Fair4Free: Generating High-fidelity Fair Synthetic Samples using Data-Free Distillation

## Abstract

Abstract This work presents Fair4Free, a novel generative model to generate synthetic fair data using data-free distillation in the latent space. Fair4Free can work on the situation when the data is private or inaccessible. In our approach, we first train a teacher model to create fair representation and then distil the knowledge to a student model (using a smaller architecture). The process of distilling the student model is data-free, i.e. the student model does not have access to the training dataset while distilling. After the distillation, we use the distilled model to generate fair synthetic samples. Our extensive experiments show that our synthetic samples outperform state-of-the-art models in all three criteria (fairness, utility and synthetic quality) with a performance increase of 5% for fairness, 8% for utility and 12% in synthetic quality for both tabular and image datasets.

## 1 Introduction

Nowadays, people rely on Artificial Intelligence-based applications to seek answers or make decisions. These AI-based models are trained with the data available in the real world. However, the available data in the real world is often full of machine or human biases (Liu et al., ). So, there is a possibility that those models will reflect biases when making a decision. For this reason, there is a strong need for bias mitigation models or bias-free datasets to ensure fairness within the models or datasets themselves. Furthermore, not all data is publicly accessible due to proprietary or sensitive cases, i.e. medical records. So, there is a need for a way to deal with these situations, too. Over the years, various approaches have been proposed to mitigate the bias issue from the model or datasets themselves, and researchers have categorized these techniques into three categories: Pre-processing, in-processing and post-processing techniques (Caton & Haas, ; Ntoutsi et al., ; Mehrabi et al., ). In the pre-processing technique, the dataset is processed to lower the correlation between the sensitive and non-sensitive attributes. However, in this process, valuable information can be lost. Post-processing techniques involve changing the output of the model in such a manner that the outcome of the model becomes fair towards demographics. These models also suffer accuracy as the model output is changed. In the in-processing techniques, the model is trained in such a way that during training time, the output of the model becomes fair. Though these approaches suffer from optimization problems (Oussidi & Elhassouny, ), a trade-off exists between fairness and accuracy. So, there is room for improvement.

Fair Generative Models (FGMs) are examples of in-processing bias-mitigation techniques. Over the years, different generative approaches have been proposed to tackle this issue. Variational autoencoder, Generative Adversarial Networks, and Diffusion-based models have seen outstanding performance in the tabular, text, and image domains (Jung et al., ; Choi et al., ; Wang et al., ). Different fairness constraints have been used to enforce the fairness quality in the generative samples, i.e., FairDisco (Liu et al., ) uses a distance correlation minimization method to weaken the connection between the sensitive and non-sensitive attributes. FairGAN (Li et al., ) uses dual discriminator-based generative adversarial networks architecture for generating fair synthetic samples. TabFairGAN (Rajabi & Garibay, ) generates synthetic fair data in two stages, first training a GAN to generate synthetic data, then adding a constraint on the synthetic samples to make it fair. FLDGMs (Ramachandranpillai et al., ) generate fair synthetic samples by generating the latent space with the help of GAN and diffusion architecture. Though these models generate high-fidelity fair synthetic samples, training these requires heavy computational resources; sometimes, these models do not converge while training, resulting in poor-quality synthetic samples. Along these issues, if the training data is unavailable for some reason, we cannot use these models as the data is necessary to train these models.

Transferring knowledge from one learned model (teacher model) to another model (student model, generally smaller architecture than the teacher model) is known as knowledge distillation. Usually, the student model tries to learn by taking the output of the intermediate or last layer of the teacher model. This approach helps reduce computational resources. However, one of the downsides of this approach is that the data label needs to be known for distillation. Recent, fair distillation works (Dong et al., ; Zhu et al., ) rely on data labels, and these approaches cannot be used while distilling data representation.

So, from these motivations, in this work, we present Fair4Free, a novel generative approach for generating high-fidelity synthetic fair data, where we use knowledge distillation to distil the fair representation. The main contribution of our work is that while distilling the fair representation, we do not use any training data; we only use noise as input for the distilled model, so the approach for distillation is entirely data-free. The data-free distillation mitigates the issue of the dataset being sensitive and inaccessible. We first train a Variational Autoencoder (VAE) to learn the fair representation, then use it as a teacher model and take a smaller architecture (student model) to distil the fair representation. After distilling the fair representation, we use the trained decoder (from VAE) and student model to reconstruct high-fidelity fair synthetic samples. Using a smaller architecture also allows the possibility of deploying the model in edge devices. We do substantial experiments with both tabular and image data and show that our data-free distillation-based generative model performs better on the fairness, utility and synthetic samples than the state-of-the-art models. Table 1 shows the high-level comparison of other works with ours.

Our contributions to this work are as follows:

- 1.
We present a Fair4Free, a novel data-free distillation-based fair generative model for generating fair synthetic samples.
- 2.
Our distillation process works on latent space and requires no training data.
- 3.
We show our distillation performance for both tabular and image datasets.

