FairGRAPE: Fairness-aware GRAdient Pruning mEthod for Face Attribute Classification

Compression of deep models involves various methods to reduce computation cost without significant loss in model performance. Major categories of compression techniques include Parameter pruning [13, 20]; Parameter quantification [19]; Lower-rank factorization [47]; knowledge distillation [24]. In this paper, we focus on examining the first one: parameter pruning, which reduces the number of weights associated with nodes or edges in a network.

Prior research in pruning has focused on the following aspects: how to maintain certain structural elements of the original model [35, 23, 53], how to rank the importance of individual features [41, 50, 60, 34, 11, 37, 40], whether pruning should be done at once or across several steps [13, 59], and how many pruning and retraining iterations are required [4, 20].

Fairness has received much attention in the recent literature on computer vision and deep learning [5, 51, 52, 36, 55, 39, 6, 16, 48, 57, 49, 29, 21]. The most common goal in these works is to enhance fairness by reducing the accuracy disparity of a model between images from different demographic sub-groups. For example, a face attribute classifier may yield a disproportionately higher error rate on images of non-White or females [5, 30]. Another line of work has investigated biased or spurious associations in public image datasets and models between different dimensions of sensitive groups and non-protected attributes such as semantic descriptions, facial expressions, and age [65, 28, 64, 6, 1]. Our paper focuses on the former: the mitigation of accuracy disparity.

The cause of demographic bias can be demographically imbalanced datasets and the design choice of learning algorithms or network architectures [10, 32]. Prior works have found that a face dataset dominated by the White race produces a poor performance for other races, while a face dataset with balanced group distribution, from either real or synthesized data, can enhance fairness [30, 17, 15, 52, 18, 58]. Algorithmic bias can be mitigated through either explicit fairness constraints [61, 31], matching learned representations to a target distribution or group-wise characteristics [8, 44, 45], or adversarial mitigation and decoupling to disconnect representation and sensitive groups that attempts to decorrelate sensitive attributes and model outputs [43, 1, 2, 54, 33, 12]. Our method estimates the importance of each connection weight toward each sub-group and maintains between-group ratios in pruning.

Only a few studies have been concerned with fairness in the compression of deep models. [25] reported that pruned models tend to forget specific subsets of data. It is examined in [26, 46] that pruning can impact demographic sub-groups disproportionately in face attribute classification and expression recognition. Another recent work [3] showed that knowledge distillation could reduce bias in pruned models. All these studies focus on measuring pruning-induced biases between output categories. To the best of our knowledge, our paper is the first to separate the pruning impact on output classes and sensitive groups and propose a pruning algorithm to mitigate biases in both dimensions.

Consider a neural network $\bm{f}$ parameterized by $\bm{\theta}\in\mathbb{R}^{m}$ and a dataset $D=\{(\bm{x_{i}},\bm{y_{i}},k_{i})\}^{n}_{i=1}$, where $\bm{x_{i}}\in\mathcal{X}$ is an input vector, $\bm{y_{i}}\in\mathcal{Y}$ is a target output, and $k_{i}\in K$ is a sensitive attribute. The goal of network pruning is to find the following parameter set:

Here $\ell(\cdot)$ denotes a loss function, and $c\in(0,1)$ is the desired sparsity level.

We further examine the network’s performance on different subsets of $D$. Let $D_{k}=\{(\bm{x_{i}},\bm{y_{i}},k_{i})|k_{i}=k\}$ denote the subset of instances from a sensitive group $k\in K$. Given a performance metric $A(D_{k};\bm{\theta})$, the difference in performance on $D_{k}$ between the full model $\bm{f}$ and a compressed model $\bm{f^{\prime}}$ is:

The mean of all group-wise performance differences is:

Our goal is to minimize the variance of performance differences in a pruned model. This task can be formulated as finding the following $\bm{\theta^{*}}$:

Note that the actual task of the model determines the choices of the performance metric $A(\bm{\theta};D_{k})$. This paper focuses on classification tasks and thus uses accuracy, false positive rate (FPR), and false negative rate (FNR) as performance metrics. The output space $\mathcal{Y}$ and sensitive groups $K$ can be either overlapping or disjoint, and this paper examines both cases.

The common idea behind model pruning methods is estimating the importance of edges and pruning less important ones. While the existing methods focus on measuring the importance to the whole dataset, our method aims to preserve important weights for each sensitive group to mitigate biases.

