Fairness-Aware Attention for Contrastive Learning

Need for further empirical results and experimental details

Please see the general comment for all reviewers addressing these points.

What are the potential trade-offs between and fairness and accuracy?

Answer

We thank the reviewer for drawing our attention to fairness-accuracy tradeoff. For the colorMNIST task, we find that sparseFARE obtains top fairness and (shared) top accuracy. This implies sparseFARE weakly Pareto dominates the other baseline models InfoNCE, Fair-InfoNCE, and CCLK. For the CelebA task, we observe that SparseFARE Pareto dominates all the kernel models except for Linear and Polynomial. SparseFARE nonetheless attains a better fairness-accuracy tradeoff than Linear and Polynomial and so is still preferable. Additionally noteworthy is that over the course of training we observe sparseFARE improving both accuracy and fairness together, implying that sparseFARE is able to learn representations that do not necessarily need to compromise fairness for higher accuracy.

What are the ethical considerations of using ML to reduce bias? Answer

We thank the reviewer for pointing out this important consideration. We have included the following discussion in Appendix E. We present the discussion here as well for convenience.

In terms of ethical considerations of using machine learning for bias reduction, we argue that fairness-aware machine learning is a powerful and ethically well-motivated approach to the problem of unfair outcomes in AI, and in particular the conceptualization of the problem we use and our proposed methods also offer benefits in terms of ethics.

We note that there are two, interconnected prevalent ethical issues in fair ML. The first is that almost all fair ML literature simplifies the problem of fairness to simple binaries and the second is that fairness metrics (which are typically built atop these binaries) and the choice of which to use themselves involve value judgements that can disadvantage certain people. People have intersectional identities and invariably belong to multiple groups simultaneously. When it comes to choosing fairness metrics, inherent to the majority of approaches in fair ML is that the researcher or practitioner decide what definition of fairness to use for their model. It has been shown that various definitions of fairness are not only mutually inconsistent but also prioritise different groups in different scenarios [1]. In a sense then, solving for fairer ML models only pushes the problem from the model and onto the practitioner, as a ‘fairer’ model itself advantages and disadvantages different groups under different settings.

These two ethical considerations motivate the approach of our paper to conceptualise fairness in a more general setting where sensitive attributes can be continuous and multi-dimensional and fairer models are measured in terms of sensitive information removal. This conception avoids the ethical issues of binaries and fairness metrics.

We do note however that there still exist ethical concerns with our approach in terms of explainability. Measuring fairness by sensitive information removal (by measuring loss from a trained classifier) does not have an intuitive scale or unit of measurement for discussing the fairness or unfairness of a model. Although we can compare two models in terms of which is fairer, saying a model is fair because it scores some number in MSE has little intuitive meaning. Being unable to communicate the specifics of how a learned representation has removed sensitive information and how will affect downstream classifiers risks undermining confidence in fair ML as well and creating accountability problems as well.

Despite the explainability issue, we nonetheless believe that this approach represents a promising and exciting direction in fair ML that deal with substantive existing ethical issues. We hope that one area of future research may be deriving theoretical frameworks that can derive guarantees between sensitive information removal from debiased representations and upper bounds on downstream fairness metrics. This would develop a practical link to well-known ideas of fairness and how unfair outcomes could appear in worst-case scenarios.

[1]: Garg, Pratyush, John Villasenor, and Virginia Foggo. "Fairness metrics: A comparative analysis." 2020 IEEE International Conference on Big Data (Big Data). IEEE, 2020.

Need for further empirical results and experimental details

Please see the general comment for all reviewers addressing these points.

What are the differences between FAREContrast and the objective in [2]

Answer

The key difference between the objective in [2] and FAREContrast is that FAREContrast contains learnable attention scores as conditioning coefficients on the sample similarity scores whereas [2] does not. [2] therefore is used only to train in the MLP and encoder where FAREContrast trains the MLP, encoder, and attention projection matrices in one end-to-end loop.

Is sparseFARE sufficiently well motivated and does its induced performance benefit justify the implementation cost?

Answer

We argue that the benefits of sparseFARE do indeed justify its implementation cost. In particular, we note that in colorMNIST sparseFARE Pareto dominates all models and is significantly more computationally more efficient than the kernel models. For CelebA, it Pareto dominates or exhibits a more favourable fairness-accuracy tradeoff than the baselines. We argue that this is because sparisification makes intuitive sense within this framework, whereby samples that are sufficiently distant in terms of bias-status (and therefore likely to bias the representations) may as well be dropped and allow attention to be focussed over the remaining samples that help learn debiased and meaningful representations.

