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1. 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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2. Cooperative Distribution Alignment via JSD Upper Bound

   Cho, Wonwoong ; Gong, Ziyu ; Inouye, David I. ( January 2022 , Advances in neural information processing systems)

   Unsupervised distribution alignment estimates a transformation that maps two or more source distributions to a shared aligned distribution given only samples from each distribution. This task has many applications including generative modeling, unsupervised domain adaptation, and socially aware learning. Most prior works use adversarial learning (i.e., min-max optimization), which can be challenging to optimize and evaluate. A few recent works explore non-adversarial flow-based (i.e., invertible) approaches, but they lack a unified perspective and are limited in efficiently aligning multiple distributions. Therefore, we propose to unify and generalize previous flow-based approaches under a single non-adversarial framework, which we prove is equivalent to minimizing an upper bound on the Jensen-Shannon Divergence (JSD). Importantly, our problem reduces to a min-min, i.e., cooperative, problem and can provide a natural evaluation metric for unsupervised distribution alignment. We show empirical results on both simulated and real-world datasets to demonstrate the benefits of our approach. Code is available at https://github.com/inouye-lab/alignment-upper-bound. 

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3. Normalizing Flows for Intelligent Manufacturing

   https://doi.org/10.1115/MSEC2023-101281  

   Russell, Matthew ; Wang, Peng ( June 2023 , American Society of Mechanical Engineers)

   Monitoring machine health and product quality enables predictive maintenance that optimizes repairs to minimize factory downtime. Data-driven intelligent manufacturing often relies on probabilistic techniques with intractable distributions. For example, generative models of data distributions can balance fault classes with synthetic data, and sampling the posterior distribution of hidden model parameters enables prognosis of degradation trends. Normalizing flows can address these problems while avoiding the training instability or long inference times of other generative Deep Learning (DL) models like Generative Adversarial Networks (GAN), Variational Autoencoders (VAE), and diffusion networks. To evaluate normalizing flows for manufacturing, experiments are conducted to synthesize surface defect images from an imbalanced data set and estimate parameters of a tool wear degradation model from limited observations. Results show that normalizing flows are an effective, multi-purpose DL architecture for solving these problems in manufacturing. Future work should explore normalizing flows for more complex degradation models and develop a framework for likelihood-based anomaly detection. Code is available at https://github.com/uky-aism/flows-for-manufacturing.

    

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4. ASC-Net: Adversarial-Based Selective Network for Unsupervised Anomaly Segmentation

   https://doi.org/10.1007/978-3-030-87240-3_23  

   Dey, Raunak ; Hong, Yi ( September 2021 , International Conference on Medical Image Computing and Computer-Assisted Intervention)

   We introduce a neural network framework, utilizing adversarial learning to partition an image into two cuts, with one cut falling into a reference distribution provided by the user. This concept tackles the task of unsupervised anomaly segmentation, which has attracted increasing attention in recent years due to their broad applications in tasks with unlabelled data. This Adversarial-based Selective Cutting network (ASC-Net) bridges the two domains of cluster-based deep learning methods and adversarial-based anomaly/novelty detection algorithms. We evaluate this unsupervised learning model on BraTS brain tumor segmentation, LiTS liver lesion segmentation, and MS-SEG2015 segmentation tasks. Compared to existing methods like the AnoGAN family, our model demonstrates tremendous performance gains in unsupervised anomaly segmentation tasks. Although there is still room to further improve performance compared to supervised learning algorithms, the promising experimental results shed light on building an unsupervised learning algorithm using user-defined knowledge. 

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5. 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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