Breaking the Spurious Causality of Conditional Generation via Fairness Intervention with Corrective Sampling
Authors: Junhyun Nam
Sangwoo Mo
Jaeho Lee
Jinwoo Shin
Venue: Accepted by TMLR ()

Abstract: Trying to capture the sample-label relationship, conditional generative models often end up inheriting the spurious correlation in the training dataset, giving label-conditional distributions that are severely imbalanced in another latent attribute. To mitigate such undesirable correlations engraved into generative models, which we call spurious causality, we propose a general two-step strategy. (a) Fairness Intervention (FI): Emphasize the minority samples that are hard to be generated due to the spurious correlation in the training dataset. (b) Corrective Sampling (CS): Filter the generated samples explicitly to follow the desired label-conditional latent attribute distribution. We design the fairness intervention for various degrees of supervision on the spurious attribute, including unsupervised, weakly-supervised, and semi-supervised scenarios. Our experimental results show that the proposed FICS can successfully resolve the spurious correlation in generated samples on various datasets.

Sangwoo Mo Published in Transactions on Machine Learning Research (07/2023)
Breaking the Spurious Causality of Conditional Generation via Fairness Intervention with Corrective Sampling
Junhyun Nam
junh. womh.nam@@smssngg.com
Samsung Advonced Institute of Technology (SAIT)"
sumo@kaist.aacm kc.
Korea Advanced Institute of Science & Technology (KAIST)
Jaeho Lee Pohang University of Science ond Technology (POSTECH)
dechollee@postech.ooo
Jinwoo Shin
jnwoos oc.kr
Korea Aduanced Institute of Science & Technology (KAIST)
Reviewed on OpenReview: https: // openreview. net/ forun? id= W4zJuLuI7
Abstract
To capture the relationship between samples and labels, conditional generative models often inherit spurious correlations from the training dataset. This can result in label-conditional distributions that are imbalanced with respect to another latent attribute. To miligate this issue, which we call spurious causality of conditional generation, we propose a general two- step strategy. (a) Fairness Intervention (FT): emphasize the minority samples that are hard to generate due the spurious correlation in the training dataset. (b) Corrective Sampling (CS): explicitly filter the generated samples and ensure that they follow the desired latent attribute distribution. We have designed the fairness intervention to work for various degrees of supervision on the spurious attribute, including unsupervised, reakly-supervisee and semi-supervise scenarios. Our experimental results demonstrate that FICS can effectively resolve spurious causality conditional generation across various datasets.
1 Introduction
Deep generative models are capable of producing syuthesized visual content that closely resembles the training data, but sometimes in undesirable ways. Similar to classifiers, generative models can be affected by dataset bias (Torralba & Efros, 2011; Buolamwini & Gebru, 2018) inherited from the training set, resulting in significantly fewer samples of minority groups compared to majority group samples (Zhao et al., 2018; Salminen et al., 2020; Jain et al., 2021). This group imbalance is usually amplified in the generated dataset compared to the original training dataset, as noted by Tan et al. (2020). The exacerbated imbalance in generated samples can lead to various fairness issues in downstream applications, such as umderrepresentationn of minority groups in content crcation (Choi al., 2020; Tan al., 2020; Jalal et al., 2021) or harm to the classifier trained with generated samples (Xu et al., 2018; Sattigeri et al., 2018; Xu et al., 2019).
Conditional generative models face different type of fairness concern due to the association of the input condition and spurious attributes in data generation. Specifically, the input-conditional distribution of generated data may be imbalanced with respect to some latent attribute, replicating the spurious correlation present in the training dataset. For instance, a BigGAN (Brock el al., 2019) model trained on the CelebA (Liu et al., 2015) dataset with the "blondness" attribute as a class label may generate severely imbalanced samples in terms of "gender," " with the vast majority of samples generated under the blond class being female (soc
Work done KAIST