## 2 Related Work

**Table 1: Comparison of existing fair models with our model over different key areas of interest: Fair Representation, Generative Models, and data-free training.**
| Models | Fair Representation | Generative Models | Support Multiple | Data Free Training |
| --- | --- | --- | --- | --- |
|  |  |  | Data Type |  |
| TabFairGAN (Rajabi & Garibay, ) | ✗ | ✓ | ✗ | ✗ |
| Decaf (Van Breugel et al., ) | ✗ | ✓ | ✗ | ✗ |
| FairGAN (Li et al., ) | ✗ | ✓ | ✗ | ✗ |
| FairDisco (Liu et al., ) | ✓ | ✗ | ✓ | ✗ |
| FLDGMs (Ramachandranpillai et al., ) | ✓ | ✗ | ✓ | ✗ |
| Fair4Free (ours) | ✓ | ✓ | ✓ | ✓ |

Research on data fairness and fair models has recently seen advancement due to their usefulness in real-life decision-making and other matters. To create a fair model, some research focuses on creating fair representation, Learning Fair Representation (LFR) (Zemel et al., ) create fair representation by turning the process into an optimization problem. Their results show better fairness gain performance in the downstream task. Optimal Fair Classifier (Zhao & Gordon, ) gives a lower bound in the classification settings to characterize the balance between accuracy and fairness. FFVAE (Creager et al., ) learns fair representation by disentangling the fair latent space for multiple sensitive attributes. Different adversarial approaches have been taken over the years to learn fair representations, i.e. NRL (Feng et al., ) learns the fair representation using a generator and a critic with the help of a min-max game they have designed. A fair contrastive learning approach has been proposed to create fair representation for datasets where sensitive attributes are not present (Chai & Wang, ). Besides creating fair representation, focuses have also been drawn into the fair generative models category. Various generative models such as VAEs, GANs, and Diffusion-based approaches have been proposed with different fairness constraints to generate fair synthetic data in different modalities (tabular, image, texts). FairGAN (Li et al., ) learns exposure-based fairness by taking negative feedback while training. TabFairGAN (Rajabi & Garibay, ) generates tabular fair data by using a fairness constraint during the training process; Decaf (Van Breugel et al., ) also uses GANs to generate fair synthetic samples by using causal inference. FLDGMs (Ramachandranpillai et al., ) uses both GANs and diffusion architecture to generate fair latent space and reconstruct fair synthetic samples from them.

Another fair representation or model learning approach is to transfer the knowledge from one model to another, i.e., using Knowledge distillation. However, most of the work on knowledge distillation relies on data labels and intermediate output from the teacher model. Recently, Graph Neural Networks (GNNs) have been used to distil fair representation (Dong et al., ; Zhu et al., ) that require data labels.

## 3 Preliminaries

In this section, we discuss the necessary background to follow the paper. First, we formulate the problem description followed by the definition of data fairness. Then, we discuss the background of knowledge distillation and generative models.

### 3.1 Problem Definition

Given a dataset tuple $(\{x_{i},y_{i},s_{i}\})_{i=1}^{B}\sim D$, where $x\in\mathcal{X}$ represents non-sensitive attributes, $y\in\mathcal{Y}$ is target variable and $s\in\mathcal{S}$ is sensitive attribute, we need to create fair generative model $\mathcal{H}$ by distilling fair representation ($z$) in a data-free distillation environment.

### 3.2 Data Fairness

Data fairness can be measured from different viewpoints, i.e., a model can be fair if it shows equal performance for all the demographics. Over the years, different approaches have been shown to create a fair model that satisfies group or individual fairness. This work focuses on creating a generative model that provides group fairness. To achieve this, a model should follow definitions 1 and 2.

###### Definition 1 (Demographic Parity (DP), Barocas & Selbst ( 2016 ) ) .

A binary prediction model $f:X\rightarrow\hat{Y}$, $\hat{Y}=\{0,1\}$ will achieve Demographic Parity (DP), iff

$$ $P[f(X)=1\mid\mathcal{S}=0]=P[f(X)=1\mid\mathcal{S}=1]$ $$

here, $\mathcal{S}$ is the sensitive attribute and {0, 1} are representing different groups.

###### Definition 2 (Equalized Odds (EO), Barocas & Selbst ( 2016 ) ) .

A binary prediction model $f:X\rightarrow\hat{Y}$, $\hat{Y}=\{0,1\}$ will achieve Equalized Odds (EO), iff

$$ $P[f(X)=1\mid Y=1,\mathcal{S}=0]=P[f(X)=1\mid Y=1,\mathcal{S}=1]$ $$

here, $\mathcal{S}$ is the sensitive attribute and {0, 1} are representing different groups.

###### Definition 1 (Demographic Parity (DP), Barocas & Selbst ( 2016 ) ) .

###### Definition 2 (Equalized Odds (EO), Barocas & Selbst ( 2016 ) ) .

### 3.3 Knowledge Distillation and Generative Models

Knowledge distillation works by taking a learned model and transfer the knowledge to a smaller architecture (smaller in layers and/or number of neurons) (Hinton et al., ). In the earliest distillation work (Hinton et al., ), the student model learned by taking the output label from the teacher model and the outcome of the student model using a supervised manner, also called response-based distillation. Most of the knowledge distillation work follows this approach (Li et al., ; Huang et al., ). However, it becomes challenging when we want to distil some distribution as they do not have any labels. Recently, Sikder et al. () used a combination of distillation loss and data-utility loss to distil the representation space without a label; however, that model requires training data to distil the latent space. Thus, distilling the model trained on private data will be difficult, especially since the data is inaccessible.

Generative models are used to learn data distribution and generate synthetic data that is not identical to the original data but follows the same distributions. Over the years, different kinds of generative models have been proposed, i.e., Variational Autoencoder (VAE) (Kingma, ) tries to compress the data into latent space and reconstruct data, and Generative Adversarial Networks (GANs) (Goodfellow et al., ) comprised two architectures, Generator and Discriminator. These two architectures compete with each other, and after the training, the generator learns to generate high-quality synthetic samples. Diffusion models (Ho et al., ) learn the distribution by destroying the data by adding noise over time and then using a neural network architecture to de-noise the data. Though these approaches are beneficial and show promising outcomes, training these generative models is challenging as they do not always converge. Also, they are known for proning into mode-collapse problems.