To this end,we propose to compute the group-wise importance score of each weight with respect to each sensitive group, and then use a greedy algorithm to select weights based on the scores. At each step, the method compares the current ratio of importance scores with the target ratio (i.e. , the ratio in the model before the current pruning step). Then the group that has the largest difference will be selected, and the method adds one weight with the highest importance for the selected group to the selected network. Once the desired number of weights is selected, the remaining weights are pruned. FairGRAPE compresses all layers of the model with this node selection process, which is illustrated in Figure 2.

To evaluate our proposed FairGRAPE, we conducted extensive experiments with four face image datasets, including FairFace [30], UTKFace [63], CelebA [38], and the person subtree of ImageNet [56]. Table 1 shows the distributions of races and genders in all datasets. Images are fairly distributed across the seven race groups in the FairFace, while the white race is dominant in the UTKFace. This allows us to validate that the effect of our method remains consistent with the presence of data bias. In UTKFace, only one “Asian” contains both Asian and Southeast Asian faces. We excluded the “Other” category in UTKFace due to its ambiguity. Race/ethnicity information is not provided in CelebA and ImageNet. FairFace, UTKFace, and CelebA provide annotations for binary genders. While the ImageNet person subtree contains three gender classes: Male, Female, and Unsure (non-binary), we only use ImageNet samples with binary genders to stay consistent with other datasets. Following the practice in [56], Imagenet samples that are from ”unsafe” categories or have imageability scores $\leq$ 4 are also excluded.

We deploy the following four baseline methods: Single-Shot Network Pruning (SNIP) [34]: calculates the connection sensitivity of edges by back-propagating on one mini-batch and prunes the edges with low sensitivity. Weight Selection (WS) [19]: prunes the weights with magnitudes below a threshold in a trained model. It is the most commonly used in mobile applications[42]. Lottery Ticket Identification (Lottery) [13]: records the initial state of the network; resets the model to its initial state after each pruning iteration. Gradient Signal Preservation (GraSP) [50]: removes the parameters with low Hessian-gradient scores to maximize gradient signal in the pruned model.

We first perform experiments to verify bias mitigation in classifying sensitive attributes. Table 2 shows classification accuracy and biases on FairFace and UTKFace datasets where we compress the ResNet-34 and MobileNet-V2, respectively. The column ‘Task’ indicates the dataset and classification task. We report overall classification accuracy, accuracy by sensitive groups, and variances in accuracy degradation. FairGRAPE consistently produces a substantially higher accuracy, lower differences in accuracy, and lower variance in performance degradation than the baseline methods. For example, SNIP sometimes produces accuracy scores close to our method, but it has a remarkably larger accuracy variance than FairGRAPE, which implies the potential biases caused by model pruning. In the only cases of FairFace, WS produced a model with a smaller race classification accuracy gap between male and female images, but at the cost of drastically worsened accuracy for both groups. These results suggest that our proposed method successfully equalizes the impact of pruning on the sensitive groups regardless of the classification task, thus achieving a better trade-off between fairness and overall accuracy.

Furthermore, FairGRAPE shows solid performances in all settings with different architectures and datasets (balanced or imbalanced), proving the proposed method’s robustness. See supplementary material for results when we jointly control race and gender groups.

We next visualize the proportion changes of False Negative Rates(FNRs)/False Positive Rate(FPRs) from the full model after pruning by FairGRAPE and other baseline methods in Figure 3. Each point in the plot represents normalized FNR and FPR change of a specific race group in the model produced by one of the pruning methods, and the ellipses are created by estimating a 95% confidence region of data points. The results reveal that the proposed FairGRAPE produces data points closer to the origin than the other data points generated by the baseline methods. More importantly, FairGRAPE creates the smallest ellipse, which demonstrates that performance changes for each group are close to each other. Thus the distribution of induced bias across sensitive groups is fair.

To evaluate the performance of FairGRAPE in more practical cases where output classes and sensitive groups are disjoint, we experiment with classification on CelebA and ImageNet datasets. CelebA contains the 39 non-sensitive categories of facial attributes such as eyeglasses, makeup, and lipsticks. We code each of these categories as a binary classification task. For the ImageNet experiment, we use the modified person subtree, which contains 10,215 images in 103 distinct classes (e.g. , basketball player, rapper) with gender labels [56]. We train the models to classify the class to which a given image belongs. Note that we use the ResNet-34 network at 50% sparsity for the ImageNet experiments and the MobileNet-V2 network at 90% sparsity for the CelebA experiments.