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Training Dataset
Conditional GAN
Generated Samples
Temale
male
do("blond")
do("blond") causes "female"?
nore nors-blona balordd
Celebé training set
51.7%
48.3%
brin
generate
Ialond
e
94.3%
5.7%
Figure 1: Motivation. Conditional generative models trained on datasets with spuriously correlated attributes may generate severely imbalanced samples when conditioned on the correlated attribute. This behavior is particularly problematic in conditional generation, as there is a causal relationship between the act of conditioning (intervention) and the distribution of generated samples, which can amplify biased beliefs held by users. We lackle this problem, which we refer to as spurious causality of conditional generation.
Figure 1). It has also recently been reported that popular text-to-image generation models exhibit gender and cultural biases (Barr, 2022). When prompted with specific occupations like "childcare worker," the generated images highly imbalanced in terms of gender and race.
The reproduction of spurious correlations by conditional generative models raises deeper fairness concern compared to imbalances in unconditional generative models. Input conditioning (i.e., providing the class label "blond") can be seen as an intervention from the perspective of counterfactual causality (Pearl, 2010). Once a spurious correlation is incorporated into conditional generative models, changing the input (intervention) leads to change in the distribution of spuriously correlated latent altributes of the conditionally generated samples, forming a cause-effect relationship. This false sense of causation in conditional generation, which we refer to spurious causality of conditional generation, is significant ethical thrcat, this misconception is likely to propagate when using generative models (Mariani et al., 2018).
To the best of our knowledge, no previous work has aimed to address the spurious causality of conditional generation. Previous studies on fair generative models have focused on addressing majority bias by either (a) reducing the discrepancy from data distribution (Grover et al., 2019; Mo et al., 2019b; Lee et al., 2021; Yu et al., 2020; Humayun et al., 2022) or (b) following the desired fair distribution specified by explicit labels of sensitive attributes (Tan et al., 2020) or reference set of desiderata (Choi et al., 2020). A naive solution to address the issue could be to extend the previous work majority bias by applying it to each condition. Instead, we propose to leverage the conditional structure to tackle the problem.
Contribution. We propose a general framework, coined fairness intervention with corrective sampling (FICS), to mitigate the severe yet underexplored problem of spurious causality in conditional generative models. FICS consists of two components. (1) Fairness intervention (FI): emphasize samples suffering from the spurious correlation in the datasct the training phase. (2) Corrective sampling (CS): explicitly filter samples after the training phase that the trained generator follows the desired distribution.
FICS provides unified approach to resolve spurious causality of conditional generation for wide range of scenarios, with various degrecs of supervision available on the latent attributes and various target ratio of latent attribute distributions. We focus on the task of generative adversarial networks (Mirza & Osindero, 2014, cGANs) and apply FICS on unsupervised, weakly supervised, and semi-supervised setups. The goal to generate the conditional distributions whose latent attribute distribution is either identical to that of the training dataset or some desired fair distribution.
image generation using conditional
Our experiments show that FICS is an effective remedy for spurious causality of conditional generation. In particular, we train BigGAN (Brock et al., 2019) on CelebA (Liu el al., 2015) and Waterbirds (Sagawa et al., 2020), and ResNetGAN (Gulrajani et al., 2017) for Colored MNIST (Arjovsky et al., 2019). FICS consistently improves upon the conditional extensions of previous fair generation methods in both unsupervised and supervised scenarios, in terms of the sample quality and the minority attribute occurrence ratio.
We the "spurious causality" an analogy to the term "spurions correlation" used classification contexts.
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2
Related Work
Generative models. Generative models have synthesized high-fidelity samples in various domains, c-g-t image (Karras et al., 2021), video (Yu et al., 2022), and language (Brown et al., 2020). Numerous methods have been proposed, including generative adversarial networks (Goodfellow et al., 2014, GANs) and diffusion models (Dhariwal & Nichol, 2021). Here, GANs are known to merit both sample quality and speed (Xiao et al., 2022). In addition, conditional GANs (cGANs) utilize additional supervision such as class labels (Mirza & Osindero, 2014), lext descriptions (Ramesh et al., 2022; Ding et al., 2022), or reference images (Zhu el al., 2017; Mo et al., 2019a) as input conditions to extend the applicability further. Specifically, cGANs control the synthesized outputs and improve sample quality by restricting the output space for each condition. Despite their utility, we find that cGANs often suffer from severe yet underexplored fairness issue. We investigate this issue, coined spurious causality of conditional generation, and propose a remedy for it.
Fairness in generative models. The fairness issue in generative models has received considerable attention due to its practical impact. Most prior work on fair generation focuses on addressing the majority bias, which is the tendency of generative models to learn the imbalances inherited from the training dataset and is often amplified during training (Tan et al., 2020). One line of work considers an unsupervised setup, where the group identities of samples are unknown. Approaches in this direction handle bias by using discrepancy metrics corrected with density ratios as the optimization objective (Grover et al., 2019; Mo et al., 2019b; Lee et al., 2021) or by imposing regularizations to enforce a uniform learning of the data manifold (Yu et al., 2020; Humayun et al., 2022). Another line of work learns the fair distribution in a supervised manner (Xu et al., 2018; Sattigeri et al., 2018; Xu et al., 2019; Tan et al., 2020; Choi et al., 2020). However, previous works only focus on the majority bias, and the spurious correlation over multiple attributes has not been investigated.
Spurious correlation of classifiers. Spurious correlations in training datasets can cause classifiers to perform poorly on distt--distiibution test sets where these correlations do not hold (Geirhos et al., 2020). To mitigate spurious correlation, several works have been proposed, such as invariant learning (Arjovsky et al., 2019) and distributionally robust optimization (Sagawa et al., 2020), but these methods require explicit supervision on the spuriously correlated attribute, which is often expensive and time-consuming to obtain. Weaker forms of supervision, such as fair validation sets (Bahng et al., 2020; Nam et al., 2020; Creager et al., 2021; Liu et al., 2021), a small set of attribute-annotatee samples (Nam et al., 2022; Sohoni et al., 2021), or pre-trained laiguale models (Kim et al., 2023), have been explored to identify and mitigate poorly performing samples. Specifically, this line of work focuses on identifying and mitigating poorly performing samples. Our method shares the same philosophy as these debiasing methods for spurious correlation but instead focuses on tackling the spurious causality issue in conditional generative models.
Casuality in generative models. While our paper focuses on achieving fairness between multiple attributes in the vision domain, research has also been conducted in the tabular domain with a similar focus. In the tabular domain, each data point typically has all attribute labels, including the sensitive attribute of interest, making it easier to directly observe all attributes (Xu et al., 2018). Moreover, some research assumes prior knowledge of the causal structure among the attributes and leverages the parent attribute to generate its child attribute (Xu et al., 2019; van Breugel et al., 2021). However, our study addresses more flexible scenarios with varying levels of supervision on the sensitive attribute.
Relation to counterfactual fairness. Our framework shares some similarities with counterfactual fairness (Kusner et al., 2017) in terms of its ability to conduct counterfactual analysis on specific attributes. However, our framework performs the do-operation on the class attribute and focuses on the distribution of the sensitive altribute in the generated images. In contrast, counterfactual fairness aims to achieve fair prediction by performing the do-operation on the sensitive attribute. Therefore, the methods used to achieve counterfactual fairness are not directly applicable to addressing the problem of interest in our framework.
Spurious correlations beyond class labels. While we focus on the class altributes in this paper, spurious correlation also appears in different domains, e.g., keyword bias (Moon et al., 2021) or scene bias (Mo et al., 2021). It can be problematic for generative models using such conditions, c.g., text-to-image models can be biased to some keywords. Here, we remark that our principle of leveraging the spurious correlation of classifiers to mitigate the spurious causality of conditional generative models can be applied in general.
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Y
A
Y
Z
X
X
cGAN
data generating process
user's perception
A
user's view
(a) data generating process
(b) spurious cansality of cGAN