## 4 Fair Generative Models using Data-Free Distillation

This section presents our approach for generating a data-free, fair, generative model. The generation of fair synthetic samples involves training a fair teacher model that takes biased dataset $D$ and produces a fair representation, then distilling the fair representation using a student architecture (smaller architecture and not using the training data in the distillation process, thus data-free distillation) and finally reconstruct synthetic fair samples from the distilled fair-representation. While training the fair teacher model, we use the distance correlation minimization technique (Liu et al., ) to weaken the connection between the sensitive and non-sensitive attributes. We break down the entire distillation and synthetic sample generation process into three stages:

- 1.
We first train a VAE that produces fair representation and acts as the teacher model for the distillation process. We take the biased data and minimize the relationship between the sensitive and non-sensitive features, so for any downstreaming task, the output will be free from the influence of sensitive features.
- 2.
We use a student model (smaller architecture than the teacher model) to distil the fair representation. In this process, the student model does not have access to the training data; it takes noise as input, so this process is data-free.
- 3.
Finally, we reconstruct high-fidelity fair synthetic samples using the distilled fair representation from the student model and the trained decoder of VAE from stage 1.

### 4.1 Fair Representation Learning

Figure: Algorithm 1 Learning Fair Representation

The first stage of our fair generative model is to learn a fair representation from biased data, $D$. We train a Variational Autoencoder (VAE) for this task and use the encoder ($\mathcal{E}_{\phi}$) to get the fair representation. The encoder creates representation $z=\mathcal{E}_{\phi}(x,s)$, here $(x,s)\in D$, $x\in\mathcal{X}$ represents non-sensitive attributes and $s\in\mathcal{S}$ represents sensitive attributes. Then the decoder reconstruct samples, $x^{\prime}=\mathcal{D}_{\theta}(z,s)$. For learning the fair representation, along with the reconstruction loss and KL-divergence loss of VAE, distance correlation minimization loss $\mathcal{V}^{2}_{\phi}(z,s)$ and penalty $\beta\in\{0,1,2,...,9\}$ is used, which is stated in Equation 1 (Liu et al., ). Steps of learning fair representation can be found in Algorithm 1.

$$ $\mathcal{V}^{2}_{\phi}(z,s)=\int_{z\in\mathcal{Z}}\int_{s\in\mathcal{S}}\mid p _{\phi}(z,s)-p_{\phi}(z)p(s)\mid^{2}\,dz\ \,ds.\$ (1) $$

### 4.2 Data-Free Fair Latent Space Distillation and Synthetic Data Generation

In this step, we take the trained fair encoder, $\mathcal{E}_{\phi}$ from step 1 and distil the knowledge of fair representation ($z$) to another architecture, $\mathcal{E}^{\prime}_{\psi}$ (we use less number of hidden features than used in $\mathcal{E}_{\phi}$) by first creating the latent fair representation, $z=\mathcal{E}_{\phi}(x,s),$ where, $x,s\in D$. The main contribution of this work is to while distilling the latent space, $z$, to the model $\mathcal{E}^{\prime}_{\psi}$, we do not use any training data, $(x,s)$. We feed Gaussian noise, $n\sim\mathcal{N}(0,1)$ to the distilled model, and it produce some representation $z^{\prime}=\mathcal{E}^{\prime}_{\psi}(n)$. We use a combination of distillation loss between the distilled representation ($z^{\prime}$) and fair representation ($z$) and KL-divergence loss on the output of the distilled model (Sikder et al., ). The overall loss function is stated in Equation 2.

$$ $\mathcal{L}_{\text{distillation}}(z,z^{\prime})=\underbrace{\sum_{j=1}^{k} \mathcal{L}(z_{j},z_{j}^{\prime})}_{\text{distillation loss}}+\underbrace{\sum _{j=1}^{k}D_{\text{KL}}(q(z^{\prime}_{j})\mid\mid p(z^{\prime}_{j}))}_{\text{ KL-loss}}$ (2) $$

Here, we use L1-loss as $\mathcal{L}$ for the distillation loss. Algorithm 2 shows the process of data-free distillation. After the distillation, we use the distilled model, $\mathcal{E}^{\prime}_{\psi}$, and trained decoder, $\mathcal{D}_{\theta}$ from stage 1 to reconstruct high-fidelity fair synthetic samples, $\hat{x}=\mathcal{D}_{\theta}(\mathcal{E}^{\prime}_{\psi}(n))$, $n\sim\mathcal{N}(0,1)$.

Figure: Algorithm 2 Data-free distillation of Fair Representation

## 5 Experiments

In this section, we present the experimental analysis of our work. We utilize two tabular and two image datasets to evaluate how our model performs across various dataset types. We compare the result of our model with several state-of-the-art fair models, i.e., Decaf (Van Breugel et al., ), TabFairGAN (Rajabi & Garibay, ), FairDisco (Liu et al., ), FLDGMs (Ramachandranpillai et al., ) in terms of fairness and utility. We further compare the works with Correlation Remover (Weerts et al., ) and Threshold Optimizer (Hardt et al., ), pre and post-processing techniques, respectively. We use FairX (Sikder et al., ), a fairness benchmarking tool to load the dataset, train and evaluate the benchmark.

