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Accurate and explainable out-of-distribution (OOD) detection is required to use machine learning systems safely. Previous work has shown that feature distance to decision boundaries can be used to identify OOD data effectively. In this…
While there has been a growing research interest in developing out-of-distribution (OOD) detection methods, there has been comparably little discussion around how these methods should be evaluated. Given their relevance for safe(r) AI, it…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
The Inverse Optimal Control (IOC) problem is a structured system identification problem that aims to identify the underlying objective function based on observed optimal trajectories. This provides a data-driven way to model experts'…
This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region ($\impre$ model) or a…
Euclidean distance matrix optimization with ordinal constraints (EDMOC) has found important applications in sensor network localization and molecular conformation. It can also be viewed as a matrix formulation of multidimensional scaling,…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers…
Out-of-distribution detection is an important component of reliable ML systems. Prior literature has proposed various methods (e.g., MSP (Hendrycks & Gimpel, 2017), ODIN (Liang et al., 2018), Mahalanobis (Lee et al., 2018)), claiming they…
The ability to detect out-of-distribution (OOD) samples is vital to secure the reliability of deep neural networks in real-world applications. Considering the nature of OOD samples, detection methods should not have hyperparameters that…
Computing the quadratic transportation metric (also called the $2$-Wasserstein distance or root mean square distance) between two point clouds, or, more generally, two discrete distributions, is a fundamental problem in machine learning,…
In this paper, we propose a fast and convergent algorithm to solve unassigned distance geometry problems (uDGP). Technically, we construct a novel quadratic measurement model by leveraging $\ell_0$-norm instead of $\ell_1$-norm in the…
In metric geometry, the question of whether a distance metric is given by the length of curves can be decided via the existence of midpoints with respect to the metric $d$. We adapt a similar characterization to the setting of Lorentzian…
Accurate and comprehensive 3D sensing using LiDAR systems is crucial for various applications in photogrammetry and robotics, including facility inspection, Building Information Modeling (BIM), and robot navigation. Motorized LiDAR systems…
This paper proposes two new algorithms for certified perception in safety-critical robotic applications. The first is a Certified Visual Odometry algorithm, which uses a RGBD camera with bounded sensor noise to construct a visual odometry…
We consider exact algorithms for Subset Balancing, a family of related problems that generalizes Subset Sum, Partition, and Equal Subset Sum. Specifically, given as input an integer vector $\vec{x} \in \mathbb{Z}^n$ and a constant-size…
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…
This paper presents a method to estimate the 3D object position and occupancy given a set of object detections in multiple images and calibrated cameras. This problem is modelled as the estimation of a set of quadrics given 2D conics fit to…