相关论文: Tight Bounds for Volumetric Spanners and Applicati…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches are focused on reduction…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive…
We study the properties of a set of vectors called tight frames that obtained as the orthogonal projection of some orthonormal basis of $\R^n$ onto $\R^k.$ We show that a set of vectors is a tight frame if and only if the set of all cross…
We give a short and easy upper bound on the worst-case size of fault tolerant spanners, which improves on all prior work and is fully optimal at least in the setting of vertex faults.
$t$-spanners are used to approximate the pairwise distances between a set of points in a metric space. They have only a few edges compared to the total number of pairs and they provide a $t$-approximation on the distance of any two…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Given a connected graph $G=(V,E)$ and a length function $\ell:E\to {\mathbb R}$ we let $d_{v,w}$ denote the shortest distance between vertex $v$ and vertex $w$. A $t$-spanner is a subset $E'\subseteq E$ such that if $d'_{v,w}$ denotes…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
A multiplicative $\alpha$-spanner $H$ is a subgraph of $G=(V,E)$ with the same vertices and fewer edges that preserves distances up to the factor $\alpha$, i.e., $d_H(u,v)\leq\alpha\cdot d_G(u,v)$ for all vertices $u$, $v$. While many…
One important question in the theory of lattices is to detect a shortest vector: given a norm and a lattice, what is the smallest norm attained by a non-zero vector contained in the lattice? We focus on the infinity norm and work with…
We give a sharp lower bound to the largest possible Euclidean norm of signed sums of $n$ vectors in the plane. This is achieved by connecting the signed vector sum problem to the isoperimetric problem for the circumradius of polygons. In…
The volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models. However, this approach still lacks theoretical support. In this paper, we…
The diameter of a graph is one if its most important parameters, being used in many real-word applications. In particular, the diameter dictates how fast information can spread throughout data and communication networks. Thus, it is a…
Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…