### 5.1 Dataset Preprocessing

We use four benchmarking datasets to train and evaluate our model. “Adult-Income” (^1^11[https://archive.ics.uci.edu/dataset/2/adult](https://archive.ics.uci.edu/dataset/2/adult)) and “Compas” (Angwin et al., ) are two widely used tabular dataset and “CelebA” (Liu et al., ) and “Colored-MNIST” (Jung et al., ) are image dataset. “Adult-Income” contains more than 48k records from US Census data containing personal information. “COMPAS” contains information about 7k inmates collected from the algorithm called COMPAS used by the US Justice system to predict the likelihood of an inmate re-offending. “CelebA” contains more than 200k facial images of celebrities with 40 attributes for each image. “Colored-MNIST” contains 60k English handwritten digit images with different colors ranging from 0-9. We use {Gender, Race} as sensitive attribute for the “Adult-Income” and “Compas” datasets. For the “CelebA” dataset, we use Smiling status, and for the Colored-MNIST, color as sensitive attributes. We follow the same setup of FairDisco (Liu et al., ) for the pre-processing and data split (80-20 ratio) technique. More details about hyperparameters in our model can be found in the Appendix section A.

### 5.2 Evaluation Metrics

We evaluate the performance of the distilled fair representation and fair synthetic samples regarding fairness, utility and synthetic sample quality (only for the synthetic samples). For both fairness and utility evaluation, we run a downstreaming task (explained in section 5.3) and evaluate the performance of the synthetic samples on Accuracy, F1-Score, Recall (utility metrics) and Demographic Parity Ratio (DPR) (Weerts et al., ), Equalized Odds Ratio (EOR) (Weerts et al., ) (fairness utility). Along with utility and fairness evaluation, we also measure the synthetic data quality of the fair generative model. We use the Density and Coverage (Alaa et al., ) metrics to validate if the generated samples have the same distribution as the original samples.

Besides empirical evaluation, we also show the quality of synthetic samples and distilled latent space with visual evaluation. We use PCA (Bryant & Yarnold, ) and t-SNE (Van der Maaten & Hinton, ) plots to show how closely the distribution of the distilled latent space and fair latent space matches. Also, we show the synthetic samples generated for the image dataset.

### 5.3 Downstreaming Task for Evaluation

For the empirical evaluation, we set up a downstreaming task to determine the performance of the synthetic samples in terms of fairness and data utility. In the setup, we train a random-forest (Breiman, ) model for a supervised task using the features (sensitive ($s$) and non-sensitive ($x$) attributes) and target ($y$) based on the sensitive attributes, then evaluate in perspective of fairness and data utility. For example, for the “Adult-Income” dataset, we have {gender, race} as sensitive attributes. Hence, we train the random forest for each sensitive attribute and measure the fairness and data utility for respective $s$.

Figure: Figure 1: Generated Samples using Fair4Free, Dataset: CelebA, Sensitive_attribute: Smiling
Refer to caption: extracted/5895535/fig/celeba.jpeg

Figure: Figure 2: Generated Samples using Fair4Free, Dataset: Colored-MNIST, Sensitive_attribute: Colors
Refer to caption: extracted/5895535/fig/colored-mnist.jpeg

## 6 Results and Discussion

We conduct extensive experiments and compare the performance of our model with six fair models. In this section, we discuss and analyze the result.