Figure 2: Causal graphs. Although there is no causal relationship between the class attribute Y and the sensitive attribute A, conditioning the class to generate data can impact the sensitive attribute of the generated data. As result, users cGANs who observe the generated data and its sensitive attribute may falsely perceive that manipulating the class attribute alters the sensitive attribute of the generated data, long spurious correlation exists between the class attribute and the sensitive attribute.
3 Spurious Causality of Conditional GAN
Conditional generative models aim to approximate the ground-truth distribution pdata(xly) of data X conditioned on label E y using model distribution (xly). For brevity, assume that the models are conditional generative adversarial networks (Mirza & Osindero, 2014, eGAN), cGAN trains a generator G: (z + x, which generates data a conditioned on a latent variable ~ p(=) drawn from a fixed prior distribution p(z), and a label y ~ (y). This procedure defines the generator distribution Pgen (zly). Simultancously, cGAN trains a discriminator D (z. y) + r E (0, 1), which predicts whether the data-label pair (x, 3) comes from the data distribution (r 1) or the generator distribution (r = 0). Formally, the training objective of cGAN is:
LEGAN (G, D) = Eyr-pans (aae))))))))) log D(r, y) + Essp(e) log(1 ((G((..))
We consider training eGANs on a training dataset with spurious correlations. Specifically, we assume that there is a sensitive attribute a(x) E A associated with the data x, which correlated but not causally related to the label y. We observe that the model distribution Pgen (xly), when naively trained, learns to replicate the spurious correlation present in the training dataset. More specifically, we define the label-conditional probability of sensitive attributes for the model distribution (xly) as follows:
Pgen (aly) = / I(a = a(x)) Pgen (xly) dr
and define Pdata (aly) similarly. We observe that the model distribution (xly) is trained in a way that Pgen (an(a)y) is significantly more imbalanced than (aly)
Such exaggerated reproduction of spurious correlation by conditional generative models is big problem, the model itself now provides causal link between the act of "conditioning the label" and the "sensitive attribute of the generated sample." Indeed, the model can be viewed black-box on which counterfactual experiment can be performed by intervening on the label with everything else fixed (e.g., latent variable =). Such analysis will lead to a conclusion that there exists a causal structure (Pearl, 2010) between the label and the spurious attribute of the generated samples.
This problem, which we call spurious causality of conditional generation, is potentially more problematic than the spurious correlation learned by classifiers. Namely, conditional generative models propagate
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Falmess Intervention (depends supervision)
Conditional GAN
Generated Samples
Corrective Sampling
Filtared Samples
(depends supervision)
do("blond")
Unsupervised Blased classifier
Weakll-superrised Reference dataset
Intervene
generate
evaluste
resample
Semi-supervised Aliribute label
Figure 3: Method overview. The proposed FICS is a general two-stage framework that aims to address the spurious causality of conditional generation. It involves fairness intervention during the training phase to encourage the generator to synthesize minority samples (FT), followed by corrective sampling during the generation phase (CS). The specific steps depend on the lype of fairness supervision.
harmful stereotypes, such as the belief that the attribute "female" is caused by being "blond," to users who directly observe the effect of providing conditions to the generated samples.
Our goal address the spurious causality of conditional generative models by learning a balanced conditional distribution (xyy()ly) that yiclds a desired sensitive attribute distribution Pgen(aly). The desired distribution may vary depending on the user intention:
(a) Approzimating the data distribution Palt) As previously discussed, standard GAN training often yields more imbalanced model distribution Pgen (aly) than the data distribution (aly) Our aim is to learn model distribution that closely approximates the data distribution, i.e., Pgen (ale(alg) Paata Paata(aly).
(b) Approzimating fair distribution Ptair (a)r(a Our aim is to approximate a sensitive attribute distribution that aligns with specific fairness criteria. For instance, may enforce the attribute to follow fair distribution, i.c., (aly) ~ (a)ir(a) for some desired (a)i
In addition to achieving desired (aly), we also consider achieving a fair generative quality for each label as an auxiliary goal. For this purpose, we also report the (fair) Intra-FID for the compared methods.
4 Breaking the Spurious Causality of Conditional GAN
4.1 Overall framework
We describe the proposed FICS (Figure 3), a general strategy for mitigating the spurious causality of conditional generation. In essence, FICS comprises two mechanisms to conditionally synthesize samples with desired attribute distributions, with each component being designed based on the level of supervision available on the latent attributes.
Fairness Intervention (FI): Encourage the generator to synthesize minority samples during the training phase. The specific intervention rules depend the degree of supervision available the latent attributes.
Corrective Sampling (CS): Apply rejection sampling on the synthesized samples during the generation phase. The criteria for rejection depend on the desired goal, follow the data distribution or fair distribution.
We consider two different scenarios and give concrete versions of FICS for each case. First, an unsupervised setup aims to recover the data distribution by fixing the bias of the current model. Second, a supervised setup aims to follow the desired fair distribution described by additional supervision, such as a reference set. of desired distribution or labels of sensitive attributes. The following subsections illustrate how design the fairness intervention and corrective sampling for unsupervised and supervised scenarios.
4.2 Unsupervised: Learning the data distribution
In the unsupervised scenario, we aim to reduce the bias in the generator by encouraging it to generate more samples that are likely to be mispredicted by a biased classifier. This approach is motivated by the
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Classifier Is "blond"?
blbnd camples
100
70th
Losg percentle rank aal
Loss percentile rank a among all blond samples
60
male eyeglasses
20th
smille
compute classification loss
Loss percentlle rank among blond male samples
Loos percentilc minority samples
Figure Observation. The relationship between the biased classifier and the generator is depicted by the percentile ranks of the classification loss of generated samples, with the x and y coordinates of point representing the percentile rank of its classification loss among blond minority samples and all blond samples, respectively. For instance, sample with a loss at the 20th percentile among blond male samples has a loss at approximately the 70th percentile among all blond samples, indicating that blond male samples typically have higher classification loss among all blond samples. The attributes of "gender" and "wearing eyeglasses" exhibit spuriously correlation with "blondness," " while the attribute of "smiling" does not.
observation that there is a strong correlation between the misprediction of the biased classifier and the generation frequency of the biased cGAN, We first introduce this observation and then describe how to adjust the training and inference of the cGAN to mitigate this bias.
4.2.1 Observation
Our observation (Figure 4) suggests the usefulness of having a separately trained classifier to mitigate the spurious correlation of conditional generative models. Specifically, we train a classifier and a conditional generative model on the CelebA (Liu et al., 2015) datasel and focused on the relationship between the "blondness" attribute and the "gender," " "wearing eyeglasses," " and "smiling" attributes. When conditioned blond, the dataset is severely imbalanced with respect to the gender and wearing eyoglasses attributes. Unlike the other two attributes, there is no clear correlation between blondness and smiling.
From the trained model, we observe that the generated samples classified as the minority group are more likely to have a higher classification loss. For example, given a blond-conditionally generated sample, a sample with a higher classification loss more likely to be male. Specifically, we observe the percentile rank of the given sample among all blond samples and specific blond male samples. For instance, a sample having the 20th percentile among blond male samples has a loss with around the 70th percentile among all blond samples. We observed a similar pattern for the "wearing eyeglasses" attribute, which is spuriously correlated with the "blondness" attribute. In contrast, the "smile" attribute, which has no clear correlation with "blondness" attribute, does not show distinct loss distribution for all blond samples and blond and no smile samples. This observation suggests that the classification loss of generated samples may contain useful information to identify minority group samples, even in cases where the generator and classifier are trained separately and receive no supervision about the correlated attributes (e.g., "gender," "wearing eyeglasses").
4.2.2 Training and sampling
Fairness intervention. Motivated by our observation, we intervene in the generator G to encourage the synthesis samples that are difficult for the biased classifier fo x + y to classify. These samples are likely to have minor attributes, i.c., low p(aly). To achieve this, we apply a regularizer that encourages the generator minimize the (sum of) cross-entropy loss over the wrong targets y' + y, rather than maximizing the correct target to ensure the convexity. This approach encourages the generator generate minority samples

