Stablizing Adversarial Invariance Induction by Discriminator Matching
Incorporating the desired invariance into representation learning is a key challenge in many situations, e.g., for domain generalization and privacy/fairness constraints. An adversarial invariance induction (AII) shows its power on this purpose, which maximizes the proxy of the conditional entropy between representations and attributes by adversarial training between an attribute discriminator and feature extractor. However, the practical behavior of AII is still unclear as the previous analysis assumes the optimality of the attribute classifier, which is rarely held in practice. This paper first analyzes the practical behavior of AII both theoretically and empirically, indicating that AII has theoretical difficulty as it maximizes variational {em upper} bound of the actual conditional entropy, and AII catastrophically fails to induce invariance even in simple cases as suggested by the above theoretical findings. We then argue that a simple modification to AII can significantly stabilize the adversarial induction framework and achieve better invariant representations. Our modification is based on the property of conditional entropy; it is maximized if and only if the divergence between all pairs of marginal distributions over between different attributes is minimized. The proposed method, {em invariance induction by discriminator matching}, modify AII objective to explicitly consider the divergence minimization requirements by defining a proxy of the divergence by using the attribute discriminator. Empirical validations on both the toy dataset and four real-world datasets (related to applications of user anonymization and domain generalization) reveal that the proposed method provides superior performance when inducing invariance for nuisance factors.
** Summary The paper studies the problem of representation learning under invariance constraints (i.e., the representation should be invariant wrt some attributes). The authors first review the adversarial invariance induction (AII) approach and they point out its limitations and then they propose a novel variant, which introduces an explicit regularization to minimize pairwise divergence (i.e., different attributes should lead to the same conditional distribution over the learned representation). The authors support the modified objective function both from a formal point of view and with an extensive empirical validation ** Evaluation The paper lies a bit outside my area of expertise. Although the paper tries to capture intrinsic limitations of the AII approach and build a more stable algorithm, my impression is that too many elements in the discussion and derivation remain too vague at the current stage and they would require better and clearer explanation. Detailed comments: 1- In many parts of the paper the notation is not very rigorous and sometimes it may create confusion. In general, the writing needs to be improved in many parts: - In eq. 1, it is not explained what the expectation is wrt. It should be x drawn from p(x). But it would be better to make it explicit. - The setting defined in sect.2 should be more rigorous: it is not clear what y is and what are the attributes we would like to be invariant for. This notation is not fully consistent with eq.1. - In the first paragraph of Sect.3, it would be very helpful to have a more complete sketch of the algorithm. In general, you mention in the Sect. 2 that you focus on the supervised case, but then it is not clear whether this is the case across the paper. 2- While the intuition behind using the divergence is sound, as it is mentioned, it seems to suffer from the same issue as the original AII: minimizing a lower bound does not guarantee that we are minimizing the actual objective. Having the support of 0, does not seem to make it much more sensible. 3- As the description of the algorithm advances in Sect.4.2, it is clear that many additional choices need to be made in order to have a full workable algorithm (e.g., how to estimate q_phi^i). In the paper, the actual algorithm is never reported in detail and this makes the experiments very hard to reproduce in my opinion. 4- At the best of my understanding, the algorithm may become more and more intractable as the number of attribute values grows. In fact, you need to check the divergence for each pair of values and estimated distributions. 5- The empirical analysis seems well executed and a good level of detail is reported on how the datasets are managed and the experiments are set up. Minor comments: - The caption of Fig.1 is not very clear. Many elements at this stage of the paper are not defined yet (e.g., *our proposal minimize the proxy of divergence ...*). - p2: *as the assumption of ... is rarely holds*, remove *is* - p3: *(encoder) that parameterized*, remove *that* - last paragraph of Sect.2 is very confusing. - p4: *updation* is not a word - p4: *In general, minimizing the upper bound...* does not seem correct. - p4: *even such a simple case* -> *even in such a simple case* - Sect 4.1 *the above theoretical*, I would not really say there is much theory behind the analysis in the previous section. - p5 *an ttribute* -> *an attribute* - p6 *the average discriminator*s perception* what is the perception?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Stablizing Adversarial Invariance Induction by Discriminator Matching
Incorporating the desired invariance into representation learning is a key challenge in many situations, e.g., for domain generalization and privacy/fairness constraints. An adversarial invariance induction (AII) shows its power on this purpose, which maximizes the proxy of the conditional entropy between representations and attributes by adversarial training between an attribute discriminator and feature extractor. However, the practical behavior of AII is still unclear as the previous analysis assumes the optimality of the attribute classifier, which is rarely held in practice. This paper first analyzes the practical behavior of AII both theoretically and empirically, indicating that AII has theoretical difficulty as it maximizes variational {em upper} bound of the actual conditional entropy, and AII catastrophically fails to induce invariance even in simple cases as suggested by the above theoretical findings. We then argue that a simple modification to AII can significantly stabilize the adversarial induction framework and achieve better invariant representations. Our modification is based on the property of conditional entropy; it is maximized if and only if the divergence between all pairs of marginal distributions over between different attributes is minimized. The proposed method, {em invariance induction by discriminator matching}, modify AII objective to explicitly consider the divergence minimization requirements by defining a proxy of the divergence by using the attribute discriminator. Empirical validations on both the toy dataset and four real-world datasets (related to applications of user anonymization and domain generalization) reveal that the proposed method provides superior performance when inducing invariance for nuisance factors.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