**Table 2: Fair Synthetic Samples evaluation, Dataset: Adult-Income. Bold indicates the best result. Synthetic Utility evaluation is only for generative models (TabFairGAN, Decaf, FLDGMs)**
|  |  | Fairness Metrics | Data Utility | Synthetic Utility |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Protected | DPR | EOR | ACC | Recall | F1- | Density | Coverage |
|  | Attribute |  |  |  |  | Score |  |  |
| TabFairGAN | Gender | 0.69 $\pm$ .01 | 0.60 $\pm$ .01 | 0.84$\pm$ .01 | 0.61 $\pm$ .01 | 0.65 $\pm$ .01 | 0.006 $\pm$ .01 | 0.03$\pm$ .01 |
|  | Race | 0.026 $\pm$ .01 | 0.00 $\pm$ .00 | 0.84 $\pm$ .01 | 0.77 $\pm$ .01 | 0.67 $\pm$ .01 | 0.01 $\pm$ .01 | 0.02 $\pm$ .01 |
| Decaf | Gender | 0.52 $\pm$ .01 | 0.42 $\pm$ .01 | 0.75 $\pm$ .01 | 0.63 $\pm$ .01 | 0.44 $\pm$ .01 | 0.70 $\pm$ .01 | 0.571 $\pm$ .01 |
|  | Race | 0.55 $\pm$ .01 | 0.46 $\pm$ .01 | 0.77 $\pm$ .01 | 0.69 $\pm$ .01 | 0.53 $\pm$ .01 | 0.58 $\pm$ .01 | 0.84 $\pm$ .01 |
| FLDGMs (DM) | Gender | 0.94 $\pm$ .01 | 0.94 $\pm$ .01 | 0.69 $\pm$ .01 | 0.90 $\pm$ .01 | 0.81 $\pm$ .01 | 1.26 $\pm$ .01 | 0.89 $\pm$ .01 |
|  | Race | 0.99 $\pm$ .01 | 0.96 $\pm$ .01 | 0.69 $\pm$ .01 | 0.91 $\pm$ .01 | 0.81 $\pm$ .01 | 1.24 $\pm$ .01 | 0.86 $\pm$ .01 |
| FairDisco (base-model) | Gender | 0.98 $\pm$ .01 | 0.85 $\pm$ .01 | 0.78 $\pm$ .01 | 0.92 $\pm$ .01 | 0.86 $\pm$ .01 | n/a | n/a |
|  | Race | 0.95 $\pm$ .01 | 0.92 $\pm$ .01 | 0.812 $\pm$ .01 | 0.71 $\pm$ .01 | 0.88 $\pm$ .01 | n/a | n/a |
| Correlation- | Gender | 0.32 $\pm$ .01 | 0.23 $\pm$ .01 | 0.86 $\pm$ .01 | 0.65 $\pm$ .01 | 0.71 $\pm$ .01 | n/a | n/a |
| Remover | Race | 0.29 $\pm$ .01 | 0.20 $\pm$ .01 | 0.86 $\pm$ .01 | 0.80 $\pm$ .01 | 0.71 $\pm$ .01 | n/a | n/a |
| Threshold | Gender | 0.95 $\pm$ .01 | 0.35 $\pm$ .01 | 0.86 $\pm$ .01 | 0.66 $\pm$ .01 | 0.65 $\pm$ .01 | n/a | n/a |
| Optimizer | Race | 0.69 $\pm$ .01 | 0.25 $\pm$ .01 | 0.87 $\pm$ .01 | 0.66 $\pm$ .01 | 0.71 $\pm$ .01 | n/a | n/a |
| Original Data | Gender | 0.32 $\pm$ .01 | 0.22 $\pm$ .01 | 0.88 $\pm$ .01 | 0.80 $\pm$ .01 | 0.72 $\pm$ .01 | n/a | n/a |
|  | Race | 0.19 $\pm$ .01 | 0.00 $\pm$ .00 | 0.88 $\pm$ .01 | 0.80 $\pm$ .01 | 0.71 $\pm$ .01 | n/a | n/a |
| Fair4Free (ours) | Gender | 0.99 $\pm$ .01 | 0.99 $\pm$ .01 | 0.76 $\pm$ .01 | 0.98 $\pm$ .01 | 0.88 $\pm$ .01 | 1.03 $\pm$ .01 | 0.96 $\pm$ .01 |
|  | Race | 0.99 $\pm$ .01 | 0.99 $\pm$ .01 | 0.76 $\pm$ .01 | 0.98 $\pm$ .01 | 0.87 $\pm$ .01 | 1.20 $\pm$ .01 | 0.97 $\pm$ .01 |

**Table 3: Fair Synthetic Samples evaluation, Dataset: Compas. Bold indicates the best result. Synthetic Utility evaluation is only for generative models (TabFairGAN, Decaf, FLDGMs)**
|  |  | Fairness Metrics | Data Utility | Synthetic Utility |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Protected | DPR | EOR | ACC | Recall | F1- | Density | Coverage |
|  | Attribute |  |  |  |  | Score |  |  |
| TabFairGAN | Gender | 0.52 $\pm$ .01 | 0.42 $\pm$ .01 | 0.68 $\pm$ .01 | 0.63 $\pm$ .01 | 0.66 $\pm$ .01 | 0.016 $\pm$ .01 | 0.014 $\pm$ .01 |
|  | Race | 0.50 $\pm$ .01 | 0.49 $\pm$ .01 | 0.69 $\pm$ .01 | 0.59 $\pm$ .01 | 0.64 $\pm$ .01 | 0.014 $\pm$ .01 | 0.011 $\pm$ .01 |
| Decaf | Gender | 0.87 $\pm$ .01 | 0.84 $\pm$ .01 | 0.45 $\pm$ .01 | 0.40 $\pm$ .01 | 0.42 $\pm$ .01 | 0.367 $\pm$ .01 | 0.39 $\pm$ .01 |
|  | Race | 0.99 $\pm$ .01 | 0.96 $\pm$ .01 | 0.45 $\pm$ .01 | 0.40 $\pm$ .01 | 0.42 $\pm$ .01 | 0.38 $\pm$ .01 | 0.39 $\pm$ .01 |
| FLDGMs (DM) | Gender | 0.92 $\pm$ .01 | 0.91 $\pm$ .01 | 0.52 $\pm$ .01 | 0.41 $\pm$ .01 | 0.44 $\pm$ .01 | 1.40 $\pm$ .01 | 0.134 $\pm$ .01 |
|  | Race | 0.98 $\pm$ .01 | 0.86 $\pm$ .01 | 0.53 $\pm$ .01 | 0.45 $\pm$ .01 | 0.47 $\pm$ .01 | 1.59 $\pm$ .01 | 0.13 $\pm$ .01 |
| FairDisco | Gender | 0.97 $\pm$ .01 | 0.92 $\pm$ .01 | 0.55 $\pm$ .01 | 0.40 $\pm$ .01 | 0.43 $\pm$ .01 | n/a | n/a |
|  | Race | 0.87 $\pm$ .01 | 0.76 $\pm$ .01 | 0.53 $\pm$ .01 | 0.41 $\pm$ .01 | 0.44 $\pm$ .01 | n/a | n/a |
| Correlation- | Gender | 0.43 $\pm$ .01 | 0.33 $\pm$ .01 | 0.64 $\pm$ .01 | 0.64 $\pm$ .01 | 0.59 $\pm$ .01 | n/a | n/a |
| Remover | Race | 0.58 $\pm$ .01 | 0.63 $\pm$ .01 | 0.65 $\pm$ .01 | 0.64 $\pm$ .01 | 0.60 $\pm$ .01 | n/a | n/a |
| Threshold | Gender | 0.92 $\pm$ .01 | 0.98 $\pm$ .01 | 0.65 $\pm$ .01 | 0.65 $\pm$ .01 | 0.61 $\pm$ .01 | n/a | n/a |
| Optimizer | Race | 0.99 $\pm$ .01 | 0.76 $\pm$ .01 | 0.63 $\pm$ .01 | 0.63 $\pm$ .01 | 0.60 $\pm$ .01 | n/a | n/a |
| Original Data | Gender | 0.37 $\pm$ .01 | 0.28 $\pm$ .01 | 0.57 $\pm$ .01 | 0.65 $\pm$ .01 | 0.61 $\pm$ .01 | n/a | n/a |
|  | Race | 0.54 $\pm$ .01 | 0.58 $\pm$ .01 | 0.66 $\pm$ .01 | 0.57 $\pm$ .01 | 0.61 $\pm$ .01 | n/a | n/a |
| Fair4Free (ours) | Gender | 0.99 $\pm$ .01 | 0.95 $\pm$ .01 | 0.52 $\pm$ .01 | 0.41 $\pm$ .01 | 0.42 $\pm$ .01 | 1.12 $\pm$ .01 | 0.97 $\pm$ .01 |
|  | Race | 0.93 $\pm$ .01 | 0.84 $\pm$ .01 | 0.52 $\pm$ .01 | 0.40 $\pm$ .01 | 0.42 $\pm$ .01 | 1.06 $\pm$ .01 | 0.98 $\pm$ .01 |