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that are hard to classify. Formally, our objective is:
min max LEGAN + A Σ (E(L(G(,..))))))) 8'Zy
(1)
where À is a weight for the regularizer and CE denoles the cross-entropy loss. We simply set = 0.01 since it worked well for all our experiments. We pretrain the classifier fo and fix it for the training of cGAN
Corrective sampling. In the unsupervised scenario, the regularizer used in the first step can distort the training distribution. Therefore, we use discriminator rejection sampling to correct the distribution of the generated samples. Although the regularizer in Eq. (1) increases the weight of the minority samples, it does not guarantee that the generative models follow the data distribution. Thus, apply correction sampling to recover the original data distribution.
Rejection sampling is a commonly used technique to sample from a probability distribution p when the ratio p/q is known and sampling from y is feasible. This technique involves sampling x from q and accepting the samples with a probability proportional p/q. This procedure is equivalent to sampling from p. In our scenario, we sample from Pgen and accept the samples with probability proportional to Pdats
which is
Pone
equivalent to sampling from Pdata- We estimate the density ratio using an optimal discriminator D for given generator G' following the discriminator rejection sampling Azadi et al. (2018). In practice, use the discriminator D of cGAN as proxy for D
Peata
Peata
4.3 Supervised: Learning the fair distribution
In the supervised scenario, we intervene in the generator to upsample the minority samples described by a fair reference set (weakly--upervised) or labels sensitive attributes (semi-supervised). We illustrate how to train the cGAN given each form of supervision.
4.3.1 Weakly-supervised
Fairness intervention. Assuming that we have a reference set See representing the desired fair distribution,
where (+ly) is the empírical distribution of Sief; we intervene in the generator to follow the reference set using the density ratio between the reference and data distributions. To achieve this, train binary classifier fret x - E (0, 1) to distinguish whether a sample belongs to the reference (r= or data (r = 0) distributions, similar to the density ratio trick used in GANs. The (unnormalized) resampling probability is given by:
w(x) = (()re(()) = 1) Mp(frer =
(2)
where M is some large constant to ensure w(x) < During training, we draw samples from P'asta (œ) w(x) W Pdata (z), where a normalizing factor that makes Plaata (z) a probability density function.
Corrective sampling. We train an additional discriminator D' which responsible for distinguishing between the reference and generator distributions. Once trained, we use rejection sampling (similar to the unsupervised scenario) to correct the samples to align with the desired fair distribution Ptai(
4.3.2 Semi-supervised
Fairness intervention. Assuming we have set of samples with sensitive attribute labels :: {(z, v, a}} and set of unlabeled samples 24 == {(x. v)}, we first train an attribute classifier fa x + using the labeled data C, which can also leverage the unlabeled data U using semi-superrvsedd learning techniques. Using this classifier, we estimate the population of each group g = (y. a) over all samples, constructing the psoudo-labeled datasct D L LUú, where i == (æ, y, for (x.y) U and â = fx). To balance the occurrence of each group, we intervene with the generator by resampling the training data with a probability inversely proportional to the group population. Specifically, the (unnormalized) resampling probability is
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given by:
w(x)= = H('' y', a') E D (v', = (v, fa())))
(3)
As in the supery-s scenario, draw samples from Paata (x) w(x) (z) during training.
Corrective sampling. Similar to the unsupervised case, we correct the generator distribution to match the desired fair distribution ptair (aly) via rejection sampling. However, we cammot simply reuse the discriminator D from cGAN since it is trained with a biased data distribution that resampled by Eq. (3). Thus, we train an additional discriminator D' to estimate the density ratio between the unbiased data and generator distributions, using D' to recover the original data distribution P After recovering (alts we apply another rejection sampling stage to control the desired group ratio Plair ptai(aly) using the predicted attribute fa()). This two-stage rejection sampling approach corrects the samples to follow the desired fair distribution.
5 Experiments
5.1 Experimental setup
Datasets and models. We evaluate our framework on the CelebA (Liu et al., 2015) dataset and the Waterbirds (Sagawa et al., 2020) dataset. The CelebA dataset consists of 162,770 face images of celebrities and has 40 attribute annotations. We select two attributes that are spuriously correlated, one as an input condition and the other to evaluate the occurrence ratio of the minority attribute. The Colored MNIST dataset (Arjovsky et al., 2019) consists of 40,000 digit images with binary labels (0 for digits 0-4, for digits 5-9). Each digit is colored either red or green to impose a spurious correlation between binary labels and colors. We do not flip the final label, unlike the original construction. The Waterbirds dataset consists of 4,795 bird images with two types of birds (waterbirds and landbirds) on two types of backgrounds (water and land); bird type is used as an input condition, and the background is used to evaluate the occurrence ratio of the minority attribute. In all our experiments, we use BigGAN (Brock et al., 2019) for the conditional generative models and ResNet-50 (He et al., 2016) for the classifiers. For Colored MNIST experiments, we use ResNetGAN (Gulrajani et al., 2017) for the conditional generative models and 4-layer convolutional network for the classifiers.
Evaluation metrics. We evaluate the conditional generative models in two aspocts: (a) sample quality, i.e,, p(rly), and (b) attribute balancing, i.e,, p(aly). For (a) in unsupervised scenarios, we use the ra-class Fr'echet Inception distance (Intra-FID) (Heusel et al., 2017), which measures both sample quality and diversity of the conditional distribution. Specifically, Intra-FID measures the distance between the feature distributions of the data and generated samples. For supervised scenarios, we use a fair version of Intra-FID (Fair Intra-FID), which measures the distance between the fair and generated samples. For (b), we report the occurrence ratio of the minority (or sensitive) attribute, which should follow the ratio of the data and fair distributions for unsupervised and supervised scenarios, respectively. We also report the estimated occurrence ratio for the teainiing/refeeeneee dataset of the classifier, as the prediction can be under- (or over-) estimated.
Baselines. We extend the prior (unconditional) fair generation methods as the baselines for the fair conditional generation, i.c., modify their formula from p(x) to p(x, y). We consider three representative methods: for unsupervised (Tee et al., 2021), weakly-supervised (Choi et al., 2020) scenarios, and supervised (Tan et al., 2020), respectively. For the unsupervised method, we consider Dia-GAN (Lee ct al., 2021), which resamples training data based on an estimated log-density ratio to emphasize minority samples. For the weakly supervised method, consider Choi et al. (2020), giving different weights for each sample based on the density ratio classifier trained to distinguish the training dataset and the reference dataset. For the supervised method, we consider FairGen (Tan et al., 2020), a latent variable modification method based on the attribute classifier trained on the latent. variable space. See Appendix B for a detailed explanation.
Computation time. Training of the original BigGAN on CclebA for 200k itcration takes 30 hours on a single TITAN Xp GPU and 40 CPU cores (Intel Xeon CPU E5-2630 v4). FICS takes a longer training time due to additional classifier; takes x 1.6 times for our training setup.
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Table Unsupervised results (CelebA). Comparison unsupervised fair conditional generation methods under CclebA, using (a) "blondness" (b) "wearing lipstick" attributes class condition. We report the Intra-FID (4) and minority occurrence ratio (%) of generated samples. We report the minority occurrence ratio of the training dataset and the estimated values by attribute classifier. Our method achieves the best of both worlds: almost matching the minority occurrence ratio of the original dataset (estimated by the classifier) while producing high-quality samples. The lowest intra-FID and the closest minority occurrence ratio to the estimated are marked in bold.
(a) Blondness
Intra-FID (L)
Minor in Blond (%)
Blond
Non-blond
Male
Eyeglasses
No lipstick
Dataset
5.72
1.66
18.78
Estimated
5.85
1.85
17.61
Unsupervised
cGAN (Mirza & Osindero, 2014)
1.86
1.64
3.97
0.88
11.04
Dia-GAN (Lee et al., 2021)
1.88
1.84
5.06
1.49
14.10
FICS (ours)
1.78
1.38
6.13
1.90
16.34
(b) Wearing lipstick
Intra-FID (L)
Minor in Lipstick (%)
Lipstick
No lipstick
Male
Eyeglasses
Hat
Dataset
0.58
1.05
1.25
Estimated
0.80
1.21
1.87
Unsupervised
cGAN (Mirza & Osindero, 2014)
1.36
1.67
0.28
0.76
1.04
Dia-GAN (Lee et al., 2021)
1.36
1.66
0.30
0.86
1.09
FICS (ours)
1.24
1.41
0.33
1.02
1.53
Table 2: Unsupervised results (Colored MNIST, Waterbirds). Comparison of unsupervised fair conditional generation methods under (a) Colored MNIST using "digit" class condition and (b) Waterbirds using "bird type" as a class condition. We report the average value over classes for Colored MNIST and the values of each class for Waterbirds. The lowest intra-FID and the closest minority occurrence ratio to the estimated are marked in bold.
Colored MNIST
Waterbirds
Landbirds
Intra-FID (4)
Minor (%)
Intra-FID (1)
Minor (%)
Intra-FID (1)
Minor (%)
Dataset
20.00
5.03
5.00
Estimated
20.00
8.72
8.96
Unsupervised
cGAN (Mirza & Osindero, 2014)
10.31
0.16
44.68
5.52
24.73
4.69
Dia-GAN (Lee al., 2021)
10.20
01.55
44.32
5.54
24.80
4.66
FICS (ours)
2.78
23.50
41.80
6.75
23.46
4.89
5.2 Unsupervised experiments
We first demonstrate the results in an unsupervised scenario, where the goal is to reduce the discrepancy between the generator and data distributions. For CelebA, we use "blondness" and "wearing lipstick" as input conditions. For each condition, we choose (male, eyoglasses, no lipstick) and (male, eyeglasses, hat) corresponding minority attributes. We report Intra-FID and minority occurrence ratio (compared to the data distribution) of the baselines and FICS in Table and Table 2.

