COMPUTATIONAL-UNIDENTIFIABILITY IN REPRESEN-TATION FOR FAIR DOWNSTREAM TASKS

Abstract

Deep representation learning methods are highlighted as they outperform classical algorithms in various downstream tasks, such as classification, clustering, generative models, etc. Due to their success and impact on the real world, fairness concern is rising with noticeable attention. However, the focus of the fairness problem was limited to a certain downstream task, mostly classification. We claim that the fairness problems to various downstream tasks originated from the input feature space, i.e., the learned representation space. While several studies explored fair representation for the classification task, the fair representation learning method for unsupervised learning is not actively discussed yet. To fill this gap, we define a new notion of fairness, computational-unidentifiability, which suggests the fairness of the representation as the distributional independence of the sensitive groups. We demonstrate motivating problems that achieving computationally-unidentifiable representation is critical for fair downstream tasks. Moreover, we propose a novel fairness metric, Fair Fréchet distance (FFD), to quantify the computationalunidentifiability and address the limitation of a well-known fairness metric for unsupervised learning, i.e., balance. The proposed metric is efficient in computation and preserves theoretical properties. We empirically validate the effectiveness of the computationally-unidentifiable representations in various downstream tasks.

1. INTRODUCTION

Thanks to the outstanding performance and development of deep learning, it has been widely applied to various domains, including natural language processing (NLP) (Devlin et al., 2018 ), computer vision (Karras et al., 2019) , and generative models (Goodfellow et al., 2014) . On the other hand, the reliability and fairness concerns (Lee & Floridi, 2020; Angwin et al., 2016; Dastin, 2018) advanced due to their impact on the real world applications. Such fairness concerns include credit limit estimation (Vigdor, 2019) , job application filtering (Dastin, 2018) , or crime prevention (Dressel & Farid, 2018) , etc. Accordingly, algorithmic fairness is getting growing attention to prevent biased predictions. Following the mainstream fairness literature, we here focus on group fairness (Dua & Graff, 2019; Zafar et al., 2015; Hardt et al., 2016) , which suggests the equality of certain statistical measures (e.g., true positive rate, positive prediction) between subgroups with different protected attribute (e.g., gender, race, religion, etc). It has been widely studied to mitigate fairness violations in downstream tasks. Numerous studies (Hardt et al., 2016; Choi et al., 2020; Pleiss et al., 2017; Madras et al., 2018) explore how to attain group fairness in classification tasks. The primary objective of this family of works is to obtain the prediction independence of a protected property. Hardt et al. (2016) suggest equal opportunity, which requires the same true positive rates for the subgroup. Calibration among the subgroups (Kleinberg et al., 2016) is to match the predicted probability and actual distribution of favorable class. Moreover, some works (Kim et al., 2020; Jang et al., 2021) study efficient multi-constraint optimization to satisfy multiple fairness notions. However, most of the works mainly focus on the supervised setting. Even though deep learning has significant success in various unsupervised learning tasks, such as clustering (Xie et al., 2016; Guo et al., 2017 ), generative model (Karras et al., 2019; Radford et al., 2019), and NLP (Hadifar et al., 2019) , the fairness of unsupervised learning is relatively not actively studied (Buet-Golfouse & Utyagulov, 2022), and how to quantify the fairness of unsupervised learning methods has not been well established yet. A widely used metric for fair clustering is called balance (Chierichetti et al., 2017) , which is analogous to demographic parity (Barocas & Selbst, 2016) in classification. However, the balance has some limitations since it quantifies fairness by computing the ratio of samples in different protected groups within a cluster. For instance, even in the ideal balance (the ratio of the samples from different groups matches the group truth), the sensitive groups can distribute samples separately within clusters. In this case, it is easy to determine which sensitive group the sample belongs to so that it might lead to a biased decision in downstream tasks. Especially in generative models, e.g., VAE (Kingma & Welling, 2013), the generated samples can be imbalanced if the latent space is dependent on the sensitive attributes. This can cause a critical problem as generative models are widely applied to mitigate the imbalance of datasets (Guo et al., 2019; Fajardo et al., 2021; Mirza et al., 2021) . Instead, we propose a novel approach, computational-unidentifiability, as a fairness notion in unsupervised learning. Analogous to the fact that biased data is responsible for the biased decision-making (Buolamwini & Gebru, 2018; Mehrabi et al., 2021) , we here claim that the learned representation itself plays a critical role in fair downstream tasks utilizing DNN. Even though deep representation has been appreciated for its superb performance (Eldan & Shamir, 2016; Kozma et al., 2018) , the fairness concerns in the space have been overlooked. Thus, we explore the fairness in representation space that could bridge DNN and the downstream tasks with fairness concerns. We validate our claim on downstream tasks by comparing the performance and fairness of two distributions: fair and unfair representation. To measure fairness in representation space, we propose a novel metric called FFD (Fair Fréchet distance) inspired by Fréchet distance (Dowson & Landau, 1982) to efficiently quantify fairness in representation space by measuring distributional independence of the sensitive groups with computational identifiability (Hébert-Johnson et al.; Lahoti et al., 2020) . Unlike the balance, we not only consider statistical independence but also distributional independence between the sensitive groups. This can be a good reference for future work to evaluate the fairness or distributional independence in the representation space of certain attributes of interest. Moreover, we propose a deep fair clustering framework to learn a fair representation that achieves comparable performance with other clustering methods while ensuring fairness. The contributions in the paper can be summarized as follows: 1. We study the motivating problem of why fair representation is important to achieve fair downstream tasks. 2. We propose a novel metric that quantifies fairness in representation space. We provide rigorous analysis of the theoretical property and complexity of our fairness metric. 3. We propose a framework for fair representation learning for downstream tasks. 4. We validate our method on various benchmark datasets comparing with state-of-the-art fair methods in the literature.

2. RELATED WORKS GROUP FAIRNESS

As a class of definitions, group fairness measures the disparity of predicted outcomes among the subgroups with certain sensitive attributes. A number of works introduce fair notions to mitigate the bias and ensure the independence of the performance measures between the subgroups to achieve group fairness. Demographic parity (Barocas & Selbst, 2016) suggests that positive prediction should be equalized and independent of the sensitive attribute. Equal opportunity (Hardt et al., 2016) states that true positive rates should match. Likewise, Predictive equality (Chouldechova, 2017) states the equality of false positive rates. Group-wise calibration (Kleinberg et al., 2016; Pleiss et al., 2017) proposed to match the probability estimate with the actual ratio of positive distribution within the group. In an unsupervised setting, balance (Chierichetti et al., 2018) is introduced to have an equal number of samples from different protected groups within a cluster as fair clustering. However, the balance only considers statistical parity, which limits the utility as a metric since perfect balance (i.e., 1) does not guarantee fairness (as the base rate differs). Moreover, none of the works explore the fairness of the representation itself.