### 6.1 Empirical Analysis for Tabular Data

We show the performance of our model in the downstreaming task regarding fairness and data utility for the “Adult-Income” dataset in Table 2 and the “Compas” dataset in Table 3. We use the {gender, race} as sensitive attributes and record the results for both tables. For the “Adult-Income” dataset, we predict the income class for an individual given their attributes (both sensitive and non-sensitive) as downstreaming task. And for the “Compas” dataset, we predict the re-offend probability for an inmate given their previous records.

#### Data Utility Analysis

We measure the Accuracy, Recall and F1-score from the downstreaming task. We observe from Table 2 that our synthetic samples achieve 5% and 8% better performance in fairness and utility compared to FLDGMs (state-of-the-art model). In Table 3, the performance of our samples’ Synthetic utility (Coverage) is better than all other methods. We also achieve a balance of fairness and accuracy scores compared with other models.

#### Synthetic Quality Analysis

Synthetic samples should perform better for both data utility and synthetic quality. Overall, the performance of the synthetic quality of Fair4Free is better than other generative models. Such as, for Table 3, though TabFairGAN and Decaf perform better in the utility metrics, their synthetic utility performance is worse than our scores. We achieve 85% better scores in the Coverage metrics than the Decaf (Compas dataset) and 12% better performance than the FLDGMs in the Adult-Income dataset.

### 6.2 Visual Analysis for Tabular and Image Data

Besides the empirical quality of our synthetic samples, we also show visual analysis. We show the synthetic image samples from both CelebA and Colored-MNIST in Figure 1 and 2. We use “Smiling” as the sensitive attribute for the CelebA and “Colors (Red, Green, Blue)” for the MNIST dataset.

For the tabular dataset, we use the PCA and t-SNE plots to show how closely the distribution matches the distilled representation and the original fair representation. We observe from Figure 3 that the distributions closely match each other; this signifies that our data-free distillation method transfers the knowledge correctly.

Figure: Figure 3: PCA and t-SNE plots of the distilled and original fair representation for both Adult-Income (left) and Compas (right) Dataset. If the orange (distilled) and blue (original) dots overlap, it signifies their distribution is similar.
Refer to caption: extracted/5895535/fig/pca-tsne-fair.png

### 6.3 Feature Importance Analysis

Along with the empirical evaluation and visual evaluation, we also test the feature importance of the original and synthetic data in downstreaming task. We set up a task, i.e., for the Compas dataset, given the inmate’s records, to predict how likely the person will re-offend. Figure 4 shows the feature importance for both original and synthetic data (in this case, we use Gender (sex) as a sensitive attribute.). We observe that, for the original dataset, gender plays a vital role in reaching the decision, on the contrary, our synthetic samples do not rely on the sensitive attribute for making a decision. This also proves the usefulness of our synthetic samples for fair decision-making process.

Figure: Figure 4: Feature Importance Analysis with the original (left) and synthetic data, Dataset: Compas, Sensitive Attribute: Sex
Refer to caption: extracted/5895535/fig/explainability.png

### 6.4 Discussion

This work presents Fair4Free, a data-free distillation-based fair generative model. With this approach, we generate high-fidelity fair synthetic samples with the help of knowledge distillation. We distil the fair representation from the trained model (teacher model) to another architecture (student model). During the distillation process, we do not use any training data; thus, the training of the student model is data-free. This helps when the dataset is unavailable for security and privacy reasons. Also, as we use a small architecture, we reduce the computational cost, and we can deploy the model into an edge device with better performance than the teacher model. Tables 2 and 3 show that our model is over-performing the state-of-the-art models in the perspective of data utility, fairness and synthetic quality. Besides empirical evaluation, Figure 1, 2 shows the synthetic data samples, and Figure 4 shows the usefulness of fair synthetic samples in decision-making.