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Published in Transactions on Machine Learning Research (07/2023)
Table 3: Supervised results. Comparison of supervised fair conditional generation methods where "blondness" attribute used as class condition. We report the Fair Intra-FID (J) and minority occurrence ratio (%) of generated samples. The lowest fair intra-FII and the closest minority occurrence ratio to the estimated are marked in bold.
Targel Male ratio: 30%
Targel Male ratio: 50%
Fair Intra-FIDD (4)
Occurrence of Male in Blond (%)
Fair Intra-FID (4)
Occurrence of
Blond
Blond
Male in Blond (%)
Reference
30.00
50.00
Estimated
28.60
47.15
Weakly-superviseed
Choi et al. (2020)
10.71
7.60
10.70
18.34
FICS (ours)
10.36
15.65
10.24
27.04
Semi-supervised
FairGen (Tan et al., 2020)
12.71
29.54
11.98
49.76
FICS (ours)
10.56
25.72
11.68
47.11
(a) Vanilla BigGAN (Brock al., 2019)
(b) FICS (ours)
Figure 5: Visualization. Blond-conditionally generated samples from the original BigGAN and our method, under the semi-supe seni-supervised scenario with target male ratio of 50%. Our method creates diverse blond male images, unlike the original BigGAN is biased toward female images.
In the CelebA dataset, the vanilla cGAN suffers from the spurious causality issue, siguificantly amplifying the imbalance of minority attributes, e.g., only creates 3.97% of blond males while the original dataset contains 5.85%. Dia-GAN relieves this amplification and increases the minority occurrence; however, it often decreases the Intra-FID, i.e., losing the diversity FICS, achieves the best of both worlds: it improves the Intra-FID of all considered cases and recovers the minority occurrence of the data distribution, e.g., producing 631% of blond males, almost matching the 5.85% of the training dataset.
cost of the boosted minority. In contrast, our proposed method,
We observe a similar lendency the Colored MNIST and Waterbirds datasels. In the Colored MNIST dataset, both vanilla cGAN and Dia-GAN fails generate sufficient number of minority group samples. In contrast, FICS achieves minority occurrence ratio close to the training dataset. In the Waterbirds datasct, the vanilla cGAN suffers from the spurious causality issue, providing only 5.52% and 4.69% of minority samples of waterbirds and landbirds, respectively. Dia-GAN shows similar results to the vanilla cGAN, resulting from the almost identical sample weights. FICS shows improved Intra-FID and the closest minority occurrence to that of the training set for both classes.
5.3 Supervised experiments
We demonstrate the results for the supervised scenario, where the goal is follow fair distribution. We conduct experiments the CelebA dataset, using "blondness" as input condition and "gender"
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Table 4: Ablation studies. Comparison of (a) unsupervised and (b) semi-supervised fair conditional generation methods with or without cach component of FICS. For (b), we use "blondness" attribute used as a class condition and 50% male in blond as the desired distribution. The lowest fair intra-FID and the closest minority occurrence ratio to the estimated are marked in bold. Both fairness intervention (FT) and corrective sampling (CS) benefits.
(a) Unsupervised
(b) Semi-supervised
Int (4)
Male in Blond (%)
Fair Intra-FID (4)
Male in Blond (%)
cGAN
1.86
3.97
13.16
3.97
Fl only
1.80
6.02
12.30
18.23
CS only
1.85
5.02
12.91
38.49
FICS (ours)
1.78
6.13
11.68
47.11
sensitive attribute. Recall that the original data distribution has only a few blond males; we aim to learn a fair distribution that produces (30%, 50%} of male images conditioned on blond. We report the Fair Intra-FID and minority occurrence ratio (should be similar to the desired fair distribution) of the baselines and our proposed framework. Table 3 shows the results on weakly- and semi-supervised scenarios: we will discuss the details and observations in the remaining section.
superve- We use the same 4,000 samples (but without sensitive altribute annotations) as the reference set for the weakly-supervised setup. We compare our method with Choi et al. (2020), and use the same binary classifier that distinguishes the reference and data distributions for both methods; recall that we resample training data with the classifier while Choi et al. reweights the loss. The results show that our method outperforms Choi et al. for all considered cases, both Fair Intra-FID (i.e., generation quality) and minority occurrence ratio (i.e., attribute balancing). Here, both methods still have a gap with the semi-supervised methods since they rely the weaker form of supervision. Still, remark that our method significantly reduces the gap between sumi-supervised and of the minority occurrence ratio.
scenarios, particularly in terms
Semi-supervised. We use 4,000 labeled (sensitive attribute) samples with the same attribule occurrence ratio the desired fair distribution for the semi-supervised setup. We compare our method with FairGen, and use the same attribute classifier for both methods, which is trained by semi-supervised learning technique called FixMatch (Sohn et al., 2020). The results show that our method shows better Fair Intra-FID than FairGen, while both methods show comparable minority occurrence ratio. Recall that FairGen modifies the prior distribution to generate minority samples; it distorts the prior to the low-density area of the original Gaussian distribution. Thus, FairGen often generates low-fidelity samples (though satisfying the desired altribule), leading to the lower FID.
Visualization. Figure visualizes the generated samples conditioned on blond from vanilla BigGAN and debaised one by FICS. We use the semi-supervised version with a target male ratio of 50% for our method. Unlike the original BigGAN mostly creates female images, our method creates diverse blond male images.
5.4 Ablation study
We conduct ablation study to the contribution of each component in our semi-supervised method. The result is shown in Table 4. With fairness intervention during the training (based on pscudo-labeling and group balancing), we could observe gain in both fair intra-FID and minority occurence ratio, still there exists large gap between the occurrence ratio achieved and the desired occurrence ratio. With corrective sampling after the training, we could obscrve reasonable occurrence ratio for male, still there room to be improved. With full components of our semi-supervised method, we can see further improvement in both minority occurrence ratio and fair intra-FID..
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6 Conclusion
We highlight the issue of spurious causality of conditional generation, important yet underexplored fairness problem in conditional generalion. To address this issue, propose the FICS framework, which leverages intervened training and corrected sampling, We hope that our work inspires further research in spurious correlation and generative models, particularly the spurious causality in text-to-image generative models.
Broader Impact Statement
Although we alleviate some spurious causality of conditional generative models, the model can still retain unrecognized biases. Since the algorithmic debiasing cannot remove all possible biases from the model, the users should carefully check the model on their usage.
Acknowledgments
This work was partly supported by Institute of Information & communications Technology Planning & Evaluation (ITTP) grant funded by the Korea government (MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program (KAIST); No. 2022-0-00184, Development and Study of AT Technologies Inexpensively Conform to Evolving Policy on Ethics), Korea Evaluation Institute of Industrial Technology (KEIT) grant funded by the Korea government (MOTIE), and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2022R1FLA 1A10700677.
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A Implementation details
A.1 Classifiers
Network architectures. For CelebA and Waterbirds, we use the torchvision implementation of ResNet-50 starting from pereereee-rellriineed weights. For Colored MNIST, we use 4-layer convolutional network with channel sizes of 32, 32, 64, 64, kernel size of 5, 3, 3, 3, and stride 2, 1, 2, 1.
Biased classifiers for FICS. It is well-known that ERM trained classifier trained with a biased dataset inherits spurious correlations existing in the dataset (Sagawa et al., 2020; Liu et. al., 2021). Thus, did not perform any additional technique to amplify the spurious correlation. To handle class imbalance in the dataset, we use group DRO (Sagawa et al., 2020) to ensure low worst-class error. We use the SGD optimizer with a learning rate of 0.001, momentum 0.9 for 100 epochs with batch size 64. In addition, we use l regularization of 0.0005 and early stopping for the best validation accuracy.
