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An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the…
Using 3D point clouds in odometry estimation in robotics often requires finding a set of correspondences between points in subsequent scans. While there are established methods for point clouds of sufficient quality, state-of-the-art still…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
Out-of-distribution (OOD) detection is essential for building reliable AI systems, as models that produce outputs for invalid inputs cannot be trusted. Although deep learning (DL) is often assumed to outperform traditional machine learning…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
A set in $\mathbb R^d$ is called almost-equidistant if for any three distinct points in the set, some two are at unit distance apart. First, we give a short proof of the result of Bezdek and L\'angi claiming that an almost-equidistant set…
State-of-the-art Object Detection (OD) methods predominantly operate under a closed-world assumption, where test-time categories match those encountered during training. However, detecting and localizing unknown objects is crucial for…
In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…
We study the minimum number of distinct distances between point sets on two curves in $R^3$. Assume that one curve contains $m$ points and the other $n$ points. Our main results: (a) When the curves are conic sections, we characterize all…
Out-of-distribution (OOD) detection is a critical task for deploying machine learning models in the open world. Distance-based methods have demonstrated promise, where testing samples are detected as OOD if they are relatively far away from…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
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…
Recent advances in the field of out-of-distribution (OOD) detection have placed great emphasis on learning better representations suited to this task. While there are distance-based approaches, distributional awareness has seldom been…
Piecewise $\alpha$-stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Euler-Maruyama (EM) scheme more difficult to analyze. We…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
Identifying out-of-distribution (OOD) data at inference time is crucial for many machine learning applications, especially for automation. We present a novel unsupervised semi-parametric framework COMBOOD for OOD detection with respect to…
Out-of-distribution (OoD) inputs pose a persistent challenge to deep learning models, often triggering overconfident predictions on non-target objects. While prior work has primarily focused on refining scoring functions and adjusting…
The goal of Inverse Optimal Control (IOC) is to identify the underlying objective function based on observed optimal trajectories. It provides a powerful framework to model expert's behavior, and a data-driven way to design an objective…
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…