#### Social Impact

The Fair Generative model can play a vital role in the decision-making process because the generated samples do not consider the sensitive attributes while making decisions. This process helps to reduce bias and discrimination in the real-world scenario, i.e. fair recommendations in the healthcare system (Ramachandranpillai et al., ), fair economic recommendation (decision making on loans). Also, the fair model can help build trust with the user so it can be widely used in society.

#### Limitations and Future Works

In our experiments, we use a single sensitive attribute to train the generative model, i.e., we use either Gender or Race (for both Adult-Income and Compas datasets). So, in order to tackle intersectional bias, we need to work on a generative model that handles multiple sensitive attributes. However, we believe the data-free distillation process we present in this work can also be used if we have fair representation with multiple sensitive attributes.

## 7 Conclusion

Real-world data is filled with human and/or machine biases, and in the era of AI-powered decision-making systems, these biased data can cause harm to specific people as these models are trained with them. Furthermore, some datasets are not available publicly due to proprietary cases or restricted by data protection laws like GDPR or HIPPA to protect privacy. So, one way to tackle the data limitation and bias issue is to use a generative model. This work presents Fair4Free, a novel fair generative model that uses data-free distillation to generate fair synthetic samples. We pre-train a VAE with the biased data and produce fair representation in the latent space, then use another architecture to distill the fair representation. The distillation process is completely data-free, and then we use the distilled fair representation to create fair synthetic samples. Our extensive experiment shows that the quality of the synthetic samples outperforms state-of-the-art models regarding fairness, utility, and synthetic quality. As we use a distillation process and smaller architecture for the distilled model, these models can be deployed in the edge devices. Also, as the synthetic samples are fair towards demographics, these can help to mitigate the biased data issue.

## Appendix A More Experimental Details

#### Hyperparameters

To train the benchmarking models, we use FairX (Sikder et al., ), a fair benchmarking tool. FairX uses the same hyperparameters for the respective benchmarking models, specified in their original publication. For our generative model, we follow the same architecture of FairDisco (Liu et al., ) for the VAE setup (teacher model) and Table 4 shows the hyperparameters for the distillation model (student model).

**Table 4: Hyperparameters for the Distillation Model of Fair4Free (Tabular Dataset)**
|  | Parameters |
| --- | --- |
| Linear Layer 1 | $64(noise_dim)\rightarrow 32$ |
| Linear Layer 2 | $32\rightarrow 2\times 8(hidden_dim)$ |
| Batch Size | $2048$ |
| Epochs | $5000$ |
| Learning rate | $1e-5$ |
| Optimizer | $Adam$ |

#### Workstation Setup

We train our model and run the benchmark using the same environment that is equipped with “AMD Ryzen 9 5900x 12-core processor, 128 GB RAM, NVIDIA GeForce RTX 3090 Ti with 24 GB of GPU memory”.

## Peer Reviews

confidence: 4
contribution: 1
initial_rating: 3
presentation: 1
questions: * The paper needs to improve the clarity of implementation details and evaluation protocols mentioned above.
* The paper needs an ablation study to justify the design choices of the method.
soundness: 1
strengths: * The paper addresses an important problem of generating synthetic fair data.
* The experiments include a wide range of evaluation metrics to thoroughly evaluate the proposed method.
summary: The authors propose Fair4Free, a novel generative approach for generating high-fidelity synthetic fair data using knowledge distillation.
Their proposed method consists of three stages: 1) train a VAE on the biased dataset to learn a fair representation, 2) use it as a teacher model and distill the fair representation to a student model, and 3) use the trained VAE decoder and student model to reconstruct high-fidelity fair synthetic samples. They show experiment results on tabular and image datasets.
weaknesses: * The contributions of this paper are unclear. Although the authors claim the method is *data-free*, it still relies on a biased dataset to train the teacher model in the first stage. Furthermore, the method combines the student encoder with the teacher decoder to generate synthetic samples. Then why not simply use the teacher model directly? What advantages are gained by distilling the teacher encoder into a smaller student encoder only to recombine it with the teacher decoder? The paper also lacks an ablation study to justify the design choices in the method.
* Overall, the paper needs substantial improvement in writing quality and clarity. Implementation details are severely lacking, e.g., hyperparameters used for training the proposed and compared methods, details on synthetic data generation during evaluation, how the random forest model is trained, and explanation of the evaluation metrics (e.g., DPR, EOR).
* The method demonstrates minimal performance gains over the compared methods across downstream tasks (Table 2,3).
* They should additionally report FID for synthetic data quality.

---

confidence: 3
contribution: 2
initial_rating: 3
presentation: 2
questions: See weaknesses.
soundness: 3
strengths: 1. Enhanced Privacy Protection: The model's ability to operate without real data makes it highly suitable for environments with strict privacy regulations or sensitive data restrictions.
2.  By employing a smaller model architecture, Fair4Free minimizes the computational demands, making it feasible for deployment on less powerful devices, including edge devices.
3. It consistently outperforms other models in generating synthetic data that scores highly on fairness, utility, and quality metrics, as validated by rigorous experimental evaluations.
summary: Fair4Free introduces an innovative generative model designed to create fair synthetic data without accessing actual datasets. It leverages a technique called data-free distillation, where knowledge is transferred from a teacher model to a smaller student model using only noise as input. The approach is touted for its effectiveness in generating data that adheres to fairness, utility, and quality benchmarks, surpassing existing models.
weaknesses: 1.  The model currently focuses on addressing bias with respect to single sensitive attributes, potentially overlooking complex bias scenarios involving multiple intersecting attributes.
2. Scalability Concerns: While the model is efficient, scaling it to handle larger or more complex datasets without compromising performance remains a challenge.
3. Can Fair4Free be adapted to efficiently manage multiple sensitive attributes to tackle intersectional biases more effectively?
4. In terms of decision-making and predictive accuracy, how do the synthetic datasets generated by Fair4Free compare to those derived from traditional data generation methods?
5. Adaptability to Data Shifts: What measures can be taken to enhance Fair4Free's robustness against dynamic changes in data distribution that are common in real-world settings?