Secondly, attention sparsification schemes typically exhibit a tradeoff between computational complexity and model performance (in this case taking both accuracy and fairness together) as sparisifation sacrifices the capacity of the attention mechanism for speed. SparseFARE, however, exhibits higher performance than the baselines while being faster as well and so again doesn’t exhibit the normal tradeoff we observe in the literature.

Hence we believe that since sparsity, in this setting, is able to offer improvements in all these areas simultaneously, it’s implementation cost is justified.

[2] Yao-Hung Hubert Tsai, Martin Q Ma, Han Zhao, Kun Zhang, Louis-Philippe Morency, and Ruslan Salakhutdinov. Conditional contrastive learning: Removing undesirable information in self- supervised representations. arXiv preprint arXiv:2106.02866, 2021c.

Notation in section 2 for matrix U is overloaded

Answer

We thank the reviewer for drawing our attention to this potential source of confusion. We noticed there is a potentially connected typo in which we wrote $U = [e^{f(x_i, y_j)}]_{ij}$ . As U is a matrix with $(i,j)$ element given by these similarity scores, this should of course be that the $[U]_ij = e^{f(x_i, y_j)}$. Regarding overloaded notation, the two references to the definition of U is simply first a general representation of U followed by an instantiation of what U is for our purposes. Specifically, the matrix U is introduced as the data matrix such that when transformed by the values projection matrix W_V, we obtain the values V. That is, $V = UW_V$. Given our FARE set up, the untransformed values in our case is the matrix of similarity scores. Hence in our model U is the matrix whose $(i,j)$ element is given by $e^{f(x_i, y_j)}$. In other words, naming U as the matrix of similarity scores $e^{f(x_i, y_j)}$ is just a specification of the data that takes the place of the values for our model.

In section 3.3, there is no $z_i$ appearing in the loss

Answer

We thank the reviewer for pointing this out and have fixed the notation. In particular FARE is now defined as an operator that takes as argument the whole batch, $FARE( \{ (x_i, y_i, z_i) \}^b_{i=1} )$. This clarifies the fact that FARE computes a finite sample estimate of the conditional similarity score between $(x_i, z_i)$ and $y$ for $y \sim P_{Z = z_i}$ by taking in information over the whole batch and weighing each sample according to their protected attribute.

There are missing citations, for example [1], on page 5 for the derivation of attention as kernel-based similarity, for example

Answer

We agree that [1] is highly relevant related work and indeed we include reference to it in our Related Work section. However, [1] is not cited here because our derivation doesn’t rely on theorems or results from [1] or other work, aside from the use of the kernel density estimator approach to estimate the joint and marginal densities which is cited. We also note that [1] is different to our work in the sense that [1] takes the attention mechanism and decomposes it into parts that, by replacing with various kernels, derive new and enriched attention mechanisms. Our work, on the other hand, doesn’t involve decomposing attention nor replacing any component of attention with kernel similarity metrics. Our work shows instead that the estimation of the similarity score (when conditioning on some additional attribute) in the contrastive objective can be approximated by an attention mechanism. In this sense we don’t perform any decompositions and we go straight from conceptualising the similarity score as an inner product to deriving an attention mechanism without appealing to kernel similarity metrics in between. For these reasons we agree that [1] is a relevant work to understand some of the research community’s work in enriching attention, however we do not cite it on this page due to the differences mentioned.

There is an incorrect math statement in section 3.1 that $\phi(g(y))$ is used to estimate $E_{y | z} [\phi(g(y)))]$

Answer

We apologise for the confusion regarding notation. To clarify, we don’t use $\phi(g(y))$ to estimate $E_{y | z} [\phi(g(y)))]$. Rather, we use $E_{y | z} [\phi(g(y)))]$ to estimate $\phi(g(y))$. $\phi(g(y))$ is the unknown quantity of interest and we use its expectation to estimate it, expanding the definition of the expectation using joint and marginal densities which we then estimate with kernel density estimators. This allows us to derive an estimator of $\phi(g(y))$.