Table 3 shows the overall accuracy, accuracy of each gender, and the standard deviation of accuracy change. FairGRAPE achieves the highest accuracy on ImageNet. Although GraSP has a smaller accuracy gender gap than our method, its overall accuracy and variance of performance degradation are drastically worse. In the CelebA experiment, FairGRAPE has a significantly lower variance in accuracy change than other methods while achieving the highest accuracy. The results demonstrate that FairGRAPE performs well on sensitive attribute classification tasks and non-sensitive attributes, thus widely applicable in various applications.

In practice, labels for sensitive attributes may not always be available. Therefore, we further examine the performance of our method on a dataset without demographic group labels through unsupervised group discovery.

Table 4 shows the accuracy and bias of experiments on the FairFace dataset. In this test, FairGRAPE conducts pruning by calculating the importance score of parameters for clusters learned from unsupervised learning as sensitive groups. Then we evaluate accuracy and bias with actual race labels. We labeled the seven clusters using K-means clustering on image embedding generated by the ResNet-34 network pre-trained on Imagenet. While all baseline methods have low accuracy and large variance of accuracy as they do not consider the sensitive groups, the FairGRAPE method consistently results in the lowest performance variance, suggesting that our proposed method has the potential to compress the model while reducing biases even in the absence of sensitive attribute information. The K-means algorithm’s simplicity further reinforced our method’s generalizability when the precise group partitioning is complex or noisy.

Table 5 shows the performance of FairGRAPE with different group importance and iterative retraining settings. We first find that group importance is the essential component in our proposed method. The baseline method, which does not use both group importance and iterative retraining, has remarkably lower accuracy, gender gap, and variance of accuracy changes than our method, which utilizes both components. As the pruning step r at each iteration increased, the accuracy decreased, and the bias increased gradually.

More specifically, the model suffers from an obvious performance drop and bias increase when $r$ increased from 0.1 to 0.2. This result agrees with previous findings [13] that iterative pruning improves performance.

Finally, we examine the percentage of training images used in importance calculation. FairGRAPE calculates group-wise importance score $I_{w,k}=(g_{w}w)^{2}$ for each weight $w$, where $g_{w}$ is calculated with respect to average loss across selected mini-batches of the training set. It has been found that the proportion of training images used in the calculation process affects pruning speed and accuracy [41]. We compared the performance using 100%, 50%, 20%, and 10% of training sets. The result indicates that 20% is the ideal ratio that produces the best performance.

This section examines whether rebalancing the dataset could mitigate pruning-induced bias. Using the UTKFace dataset, where white faces are dominant, we tested SNIP and GraSP with their gradient calculation and parameter selection conducted on non-white examples only (i.e., Black, Asian, Indian) Table 6 shows the result. Interestingly, using a subset of data did not significantly change overall accuracy. However, the overall biases increased compared to the case of using all data. This change shows that the problem of biases in pruned methods cannot be solved by simple data rebalancing and our method effectively addresses this challenging problem.

We next evaluate the performance of FairGRAPE across different sparsity levels to understand its effectiveness. Figure 4 shows changes in accuracy and biases over different sparsity levels. FairGRAPE outperforms the baseline methods by producing the highest accuracy and lowest disparity of performance degradation across sensitive groups at various pruning rates. As sparsity changes from 90% to 99%, most baseline methods exhibit a sharp decrease in accuracy and increase in bias, while performance change in FairGRAPE is substantially smaller. This confirms that our method can be widely deployed to real-world systems with various sparsity levels.

This subsection performs an in-depth structural analysis on pruned networks. Figure 5 visualizes the ratio of importance scores at each layer for each gender group. Each bar represents a convolutional or linear layer. and the width of a colored segment indicates the ratio of importance score for the corresponding gender group. FairGRAPE preserves the balanced importance distribution of the full network, with similar scores for both genders, leading to substantially smaller gaps in accuracy and accuracy change. The group-agnostic pruning methods, including SNIP and Weight Selection, select weights with higher importance for the female group, which is already showing higher accuracy in the original model. Consequently, the accuracy of the male group suffered from a substantially greater loss and the gap is much larger than the model pruned by FairGRAPE.