Related papers: On Approximating the Lp Distances for p>2
Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We consider the problem of computing the distance between two piecewise-linear bivariate functions $f$ and $g$ defined over a common domain $M$. We focus on the distance induced by the $L_2$-norm, that is $\|f-g\|_2=\sqrt{\iint_M (f-g)^2}$.…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
The well-known M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given matrix is sparse,…
Random projection (RP) is a powerful dimension reduction technique widely used in the analysis of high dimensional data. We demonstrate how this technique can be used to improve the computational efficiency of gravitational wave searches…
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given evidence. Unlike computing marginals, posteriors, and MPE (a special case of MAP), the time and space complexity of MAP is not…
Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Approximating distance is one of the key challenge in a facility location problem. Several algorithms have been proposed, however, none of them focused on estimating distance between two concave regions. In this work, we present an…
Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…
Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…
Recently, $p$-presentation distances for $p\in [1,\infty]$ were introduced for merge trees and multiparameter persistence modules as more sensitive variations of the respective interleaving distances ($p=\infty)$. It is well-known that…