Attribute classifters for evaluation. For the attribute classifiers for evaluation, we train the models with group DRO to ensure low worst-group error. We use the SGD optimizer with a learning rate of 0. 0.0001, momentum 0.9 for 15 epochs with batch size 64. In addition, we use l regularization of 0.01 and early stopping for the best validation accuracy. Table 5, 6 reports the accuracy of attribute classifiers CelebA and Waterbirds dataset, respectively. The attribute classifier for classilying color on the Colored MNIST dataset showed 100% accuracy for all groups.
the
Table 5: Accuracy of the attribute classifiers used for evaluation the CelebA dataset.
Blond
Non-blond
Attribute of interest
Present
Absent
Present
Absent
Male
86.11
97.18
97.20
96.08
Eyeglasses
96.77
99.30
92.91
99.56
Lipstick
82.47
83.79
86.83
92.10
Table 6: Accuracy of the attribute classifiers used for evaluation on the Waterbirds datasct.
Waterbirds
Landbirds
Attribute of interest
Water
Land
Water
Land
Background
94.74
90.98
89.70
95.93
Reference set classifiers for weak-supervision. For the reference set classifiers, we follow the details from the original paper (Choi et al., 2020). We use the Adam optimizer with a learning rate of 0.0001 without any f2 regularization for 15 epochs with batch size 64. We use the same reference set classifiers for the weakly-supervised baseline Choi et al. (2020) proposed and our weakly-supervised version. We use = 0.3 for target male ratio 30% and a = 0.5 for target male ratio 50% for the weakly-supervised bascline.
Attribute classifiers for semi-supervision. We use 4,000 samples with the sensitive attribute annotation and the rest of the samples in the training set without the sensitive attribute annotation to train the sensitive attribute classifier. We use FixMatch (Sohn et al., 2020), recent SOTA semi-supervised learning technique, to train the sensitive altribute classifier. We only use random horizontal flip for data augmentation and use a fixed threshold of 0.95 for т. We use the SGD optimizer with a learning rate of 0.001, momentun 0.9 for 100 epochs with batch size 64. In addition, we use l2 regularization of 0.005 and early stopping for the best validation accuracy.
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A.2 Generative models
Network architectures. For generative model, we implement our code based on PyTorch-StudioGAN repository². We use BigGAN for the CelebA and Waterbirds experiments, and ResNetGAN with spectral normalization (Miyato et al., 2018) for the Colored MNIST experiments. For CelebA and Colored MNIST, we train our generative model from scratch. For Waterbirds, we train our model starting from ImageNet- pretrained weights provided by Crforch-StudioGAe repository.
Training details. For all the baselines and our method on the CelebA dataset, we train BigGAN with the same configurations. We train the models using the Adam optimizer with learning rate of 0.0002, 31 = 0, B2 0.999, for total 200k iterations with batch size 32. We update the discriminator 4 times per one generator step. For our Waterbirds experiments, for the generator and 0.0002 for the discriminator, 31 0, B2 0.999, for Lotal 20k iteration with batch size 128. We update the discriminator 2 times per one generator step. We use DiffAug (Zhao et al., 2020) to supplement the limited number of training data. For the Colored MNIST experiments, we train the models using the Adam optimizer with learning rale of 0.0002, 31 0.5, B2 = 0.999, for total 20k ilerations with batch size 64. We update the discriminator 5 times per one generator step.
train models using the Adam optimizer with learning rate of 0.0001
Dia-GAN. For the CelebA datasct, we train 150k iterations for phase 1 and use log density ratios from 140k to 150k iterations to reweight samples for phase 2. For the Waterbirds dataset, we train 5k iterations for phase and use log density ratios from 500 to 5 iterations to reweight samples for phase 2. For the Colored MNIST dataset, we train 4k iteration for phase and use log density ratios from 100 to 4k iterations to reweight samples for phase 2. Following the original paper, we clip the sample weights from 0.01 to 0.5.
FICS. For the CelebA datasct, we first pretrain 100k itcrations with the vanilla configurations and then finetune for the next 100k ilerations. For finetuning, we freeze the discriminator until 4 layers using FreezeD (Mo et al., 2020) and add the proposed regularizer. We also start to resample after 100k iterations when supervision is provided. For the Waterbirds and Colored MNIST dataset, we did not perform any additional finetuning before FICS training. For the À of FICS regularizer, we tuned over {0.002, 0.005, 0.01, 0.02} and use the values with the best FID.
B Baselines
We exlend the prior (unconditional) fair generation methods as the baselines for the fair conditional generation, i.e., modify their formula from p(r) to v() We consider three representative methods for unsupervised (Lee et al., 2021), supervised (Tan et al., 2020), and weakly-supervised (Choi et al., 2020) scenarios.
Unsupervised. Unsupervised fair generation aims to promote underrepresented samples and reduce the gap between data and generator distributions. For instance, Dia-GAN (Lee et al., 2021) resamples the training data based on the log-density ratio log (data(x)) (r)//Pem()) estimated by the discriminator.
Supervised. Given annotations of sensitive attribute E A, straight forward solution for a fair conditional generation is conditioning both y and a, as one can explicitly control the generated attributes using p(rly, a). However, this joint-condition approach is hard to train when the data is imbalancod; too scarce for the minority group (y. As an alternative, FairGen (Tan et al., 2020) propose a latent modification approach that modifies an unconditional generative model to conditional model by learning a prior distribution pa (2) that restricts the samples under p(r(a), unlike the original prior p(z) sampling p(x). Note that the supervised method performs well if the target attribute is known; however, it requires heavy annotation costs and cannot prevent the unknown biases.
Weakly-superviseed. Choi et al. (2020) consider a weaker form of the fairness supervision, assuming a reference set S, with empirical distribution Pref (z) z (x)) Specifically, they reweighted the training data with density ratio Pref (z))/aaaa Paata (z) estimated by a classifier distinguishing the reference and data distributions. Note that the weakly-superve unrealistic to collect the oracle reference set in practice.
method heavily depends on the collection of the reference set; it is often
Phttps://githhnn wttel/..cccm/saaa/eeeeee htwp:/PSSEEC---T http:////STTTTTCCCTTT/////////// StudiooAA
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C
Additional experiments
C.1
The relationship between the biased classifier and the generator
Loss percentile rank in all blond samples
Loss percentile rank all blond samples
100
100
80
60
60
40
40
20
male
20
male
eyeglasses
eyeglasses no smile
no smile
0
0
20
40
60
80
100
0
20
40
60
80
100
Loss percentile rank in blond minority samples
Loss percentile rank in blond minority samples
(a) Vanilla BigGAN (Brock et al., 2019)
(b) FICS (ours)
Figure 6: The relationship between the biased classifier and the generator represented through classification loss percentile ranks of generated samples. Given a point, its x, y coordinate represents the percentile rank of its classification loss among blond minority samples and all blond samples respectively. The correlation between the classification loss and the chance to be minority still remains after the FICS training.
To validate the effectiveness of our proposed regularization approach, we conducted an investigation into the correlation between the classification loss and the probability of sample being minority at the end of the FICS training. We present the results in Figure 5, where we plot the classification loss percentile ranks shown in Figure 3. As the number of minority samples generated by the FICS training increased, we observed that a sample with a loss ranking in the 20th percentile among blond male samples had a relatively lower rank in the FICS-trained cGAN compared to the vanilla cGAN. However, we found that the correlation between the classification loss and the likelihood of sample being a minority persisted even after the FICS training. Based on these findings, can conclude that our regularizer, which is based on the observed correlation, consistently encouraged the eGAN to generate minority samples throughout the entire training process.
18


