Towards Practical Non-Adversarial Distribution Alignment via Variational Bounds

Distribution alignment can be used to learn invariant representations with applications in fairness and robustness. Most prior works resort to adversarial alignment 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 alignment. To overcome these limitations, we propose a non-adversarial VAE-based alignment method that can be applied to any model pipeline. We develop a set of alignment upper bounds (including a noisy bound) that have VAE-like objectives but with a different perspective. We carefully compare our method to prior VAE-based alignment approaches both theoretically and empirically. Finally, we demonstrate that our novel alignment losses can replace adversarial losses in standard invariant representation learning pipelines without modifying the original architectures -- thereby significantly broadening the applicability of non-adversarial alignment methods.

Assessment of Anterior Cruciate Ligament Injury Risk Based on Human Key Points Detection Algorithm

This paper aims to detect the potential injury risk of the anterior cruciate ligament (ACL) by proposing an ACL potential injury risk assessment algorithm based on key points of the human body detected using computer vision technology. To obtain the key points data of the human body in each frame, OpenPose, an open source computer vision algorithm, was employed. The obtained data underwent preprocessing and were then fed into an ACL potential injury feature extraction model based on the Landing Error Evaluation System (LESS). This model extracted several important parameters, including the knee flexion angle, the trunk flexion on the sagittal plane, trunk flexion angle on the frontal plane, the ankle knee horizontal distance, and the ankle shoulder horizontal distance. Each of these features was assigned a threshold interval, and a segmented evaluation function was utilized to score them accordingly. To calculate the final score of the participant, the score values were input into a weighted scoring model designed based on the Analytic Hierarchy Process (AHP). The AHP based model takes into account the relative importance of each feature in the overall assessment. The results demonstrate that the proposed algorithm effectively detects the potential risk of ACL injury. The proposed algorithm demonstrates its effectiveness in detecting ACL injury risk, offering valuable insights for injury prevention and intervention strategies in sports and related fields. Code is available at: https://github.com/ZiyuGong-proj/Assessment-of-ACL-Injury-Risk-Based-on-Openpose

Cooperative Distribution Alignment via JSD Upper Bound

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 present empirical results of our framework on both simulated and real-world datasets to demonstrate the benefits of our approach.

Iterative Barycenter Flows

The task of mapping two or more distributions to a shared representation has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. However, most existing formulations only consider the setting of two distributions, and moreover, do not have an identifiable, unique shared latent representation. We use optimal transport theory to consider a natural multiple distribution extension of the Monge assignment problem we call the symmetric Monge map problem and show that it is equivalent to the Wasserstein barycenter problem. Yet, the maps to the barycenter are challenging to estimate. Prior methods often ignore transportation cost, rely on adversarial methods, or only work for discrete distributions. Therefore, our goal is to estimate invertible maps between two or more distributions and their corresponding barycenter via a simple iterative flow method. Our method decouples each iteration into two subproblems: 1) estimate simple distributions and 2) estimate the invertible maps to the barycenter via known closed-form OT results. Our empirical results give evidence that this iterative algorithm approximates the maps to the barycenter.