Related papers: Approximating Higher-Order Distances Using Random …
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
Given a distance $D$ on a finite set $X$ with $n$ elements, it is interesting to understand how the ranking $R_x = z_1,z_2,\dots,z_n$ obtained by ordering the elements in $X$ according to increasing distance $D(x,z_i)$ from $x$, varies with…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…
Differentiable rendering aims to compute the derivative of the image rendering function with respect to the rendering parameters. This paper presents a novel algorithm for 6-DoF pose estimation through gradient-based optimization using a…
This paper studies the problem of having mobile robots in a multi-robot system maintain an estimate of the relative position and relative orientation of near-by robots in the environment. This problem is studied in the context of large…
Deep metric learning has been effectively used to learn distance metrics for different visual tasks like image retrieval, clustering, etc. In order to aid the training process, existing methods either use a hard mining strategy to extract…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability…
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…
This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…
This paper focuses on learning efficient sensor allocations that ensure observability of unknown high-dimensional linear systems using only a small number of sensors. Existing methods either require an impractically large number of sensors…
Real-time robotic grasping, supporting a subsequent precise object-in-hand operation task, is a priority target towards highly advanced autonomous systems. However, such an algorithm which can perform sufficiently-accurate grasping with…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…