** Summary The paper studies the problem of representation learning under invariance constraints (i.e., the representation should be invariant wrt some attributes). The authors first review the adversarial invariance induction (AII) approach and they point out its limitations and then they propose a novel variant, which introduces an explicit regularization to minimize pairwise divergence (i.e., different attributes should lead to the same conditional distribution over the learned representation). The authors support the modified objective function both from a formal point of view and with an extensive empirical validation ** Evaluation The paper lies a bit outside my area of expertise. Although the paper tries to capture intrinsic limitations of the AII approach and build a more stable algorithm, my impression is that too many elements in the discussion and derivation remain too vague at the current stage and they would require better and clearer explanation. Detailed comments: 1- In many parts of the paper the notation is not very rigorous and sometimes it may create confusion. In general, the writing needs to be improved in many parts: - In eq. 1, it is not explained what the expectation is wrt. It should be x drawn from p(x). But it would be better to make it explicit. - The setting defined in sect.2 should be more rigorous: it is not clear what y is and what are the attributes we would like to be invariant for. This notation is not fully consistent with eq.1. - In the first paragraph of Sect.3, it would be very helpful to have a more complete sketch of the algorithm. In general, you mention in the Sect. 2 that you focus on the supervised case, but then it is not clear whether this is the case across the paper. 2- While the intuition behind using the divergence is sound, as it is mentioned, it seems to suffer from the same issue as the original AII: minimizing a lower bound does not guarantee that we are minimizing the actual objective. Having the support of 0, does not seem to make it much more sensible. 3- As the description of the algorithm advances in Sect.4.2, it is clear that many additional choices need to be made in order to have a full workable algorithm (e.g., how to estimate q_phi^i). In the paper, the actual algorithm is never reported in detail and this makes the experiments very hard to reproduce in my opinion. 4- At the best of my understanding, the algorithm may become more and more intractable as the number of attribute values grows. In fact, you need to check the divergence for each pair of values and estimated distributions. 5- The empirical analysis seems well executed and a good level of detail is reported on how the datasets are managed and the experiments are set up. Minor comments: - The caption of Fig.1 is not very clear. Many elements at this stage of the paper are not defined yet (e.g., *our proposal minimize the proxy of divergence ...*). - p2: *as the assumption of ... is rarely holds*, remove *is* - p3: *(encoder) that parameterized*, remove *that* - last paragraph of Sect.2 is very confusing. - p4: *updation* is not a word - p4: *In general, minimizing the upper bound...* does not seem correct. - p4: *even such a simple case* -> *even in such a simple case* - Sect 4.1 *the above theoretical*, I would not really say there is much theory behind the analysis in the previous section. - p5 *an ttribute* -> *an attribute* - p6 *the average discriminator*s perception* what is the perception?
assistant
** Summary The paper studies the problem of representation learning under invariance constraints (i.e., the representation should be invariant wrt some attributes). The authors first review the adversarial invariance induction (AII) approach and they point out its limitations and then they propose a novel variant, which introduces an explicit regularization to minimize pairwise divergence (i.e., different attributes should lead to the same conditional distribution over the learned representation). The authors support the modified objective function both from a formal point of view and with an extensive empirical validation ** Evaluation The paper lies a bit outside my area of expertise. Although the paper tries to capture intrinsic limitations of the AII approach and build a more stable algorithm, my impression is that too many elements in the discussion and derivation remain too vague at the current stage and they would require better and clearer explanation. Detailed comments: 1- In many parts of the paper the notation is not very rigorous and sometimes it may create confusion. In general, the writing needs to be improved in many parts: - In eq. 1, it is not explained what the expectation is wrt. It should be x drawn from p(x). But it would be better to make it explicit. - The setting defined in sect.2 should be more rigorous: it is not clear what y is and what are the attributes we would like to be invariant for. This notation is not fully consistent with eq.1. - In the first paragraph of Sect.3, it would be very helpful to have a more complete sketch of the algorithm. In general, you mention in the Sect. 2 that you focus on the supervised case, but then it is not clear whether this is the case across the paper. 2- While the intuition behind using the divergence is sound, as it is mentioned, it seems to suffer from the same issue as the original AII: minimizing a lower bound does not guarantee that we are minimizing the actual objective. Having the support of 0, does not seem to make it much more sensible. 3- As the description of the algorithm advances in Sect.4.2, it is clear that many additional choices need to be made in order to have a full workable algorithm (e.g., how to estimate q_phi^i). In the paper, the actual algorithm is never reported in detail and this makes the experiments very hard to reproduce in my opinion. 4- At the best of my understanding, the algorithm may become more and more intractable as the number of attribute values grows. In fact, you need to check the divergence for each pair of values and estimated distributions. 5- The empirical analysis seems well executed and a good level of detail is reported on how the datasets are managed and the experiments are set up. Minor comments: - The caption of Fig.1 is not very clear. Many elements at this stage of the paper are not defined yet (e.g., *our proposal minimize the proxy of divergence ...*). - p2: *as the assumption of ... is rarely holds*, remove *is* - p3: *(encoder) that parameterized*, remove *that* - last paragraph of Sect.2 is very confusing. - p4: *updation* is not a word - p4: *In general, minimizing the upper bound...* does not seem correct. - p4: *even such a simple case* -> *even in such a simple case* - Sect 4.1 *the above theoretical*, I would not really say there is much theory behind the analysis in the previous section. - p5 *an ttribute* -> *an attribute* - p6 *the average discriminator*s perception* what is the perception?