Response to Reviewer KXKr (1/2)
`Response [1/2]`
Thank you for the constructive feedback, which has helped us improve the quality of our paper. We respond below to your questions and concerns:
***W1: This paper kind of mixing fairness and bias and uses both terms interchangeably, especially for the experiment evaluation part, they define the metric for bias by themself which reduces the credential of the evaluation. I wonder if any other metrics from other research papers have been used for evaluation. Is it possible to use well-defined fairness metrics like demographic parity/ equal opportunity, etc?***
We apologize for the confusion arising from our uncareful use of the terms fairness and bias. They indeed have different meanings in our paper. We consider fairness as the distributional alignment with a user-defined target distribution, a flexible notion. Since our main experiments use a perfectly balanced target distribution, we define the metric bias to measure how far the generated images are from the perfectly balanced target distribution. When evaluating fairness for age, where we consider 75% young and 25% old as the target distribution, we directly report the percentage of age=old. We added clarification in the second paragraph of section 5.1, highlighted in blue.
We note that demographic parity (DP) and equal opportunity (EO) are defined for prediction problems, where every individual has a protected attribute $S$, a true label $Y$, and a prediction $\hat{Y}$ (chapter 3 of [1]). For T2I generative models, every generated image has only a protected attribute $S$. Therefore, DP and EO do not exactly apply here. In a way, the fairness problem in T2I generative models is simpler than that in prediction problems. Our objective is simply to control the generated images’ marginal distribution in terms of $S$ towards a target distribution.
We understand the reviewer has concern over whether the bias metric is truthful. In response, we have added plots of gender and racial representations by each prompt in Appendix Fig. A.2, A.3, A.4, and A.5, specifically at page15 & 16. These results provide a more detailed analysis than those presented in Tab. 1.
***Q1: for the equation 4, what is the u?***
We have significantly revised Section 4.1 to enhance the clarity of our presentation. Eq. 4 in the initial paper corresponds to Eq. 4 and 5 in the updated paper. $\\{\boldsymbol{u}_1,\cdots,\boldsymbol{u}_N\\}$ are $N$ iid samples drawn from the target distribution $\mathcal{D}$. Say we use the one-hot vectors [0,1] and [1,0] to denote male and female, and consider a balanced target distribution over these two classes. Then approximately half of $\\{\boldsymbol{u}_1,\cdots,\boldsymbol{u}_N\\}$ will be the vector [0,1] and the other half will be [1,0]. We construct $\\{\boldsymbol{u}_1,\cdots,\boldsymbol{u}_N\\}$ in this way so that it represents the target distribution and the optimal transport finds the most efficient modification of the current images towards the target distribution.
***Q2: As for the alignment loss, have you tried some other metrics other than the optimal transport loss? And why did you choose the optimal transport metric?***
We naturally arrived at the optimal transport (OT) formulation and didn’t experiment with other losses. We start by considering the following problem: suppose we have a set of 10 images, composed of 2 female and 8 male images, and our goal is to reconfigure this set to contain an equal number of female and male images, specifically 5 of each. The key question is determining which gender class every image should be reconfigured to. Additionally, it is essential to minimise alterations to the images when striving to attain an equal distribution of 5 female and 5 male images. This is naturally the OT (or linear assignment) problem, identifying which class every image should be transported to while minimising the transport distance. Finally, the OT problem considered here is low dimensional (2 for gender, 4 for race, and 8 for gender$\times$race) and therefore efficient to solve.
We sample $\\{\boldsymbol{u}_1,\cdots,\boldsymbol{u}_N\\}$ from the target distribution and compute the expectation of OT because it (1) acknowledges even a perfectly balanced distribution can still produce unbalanced finite samples, (2) takes into account the sensitivity of OT, and (3) produce a confidence measure for the target class assignment.