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Existing 3D object detectors encounter extreme challenges in localizing unseen 3D objects and recognizing them as unseen, which is a crucial technology in autonomous driving in the wild. To address these challenges, we propose practical…
In 2D/3D object detection task, Intersection-over-Union (IoU) has been widely employed as an evaluation metric to evaluate the performance of different detectors in the testing stage. However, during the training stage, the common distance…
This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism…
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…
Let $\pi\in \Pi(\mu,\nu)$ be a coupling between two probability measures $\mu$ and $\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\mu$ and $\nu$, which we call…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
Accurate pedestrian classification and localization have received considerable attention due to their wide applications such as security monitoring, autonomous driving, etc. Although pedestrian detectors have made great progress in recent…
This paper will introduce a family of sliced Wasserstein geodesics which are not standard Wasserstein geodesics, objects yet to be discovered in the literature. These objects exhibit how the geometric structure of the Sliced Wasserstein…
Small objects have relatively low resolution, the unobvious visual features which are difficult to be extracted, so the existing object detection methods cannot effectively detect small objects, and the detection speed and stability are…
In the last couple of years, several adversarial attack methods based on different threat models have been proposed for the image classification problem. Most existing defenses consider additive threat models in which sample perturbations…
In object detection, the intersection over union (IoU) threshold is frequently used to define positives/negatives. The threshold used to train a detector defines its \textit{quality}. While the commonly used threshold of 0.5 leads to noisy…
Previous work shows that humans tend to prefer large bounding boxes over small bounding boxes with the same IoU. However, we show here that commonly used object detectors predict large and small boxes equally often. In this work, we…
Detection of small objects and objects far away in the scene is a major challenge in surveillance applications. Such objects are represented by small number of pixels in the image and lack sufficient details, making them difficult to detect…
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…