Reviews:
[{"review_id": "d2q5fWoLmZ", "reviewer": "Reviewer_4jmF", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "STR.\n\n- the authors acknowledge the importance of causality in a fairness definition and use it to their benefit. I like this perspective and would advocate more research on this topic. \n\n- It seems the proposed method can be used post-hoc after training other generative models (though this needs confirming -> I asked a question in this vain below)\n\n\nWKN.\n\n- The proposed idea seems quite related to counterfactual fairness which should probably be discussed and compared against since it is quite a popular paper (https://proceedings.neurips.cc/paper/2017/hash/a486cd07e4ac3d270571622f4f316ec5-Abstract.html)\n\n- following the above, there are quite some relevant papers missing from the authors' comparison (some of them also casual GANs which are trained to promote fair sampling). I listed them below. \n\n- on p4 the authors introduce the notion of \"spurious causality\", whereby a generative model introduces a causal link based on supriously correlated variables. I don't understand why we need such new terminology, what the authors describe as spurious causality is still spurious correlation? why would this be different? Nothing in a GAN makes a correlation causal, just as there is nothing in a GAN that makes a spurious correlation spuriously causal.\n\n- Fig 2 shows that we sample from the model by first performing a do-operation. Later in sec. 4.3.2 we see that the authors translate this do operation by simply weighting the likelihood of each sample, such that the complete sample matches a fair distribution. How is this causal? Especially when p^{do} is given (in the form of a reference distribution), I'm completely at a loss why the proposed model is in any way causally more aware than subsampling from another model.\n\n- There are more fairness notions than simple class imbalance (see the refs I listed below), how would this model translate those into a new ref. distribution? Furthermore, am I correctly understanding that the model requires retraining whenever we want to update our fairness definition?\n\n\n### Refs.\n\nvan Breugel, B., Kyono, T., Berrevoets, J., & van der Schaar, M. (2021). Decaf: Generating fair synthetic data using causally-aware generative networks. Advances in Neural Information Processing Systems, 34, 22221-22233.\n\nLu Zhang, Yongkai Wu, and Xintao Wu. A causal framework for discovering and removing direct and indirect discrimination. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI-17, pages 3929–3935, 2017. doi: 10.24963/ijcai. 2017/549. URL https://doi.org/10.24963/ijcai.2017/549.\n\nFlavio P. Calmon, Dennis Wei, Karthikeyan Natesan Ramamurthy, and Kush R. Varshney. Optimized data pre-processing for discrimination prevention, 2017\n\nMichael Feldman, Sorelle A Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkata subramanian. Certifying and removing disparate impact. In proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pages 259–268, 2015.\n\nRich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. In International conference on machine learning, pages 325–333. PMLR, 2013.\n\nDepeng Xu, Yongkai Wu, Shuhan Yuan, Lu Zhang, and Xintao Wu. Achieving causal fairness through generative adversarial networks. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019.\n\n\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors introduce FICS, a generative model that learns a fair distribution (wrt a protected feature) of the data. In particular, fairness is defined as being robust against \"spurious causality\" whereby a model may wrongly learn relationships such as hair colour -> gender (the example being blonde -> female). \n\nFICS learns a fair distribution through an adversarial term in their loss function where the distribution is corrected by \"worsening\" the ability to classify a protected attribute from the representation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please consider the weaknesses I listed above and provide a new insight/answer to rebut those.\n\nSome additional questions:\n\n- How would this approach work on tabular data? Causality is definitely more evolved in a tabular domain.\n\n- Couldn't you just use _any_ generative model in combination with subsampling?", "broader_impact_concerns": "I don't think there are any BI concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "U7xWV3D4kt", "reviewer": "Reviewer_9tsi", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "S\n- This work investigates an important fairness problem -- the amplified bias (imbalance) in conditional generative models.\n- This work covers the setting of unsupervised, weakly supervised and semi supervised learning.\n\nW\n- It is not clear, from eq.(2) and the paragraphs following it, why do conditional generative models always amplify the imbalance conditioned on certain attribute in the dataset.\n\n- Although empirically, with a cGAN trained with the original loss, authors find the imbalance in sampling is correlated with the classification loss. Note that this correlation is a property of the cGAN model trained with original loss. But it is not clear why training the cGAN model with eq.(3) can guarantee that more balanced samples would be generated.\n\n- The presentation can be improved.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work aims to solve the unfairness/spurious correlations caused by data imbalance in conditional generative models. For example, BigGAN conditioning on the attribute \"blond\" will generated female samples more frequently. It formulates the problem as approximate p(a|y) from the original dataset. It proposes different corrective sampling methods for different settings. Experiments show the proposed method can achieve high quality as well as mitigate the imbalance issue in conditional generation.\n", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- In the unsupervised setting, the authors use a classifier to classify minority and majority groups, how did they train this classifier and how this is unsupervised if a classifier is trained in a supervised manner?\n\n- Can the authors explain, in the rejection sampling of unsupervised setting, why the samples have to be accepted with the probability proportional to p_{data}/p_{gen}?\n\n- Is eq.(2) correct? It looks to me the RHS is not a probability density function.\n\n- Does FICS always take the same training time under different settings (unsupervised, weakly supervised and semi supervised).\n\n- The authors did not specify how w(x) will be used in resampling.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "Fvy32ncyDD", "reviewer": "Reviewer_HYiU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength\n\nThe paper studies the unsupervised setting which is different from prior work on fair generation where the sensitive attribute is given. The idea of using the classification loss to infer underrepresented samples is reasonable.\n\nWeakness\n\nTo explain the motivation of the paper, the authors introduce the concept of spurious causality, which is not quite convincing to me. To create a causal path from $Y$ (the act of conditioning on the label) to $A$ (the sensitive attribute), the authors assume that $A$ is a function of $X$. However, in reality we often assume that $X$ is a function of $A$ since sensitive attributes like gender and race represent the inherent natures of individuals. In addition, the paper does not explain why spurious causality is more problematic to downstream classifiers than spurious correlations.\n\nThe proposed method FICS is actually decoupled with the proposed spurious causality concept and is directly based on the observation that “the generated samples that are classified as the minority group are more likely to have higher classification loss”. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the mitigation of conditional generative models in an unsupervised setting where the sensitive attribute is unknown. The idea is to build a classifier separately on the training data and use the classification loss to indicate underrepresented samples. Then, a regularizer is added to the loss of the generative model to promote the generation of samples with large classification losses. Finally, rejection sampling is used to recover the original distribution.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "It would be helpful for comprehension if the authors can add causal graphs in Section 3 to explain the difference between spurious causality and spurious correlation.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: ### Summary