---

confidence: 3
contribution: 2
initial_rating: 3
presentation: 2
questions: see weaknesses.
soundness: 2
strengths: 1.  The data-free approach allows the generation of fair data even when access to original datasets is restricted, addressing significant privacy concerns.
2.  By using a smaller student model, Fair4Free reduces computational resources and enables potential deployment on edge devices.
3.  The model demonstrates superior performance across fairness, utility, and synthetic quality metrics compared to state-of-the-art models.
summary: Fair4Free presents a novel approach to generating synthetic data that is fair and unbiased using data-free distillation. This method is particularly useful when access to training data is restricted due to privacy concerns. The process involves distilling knowledge from a pre-trained teacher model to a smaller student model without using real data, relying instead on noise input. The paper claims significant improvements over other models in terms of fairness, utility, and synthetic quality.
weaknesses: 1. Complexity and Overhead: While reducing computational costs via a smaller model, the initial setup of training and distilling between models can be complex and resource-intensive.
2.  How does the performance of synthetic samples generated by Fair4Free compare to non-synthetic data in terms of real-world utility and fairness?
3. How robust is Fair4Free to shifts in data distributions that might occur in practical scenarios?

---

confidence: 2
contribution: 2
initial_rating: 3
presentation: 2
questions: I'm a bit confused about the motivation for using data-free distillation. The authors claim that the method's benefit is that it can be applied when data is inaccessible; however, the teacher model required in the method is trained with a designed loss function to have a fair representation. 

I assume the underlying assumption of this work is that the existing foundational generative models do not have the desired fairness property, so in reality, the original training data is still required to apply the proposed method. Then, my question is, why does data-free distillation matter in this case? Would it be easier to use a single model to learn how to generate fair data from scratch?

As a non-practitioner in fairness, I would appreciate if the author could clarify if I misunderstood the setting or the motivation of the work.
soundness: 2
strengths: 1. The empirical results look promising as they outperform most baselines.
2. The experiment is performed on both visual and tabular data 
3. The proposed method is well presented and easy to understand
summary: This work proposes a generative model for fair synthetic data generation with data-free distillation. The proposed method involves first training a fair teacher model on the biased dataset and producing a fair representation, then distil using a student architecture. Finally, synthetic fair samples are reconstructed from the distilled fair representation. The authors apply the method on image and tabular data, and outperform all baseline methods.
weaknesses: 1. The teacher model trained in this paper is assumed to have fair representation. This involves using a regularized distance correlation minimization loss to weaken the connection between the sensitive and non-sensitive attributes. This limits the applicability of the proposed method (i.e. distilling from pre-trained large generative models without a fairness guarantee).
2. Experiment on visual data (i.e. CelebA and Colored-MNIST) has no quantitative benchmarking and comparison with baseline methods. Comparison with baseline such as EDM [1] and showing better fairness can strength the soundness of the experiment, even without outperforming it in terms of visual quality.
3. The claim about data-free training is a bit confusing; please refer to the Questions section.

[1] Karras, T., Aittala, M., Aila, T. and Laine, S., 2022. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems, 35, pp.26565-26577.

Meta-review: The submission proposes "Fair4Free," a generative approach to creating synthetic fair data via data-free distillation. While the paper addresses an important issue in fairness and privacy, it fails to convincingly justify its contributions and practical advantages. Below is a summary of the key feedback:

Strengths:
* Addresses a relevant problem of fairness in synthetic data generation.
* The approach operates in privacy-restricted scenarios, which is a valuable consideration.
* Includes evaluation across multiple metrics on tabular and image datasets.

Weaknesses:
* Unclear Contributions: The method's claim of being "data-free" is misleading as it still relies on a biased dataset to train the teacher model. Reviewers questioned the necessity of distilling knowledge from the teacher model rather than using it directly. The novelty and advantage of the distillation process, particularly when reusing the teacher model’s decoder, are insufficiently justified.
* Limited Empirical Validation: Quantitative results demonstrate marginal improvements over baselines, and the performance gains (5%-12%) are not compelling. Key experimental details, such as hyperparameters and ablation studies, are missing, undermining the reproducibility and validation of design choices. Evaluation on image datasets (e.g., CelebA, Colored-MNIST) lacks robust benchmarking against advanced baselines (e.g., diffusion models).
* Presentation and Clarity: The writing lacks clarity, and the methodology is not well-explained. Several questions from reviewers (e.g., on teacher-student architecture rationale and multi-attribute fairness) remain inadequately addressed.
* Scalability and Applicability: The approach struggles with scaling to larger datasets or complex bias scenarios, limiting its generalizability.
Intersections of multiple sensitive attributes, an essential aspect of fairness, are not addressed.

Based on the unclear novelty, lack of robust validation, and insufficient responses to reviewer concerns, I recommend rejection. While the paper has potential, it requires significant improvements in methodology, experimental rigor, and presentation to meet the standards of acceptance.

Decision: Reject