CelebA-single with 2.5% reference set size, Faces above the yellow line are female, while the rest are male.
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(a) Baseline I (91
(b) Baseline II (87 13)
(c) Choi et al. (76 24)
(d) proposed (65 : 35)
Figure 14: Generated samples trained on CelebA-single with 1 % reference set size. Faces above the yellow line are female, while the rest are male.
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Reviews:
[{"review_id": "uDpUcwKDDZ", "reviewer": "Reviewer_E8Px", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "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": "Overall, the idea and approach are clearly presented. The experiment section also contains multiple different empirical studies. It would be very helpful if the authors can kindly clarify the following points:\n\n### q1: the utilization behind the distance metric w.r.t. the practical scenario described\n\nIn the abstract, if I understand it correctly, the practical problem that motivated the study is the unavailability of demographic group labels. It is not entirely clear to me how the technique (of fair generative model w/ the TV distance metric) can help solve this practical issue. Please kindly let me know if there is any misunderstanding.\n\n### q2: regarding Theorem 1\n\nWhile I understand the content of the theorem itself, I am wondering if the denotation of \"(Nowozin et al., 2016)\" is trying to indicate the fact that Theorem 1 is already proposed in the referred paper. Please kindly clarify this as this theoretical result seems to be an essential part of the contribution (apart from the empirical findings).\n\n### q3: regarding experiments\n\n- Table 2, Baseline II, 2.5% reference set size: I am wondering if the authors could kindly share some insights regarding why the fairness metric is so small (seems to be even better than the proposed approach in all listed cases).\n- I am wondering if the TV measure has anything to do with the sample size of the reference set. With a very big size difference (e.g., 1% reference set size), how can we justify that TV distances are well-estimated?\n- Figure 3 shows the generated images, both in terms of the representation balance and the quality. I am wondering if the authors can share some insights regarding why the proposed approach can (1) generate better-quality images (2) use weaker supervision (smaller reference sets) at the same time. Is it all about the TV metric, which does not seem to be the case based on the msg conveyed by Table 3, or something else?", "summary_of_the_paper": "This paper focuses on the fair generative model problem. In particular, \"fairness\" lies in the balance of representation among groups in the data. The paper proposes to use TV as the distance metric in order to capture the difference between the generated distribution and the reference distribution. Empirical results are also provided.", "summary_of_the_review": "The paper proposes to utilize TV distance in the task of fair representation learning. The empirical experiments suggest a strong performance. It would be very helpful if the authors can kindly comment on the questions in the `Main Review`, so that the significance of the results can be better appreciated.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "ob_WwqGIeWk", "reviewer": "Reviewer_4j8d", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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": "I have enjoyed reading this paper. It is clearly written (though some additional polishing would not hurt), the goal is clearly defined, and the method seems to solve it. However, there still remain some questions from my part which I list below.\n\n## Questions\n**[Q1]** Compared to related work, like Choi et al. (2020), the authors do no longer need a classification model (for training). This is a clear step forward from existing work. However, the authors _**do**_ need a \"reference distribution/dataset\". _Is this not a stricter assumption than needing a classification model?_ \n\nI can imagine having a dataset, unlabelled, which I would like to evaluate on its fairness. If I want to quantify exactly how unfair the dataset is, I would need some kind of label to provide a metric of unfairness (which is why the authors still need a classification model to evaluate their model). Using these labels, I can much more easily identify where my data is unfair. For example, if there is a gender discrepancy, a gender-label would indicate this. Using TVD-GAN, we have to assume that the reference dataset does indeed solve for this discrepancy. However, what if besides gender, there is also an ethnic discrepancy? Can I further assume the reference dataset to be fair? Minimising the distributional difference between $\\mathbb{P}\\_{\\text{ref}}$ and $\\mathbb{P}\\_G$ promotes fairness implicitly, which not only requires additional assumptions about $\\mathbb{P}_{\\text{ref}}$, but it also seems much less convenient.\n\n\n**[Q2]** The latter brings me to my second question. _How does this approach relate to domain adaptation and transfer learning?_ The setup detailed in this paper seems very much related. Mainly we wish to learn on one dataset ($\\mathcal{D}\\_{\\text{bias}}$), with a better performance on a second dataset ($\\mathcal{D}\\_{\\text{ref}}$). While there is no explicit prediction target, learning from one \"domain\" to increase performance in another, seems very much related. Would it be possible to use methods from these fields (e.g. see Table 1 in Wang and Deng (2018) for an overview)?