In this paper, we propose a novel conceptual framework to detect outliers
using optimal transport with a concave cost function. Conventional outlier
detection approaches typically use a two-stage procedure: first, outliers are
detected and removed, and then estimation is performed on the cleaned data.
However, this approach does not inform outlier removal with the estimation
task, leaving room for improvement. To address this limitation, we propose an
automatic outlier rectification mechanism that integrates rectification and
estimation within a joint optimization framework. We take the first step to
utilize an optimal transport distance with a concave cost function to construct
a rectification set in the space of probability distributions. Then, we select
the best distribution within the rectification set to perform the estimation
task. Notably, the concave cost function we introduced in this paper is the key
to making our estimator effectively identify the outlier during the
optimization process. We discuss the fundamental differences between our
estimator and optimal transport-based distributionally robust optimization
estimator. finally, we demonstrate the effectiveness and superiority of our
approach over conventional approaches in extensive simulation and empirical
analyses for mean estimation, least absolute regression, and the fitting of
option implied volatility surfaces.

通过使用凸凹成本函数的最优传输，我们提出了一个新颖的概念框架来检测异常值，并在自动异常值矫正机制中进行了集成和优化，实验证明了我们方法在众多模拟和实证分析中对均值估计、最小绝对回归和期权隐含波动率曲面拟合的有效性和优越性。

基于最优输运的自动异常数据矫正

Automatic Outlier Rectification via Optimal Transport

We present a method to estimate human motion in a global scene from moving
cameras. This is a highly challenging task due to the coupling of human and
camera motions in the video. To address this problem, we propose a joint
optimization framework that disentangles human and camera motions using both
foreground human motion priors and background scene features. Unlike existing
methods that use SLAM as initialization, we propose to tightly integrate SLAM
and human motion priors in an optimization that is inspired by bundle
adjustment. Specifically, we optimize human and camera motions to match both
the observed human pose and scene features. This design combines the strengths
of SLAM and motion priors, which leads to significant improvements in human and
camera motion estimation. We additionally introduce a motion prior that is
suitable for batch optimization, making our approach significantly more
efficient than existing approaches. Finally, we propose a novel synthetic
dataset that enables evaluating camera motion in addition to human motion from
dynamic videos. Experiments on the synthetic and real-world RICH datasets
demonstrate that our approach substantially outperforms prior art in recovering
both human and camera motions.

通过结合人体运动先验知识和场景特征，提出了一种估计全局场景下人体运动的联合优化框架，该方法在人体和相机运动估计方面相较于现有方法有显著的改进。

PACE：野外视频中人体和摄像机运动的估计

PACE: Human and Camera Motion Estimation from in-the-wild Videos

Enhancing feature transferability by matching marginal distributions has led
to improvements in domain adaptation, although this is at the expense of
feature discrimination. In particular, the ideal joint hypothesis error in the
target error upper bound, which was previously considered to be minute, has
been found to be significant, impairing its theoretical guarantee. In this
paper, we propose an alternative upper bound on the target error that
explicitly considers the joint error to render it more manageable. With the
theoretical analysis, we suggest a joint optimization framework that combines
the source and target domains. Further, we introduce Joint Contrastive Learning
(JCL) to find class-level discriminative features, which is essential for
minimizing the joint error. With a solid theoretical framework, JCL employs
contrastive loss to maximize the mutual information between a feature and its
label, which is equivalent to maximizing the Jensen-Shannon divergence between
conditional distributions. Experiments on two real-world datasets demonstrate
that JCL outperforms the state-of-the-art methods.

本文提出了一种将源域和目标域相结合的联合优化框架，并引入了一种称为 JCL 的新方法，它利用对比损失来最大化特征和标签之间的互信息，以最小化联合误差，从而有效提高了特征传递性和分类效果。