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1. Iterative Alignment Flows

   Zhou, Zeyu; Gong, Ziyu; Ravikumar, Pradeep; Inouye, David I. (March 2022, International Conference on Artificial Intelligence and Statistics (AISTATS))

   The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions. 

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2. Iterative Alignment Flows

   Zhou, Z.; Gong, Z.; Ravikumar, P.; Inouye, D. (March 2022, International Conference on Artificial Intelligence and Statistics (AISTATS))

   The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions. 

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3. Towards Practical Non-Adversarial Distribution Matching

   Gong, Ziyu; Usman, Ben; Zhao, Han; Inouye, David I (May 2024, International Conference on Artificial Intelligence and Statistics (AISTATS))

   Distribution matching can be used to learn invariant representations with applications in fairness and robustness. Most prior works resort to adversarial matching methods but the resulting minimax problems are unstable and challenging to optimize. Non-adversarial likelihood-based approaches either require model invertibility, impose constraints on the latent prior, or lack a generic framework for distribution matching. To overcome these limitations, we propose a non-adversarial VAE-based matching method that can be applied to any model pipeline. We develop a set of alignment upper bounds for distribution matching (including a noisy bound) that have VAE-like objectives but with a different perspective. We carefully compare our method to prior VAE-based matching approaches both theoretically and empirically. Finally, we demonstrate that our novel matching losses can replace adversarial losses in standard invariant representation learning pipelines without modifying the original architectures—thereby significantly broadening the applicability of non-adversarial matching methods. 

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4. Learning Adversarially Robust Representations via Worst-Case Mutual Information Maximization

   Zhu, Sicheng; Zhang, Xiao; Evans, David (January 2020, Proceedings of the International Conference on Machine Learning)

   Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges. To better understand adversarial robustness, we consider the underlying problem of learning robust representations. We develop a notion of representation vulnerability that captures the maximum change of mutual information between the input and output distributions, under the worst-case input perturbation. Then, we prove a theorem that establishes a lower bound on the minimum adversarial risk that can be achieved for any downstream classifier based on its representation vulnerability. We propose an unsupervised learning method for obtaining intrinsically robust representations by maximizing the worst-case mutual information between the input and output distributions. Experiments on downstream classification tasks support the robustness of the representations found using unsupervised learning with our training principle. 

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5. Understanding the Limits of Unsupervised Domain Adaptation via Data Poisoning

   https://doi.org/10.48550/arXiv.2107.03919  

   Mehra, Akshay; Hamm, Jihunn; Chen, Pen-Yu; Khailkhura, Bahia (November 2021, ArXivorg)

   Unsupervised domain adaptation (UDA) enables cross-domain learning without target domain labels by transferring knowledge from a labeled source domain whose distribution differs from the target. However, UDA is not always successful and several accounts of ‘negative transfer’ have been reported in the literature. In this work, we prove a simple lower bound on the target domain error that complements the existing upper bound. Our bound shows the insufficiency of minimizing source domain error and marginal distribution mismatch for a guaranteed reduction in the target domain error, due to the possible increase of induced labeling function mismatch. This insufficiency is further illustrated through simple distributions for which the same UDA approach succeeds, fails, and may succeed or fail with an equal chance. Motivated from this, we propose novel data poisoning attacks to fool UDA methods into learning representations that produce large target domain errors. We evaluate the effect of these attacks on popular UDA methods using benchmark datasets where they have been previously shown to be successful. Our results show that poisoning can significantly decrease the target domain accuracy, dropping it to almost 0% in some cases, with the addition of only 10% poisoned data in the source domain. The failure of UDA methods demonstrates the limitations of UDA at guaranteeing cross-domain generalization consistent with the lower bound. Thus, evaluation of UDA methods in adversarial settings such as data poisoning can provide a better sense of their robustness in scenarios unfavorable for UDA. 

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