\n\n\n**[Q3]** There is much work on fairness and generative models. While I don't want to be _that_ reviewer, I do believe some comparison is useful. In particular: FairGAN (Xu et al. (2018)), CFGAN (Xu et al. (2019)), DECAF (van Breugel et al. (2021)), FairGen (Tan et al. (2020)) (which is cited, but not compared against like with Choi et al. (2020)).  \n\n## Minor questions\n**[MQ1]** In Eq.(5), you introduce a hyperparameter, $\\lambda$. Essentially, $\\lambda$ controls how fair the eventual generative distribution should be. Higher $\\lambda$ indicates to regularise more towards $\\mathbb{P}\\_{\\text{ref}}$, whereas lower $\\lambda$ steers the optimisation more towards $\\mathbb{P}\\_{\\text{bias}}$. How does this affect performance (wrt fairness, and FID)? \n\n**[MQ2]** This remark is more a subjective remark, mainly because it concerns Fig.3, which in itself is an almost subjective result. The split between female/male in Fig.3 is quite close between Choi et al. and TVD-GAN. While this in itself is not an issue, it may become one if the generated samples are also quite close to the classification threshold between male and female. Numbering columns as c1, c2, ... and rows as r1, r2, ...; The bottom set includes samples like (r4, c1 -> male), or (r3, c15 -> female), (r4, c5 -> male), (r5, c15 -> male) that could equally well be classified with the opposite gender, making performance the same/worse as Choi et al. I wonder whether tuning $\\lambda$, more to $0$ would decrease ambiguity of samples (and how much fairness would suffer as a result)?\n\n**[MQ3]** Perhaps somewhat related to **[Q2]**, but would it not be easier to train only 1 discriminator? First on the biased data, and when converged on the reference data? This would not only make TVD-GAN composable with different notions of fairness (of which there are many), but it would also allow for any trained model to be adjusted when other unfairly distributed attributes need to be dealt with.\n\n\n_I wish to end my main review by stating that I look forward to discussing further with the authors and reviewers of this paper. My review, nor my score, is set in stone._\n\n### Additional references\n\nMei Wang, Weihong Deng, _Deep visual domain adaptation: A survey_, Neurocomputing, Volume 312, 2018, Pages 135-153, ISSN 0925-2312, https://doi.org/10.1016/j.neucom.2018.05.083. (https://www.sciencedirect.com/science/article/pii/S0925231218306684)\n\nDepeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu. _FairGAN: Fairness-aware generative adversarial networks._ In 2018 IEEE International Conference on Big Data (Big Data), pages 570–575. IEEE, 2018.\n\nXu, Depeng, Wu, Yongkai, Yuan, Shuhan, Zhang, Lu, & Wu, Xintao. _Achieving Causal Fairness through Generative Adversarial Networks._ Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, (2019). \n\nBoris van Breugel, Trent Kyono, Jeroen Berrevoets, Mihaela van der Schaar. _DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networks_ In Neural Information Processing Systems (2021)\n\n\n\n\n", "summary_of_the_paper": "In their paper, the authors propose a novel generative adversarial network (GAN) which, more than realistic outputs, promotes fairness in the generative distribution. Specifically, when the training dataset is trademarked by some _unfair_ property (the authors' example being unevenly distributed gender or ethnicity), their proposed method-- a \"TVD based\" approach, which I will call TVD-GAN going forward --will rectify this in their generative distribution. The generative distribution is evaluated using an $L_2$ norm between the likelihoods of some samples given a reference distribution and the generative distribution ($\\mathbb{P}_{\\text{ref}}$ and $\\mathbb{P}_G$, respectively in eq.(1)).\n\nTVD-GAN minimises the \"total variational distance\" (TVD), through regularisation in eq.(5). As claimed on p.4, TVD \"offers the best trade-off performances in fairness and sample quality compared to other divergence measures\", as the results indeed seem to suggest. The main goal-- I believe --is to provide a more realistic sample using the larger training dataset, while still maintaining a fair distribution using the smaller reference dataset.", "summary_of_the_review": "The topic handled in this paper is important, and the contribution is interesting. There are some remaining questions I have regarding the paper in general (listed in my main review above). Given that there are some points the authors have to clarify further, concerning their method as well as related work, I believe a score of 5 is correct at this stage. \n\nHowever, I do believe the points I raise can be handled during a rebuttal period. Hence, I look forward to discussing more with other reviewers and the authors of this work. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "a2ezHo79Q-h", "reviewer": "Reviewer_VNCK", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "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": "Even though the paper studies an interesting topic and tries to address a vital problem, in its current form the paper is not ready to go under revision. The paper is poorly written. The authors may find below my major and minor comments.\n\n## Major Comments:\n\n1) The optimization problem in~(6) is not a three-player game. Two players that are maximizing are collaborating. Therefore, this is still a 2-player game. It would have been a 3-player game if the optimization problem was in the form of min-max-min, which is not the case.  \n\n2) Why does the TVD regularization offer the best trade-off performances in fairness and sample quality compared to other divergence measures?\n\n3) Algorithm 1 proposes to use stochastic gradient descent with mini-batch. Are the gradients of the objective are unbiased?\n\n4) I am not sure how does reference dataset is collected in real-life? How one can ensure that the reference dataset is balanced in real-life?\n\n5) I do not fully understand why increasing the size of the reference set has a detrimental effect on the performance of the framework?  Can you provide more additional insights into the explanations in Appendix C.2?\n\n## Minor Comments:\n\n1) I am not sure what does the first sentence of the contributions section means. Which key benefit feature is mentioned in~Roh et al.?\n2) The paper is not self-contained. What is the attribute classifier introduced in Choi et al. (2020)?\n3) The first paragraph of Section 3.1 is very badly written. I would suggest the authors improve the English of this sentence. ", "summary_of_the_paper": "This paper studies fairness in generative models. When the training data is biased, it may result in imbalanced generated samples. They assume that they have access to scarce reference samples that are balanced.\nThey measure the unfairness of the model through total variation and propose a fairness-aware model that is regulated by total variation distance between the generated samples (biased) and reference samples (unbiased). The authors further assume that the sensitive attributes are not available. Finally, they provide numerical experiments to demonstrate the performance of their proposed framework. ", "summary_of_the_review": "This paper is not ready to go under review. I think this paper can be further improved in terms of writing. Once, it is written at an academic level it can go under review. I would suggest the authors improve the presentation of their paper. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "VTXsZDSAtsA", "reviewer": "Reviewer_P5wy", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "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": "Overall, the paper is well written and easy to follow. The problem of studying fairness in generative models is significant. This paper also conducts an interesting approach by using total variation for regulating “fairness”. However, I have the following major comments.\n\n1. The definition of fairness adopted in this paper is unclear to me and needs further discussion. In particular, I have the following main concerns. \n\n(1) The definition relies on an attribute classifier. What if this classifier itself is biased? \n\n(2) In the same vein, it seems that generative models may produce unrealistic images which are wrongly labeled as female/male by the attribute classifier. How to deal with this situation?\n\n2. My second concern is the comparison with benchmarks in the experiments. In Table 1, the proposed method seems to have a higher discrimination score than Choi et al when the reference size = 25%. Hence, it is unclear if the performance improvement in this paper is significant. \n\n3. The authors observe that “the fairness performance exhibits slight degradation with an increase in the reference set size” in the experiments. However, the explanation given in Appendix C.2 is unclear to me. \n\n4. The authors compare the total-variation-based regularization with other regularization techniques through experiments and demonstrate the results in Table 3. Can the authors provide more implementation details? In particular, which ground metric (i.e., cost function) do they use for the Wasserstein distance? I guess a typical choice is the L2 loss but in the setting of measuring distance between facial images, L2 loss does not seem to be an optimal solution. There are a number of works on ground metric learning for the Wasserstein distance. I wonder what the author did.\n\n#####################\nAfter rebuttal\n#####################\nI would like to thank the authors for providing a detailed response to my previous comments. However, I still find the fairness definition adopted in this paper a bit strange, especially because it relies on a pre-trained attribute classifier. Hence, I will keep my score unchanged.", "summary_of_the_paper": "This paper proposes a new generative model with “fairness” constraints by adding a total-variation regularization. The authors conduct several experiments and compare them with benchmark methods. ", "summary_of_the_review": "The definition of fairness adopted in this paper needs further discussion.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper is concerned with fairness in the generative setting, specifically the setting in which various groups have very different sizes, and are therefore treated disproportionately by the model, with the group memberships further being unknown.

The reviewers generally agreed that the setting was interesting and important. However, they were critical of the writing quality, significance, and quality of the theoretical contribution.

The authors made significant improvements in the review period, and while these were not quite enough to satisfy enough reviewers, opinions clearly changed in a positive direction during the discussion period. Future changes motivated by the existing reviewer concerns should significantly improve the paper.
Decision: Reject