The paper identifies the problem of spurious correlations in conditional generative models (such as cGANs). The authors term this problem as "spurious causality", as users may use such models to make causal deductions. They propose solutions to this problem for both the unsupervised and supervised setting, by minimising the effect of such spurious correlations on the cGAN objective.

### Reviewer Recommendations

Two reviewers found the paper to be interesting, and were overall supportive of acceptance. A third reviewer had concerns on the usage of the term "spurious causality", since this does not refer to any causal structure in the original data, and the techniques proposed are about mitigating spurious correlation (and do not use any techniques from causality). I note that one of the positive reviewers had also raised the question of the difference between spurious correlation and causality.

### AE Recommendation

From my review of the paper, I find the points raised by all reviewers to be valid: the paper tackles what appears to be a novel problem, offers solutions for a few different settings, and shows good empirical results. It is also well-written. At the same time, the notion of "spurious causality" appears to be equivalent to the established notion of "spurious correlation", but specialised for the setting of conditional generative models. While I do understand the authors' motivation for using the former, there are some reasons to argue against it:
- as two reviewers were unclear on this point, it is plausible that other members of the TMLR audience might also be confused about the precise distinction to regular spurious correlations.

- the methods proposed are entirely in line with the spurious correlations literature, and are not apparently generalisable to other causality problems.

- in the precise examples used to evaluate the method, it is not immediately clear that an end-user might make causal inferences based on the suggested interventions. e.g., on Waterbirds, it is not apparent that an end-user might make inferences about the type of bird backgrounds affecting the background. Even on CelebA, it is not obvious that one might infer that "Blondness" _causes_ "Eyeglasses". (I understand that there may be other scenarios where such causal inference could be more plausible.)

On the other hand, if the problem were simply referred to as "spurious causality for generative models", it would not affect any of the technical details of the methods and experiments. While perhaps more verbose, even if one were to retain usage of the term "spurious causality", it would be appropriate to qualify that it is "spurious causality for conditional generation". This is because one could imagine encountering a problem of spurious causality in regular (i.e., non-generative) classification problems, where one attempts to make causal inferences using techniques from the causality literature.

Our recommendation is thus for the paper to be accepted, subject to a softening of the usage of the term "spurious causality". Our suggestion is for the authors to primarily use a term such as "spurious causality for generative models", or a suitable abbreviation. (The discussion on causality could perhaps be contained in one or two focussed sub-sections.) While the term "spurious causality" is used at various points in the paper, the total usage is about 20 times; thus, we believe this terminology change can be accommodated in a minor revision to be reviewed by the AE.

Decision: Accept (poster)