Related papers: ProHD: Projection-Based Hausdorff Distance Approxi…
Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…
We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage.…
Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced similarity measure for quantifying the closeness of two graphs.…
We introduce HybridPose, a novel 6D object pose estimation approach. HybridPose utilizes a hybrid intermediate representation to express different geometric information in the input image, including keypoints, edge vectors, and symmetry…
Predicting the object's 6D pose from a single RGB image is a fundamental computer vision task. Generally, the distance between transformed object vertices is employed as an objective function for pose estimation methods. However, projective…
In recent years, large high-dimensional data sets have become commonplace in a wide range of applications in science and commerce. Techniques for dimension reduction are of primary concern in statistical analysis. Projection methods play an…
We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
Hyperdimensional computing (HDC) is emerging as a promising AI approach that can effectively target TinyML applications thanks to its lightweight computing and memory requirements. Previous works on HDC showed that limiting the standard 10k…
Depth measures quantify central tendency in the analysis of statistical and geometric data. Selecting a depth measure that is simple and efficiently computable is often important, e.g., when calculating depth for multiple query points or…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
Recent advances in image-based 3D human shape estimation have been driven by the significant improvement in representation power afforded by deep neural networks. Although current approaches have demonstrated the potential in real world…
Due to the falling costs of data acquisition and storage, researchers and industry analysts often want to find all instances of rare events in large datasets. For instance, scientists can cheaply capture thousands of hours of video, but are…
In a real Hilbert space $\mathcal{H}$. Given any function $f$ convex differentiable whose solution set $\argmin_{\mathcal{H}}\,f$ is nonempty, by considering the Proximal Algorithm $x_{k+1}=\text{prox}_{\b_k f}(d x_k)$, where $0<d<1$ and…