[1]: Yao-Hung Hubert Tsai, Shaojie Bai, Makoto Yamada, Louis-Philippe Morency, and Ruslan Salakhutdinov. 2019. Transformer Dissection: An Unified Understanding for Transformer’s Attention via the Lens of Kernel. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP).

Need for further empirical results and experimental details

Please see the general comment for all reviewers addressing these points.

Considering the performance of the Laplacian kernel, does FARE alleviate significantly more bias? If the performance gain isn’t significant, what are the benefits of the attention-based approach compared to the kernel-based approach?

Answer It’s true that when implementing CCLK with a Laplacian kernel, the baseline model achieves bias removal close to SparseFARE. We note that our method nonetheless provides 3 simultaneous benefits over the Laplace method in particular, and over the baselines more generally: Using the Laplacian method can indeed remove similar bias to our proposed models, but it does so at the expense of accuracy, shown by the drop in accuracy of 1.4%. Our SparseFARE does not suffer from this tradeoff, producing the same high bias removal with high accuracy concurrently. In this sense, we find that sparseFARE still Pareto dominates CCLK and the other baseline models. An additional benefit of our approach is ease of implementation. In order to discover the best performing kernel baseline method, the user would have to exhaustively search over candidate kernels, each with their own hyperparameters, where there is in general little intuitive guidance in terms of knowing prior to the problem which kernel is suitable. Our approach does not need to consider a host of similarity metrics since the attention mechanism can adaptively learn it given the task, and so in this sense our model is easier to implement and fine-tune. Lastly, we also refer to the benefits in computational complexity of our approach in reducing cubic computational complexity to $O(b^2)$ or $O(b log b)$.

Overall, we agree that there probably will exist situations in which a pre-defined kernel performs close to our proposed method in terms of debiasing. In such situations we note that our methods can and do indeed match that debiasing performance without sacrificing accuracy, are faster to implement and fine-tune, and less computationally complex.

What are additional intuitive explanations for why attention is more effective than kernel for calculating similarity of sensitive attributes?

Answer

An alternate way of seeing the benefit of attention is that it is trained in an end-to-end manner alongside the encoder whereas any given kernel is simply pre-specified. In this way, the attention mechanism helps to focus attention on samples that learn meaningful representations. For example, suppose in a contrastive step that in a given batch there are n samples with highly similar sensitive attributes to the anchor. A kernel would indiscriminately assign all these n samples high weights irrespective of those samples’ effect on the loss. Attention, by taking in information from the loss, is adapted to not only measure similarity over protected attributes, but be adapted by information coming from the gradients to better focus on samples that help minimize the loss and thereby learn meaningful representations.

In Table 1, the result for SpareFARE appears to use the adjacent bucket scheme, but it differs from the result in Table 2 of the appendix. Which is correct?

Answer

We thank the reviewer for picking this up and we apologize for the oversight. The original number in the main body is correct - we’ve made the correction.

In Eqn. (12), does FARE use a feature map associated with the Cosine kernel for $\phi$ ?

Answer

$\phi$ is the feature map associated with the exponentiation of the cosine kernel, which is what we need to aim for to estimate the similarity score in the objective. You can refer to equation 3 on page 3 to see the definition.

Thank you for the replies. I have some comments on Figure 3 and the new results on CelebA dataset.

Regarding Figure 3 in Appendix C.2:

• The blue curve in Figure 3 does not show an appropriate trade-off between fairness and accuracy, but rather shows an improvement in accuracy as fairness improves. Typically, accuracy decreases as fairness improves (e.g., Figure 6 of [3]).
• This might be because the figure was plotted with a model that hadn't been fully trained yet. Namely, the authors chose to plot using a single model during its training, interrupted at 25, 50, 75, and 100 epochs.
• However, I think that it makes sense to use different models, each with distinct hyperparameters, after they have reached convergence. Then, the author’s comments based on Figure 3 are not convincing.

On the new results with the CelebA dataset:

• In the additional experimental results on CelebA dataset, the authors used ‘Attractive' as the target attribute; however, since ‘Attractive’ is subjective and controversial, it is recommended to use one of the other 40 attributes in the dataset for discussion of fairness.
• For instance, a setting that classifies hair color while incorporating gender as a sensitive attribute can be considered, as reviewer Nbdh suggested.

[3]: Zhang et al. Fairness-aware Contrastive Learning with Partially Annotated Sensitive Attributes. ICLR, 2023.