相关论文: Stability of epsilon-Kernels
The Gaussian Elimination with Partial Pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically…
In the Feedback Arc Set in Tournaments (Subset-FAST) problem, we are given a tournament $D$ and a positive integer $k$, and the objective is to determine whether there exists an arc set $S \subseteq A(D)$ of size at most $k$ whose removal…
We give new upper and lower bounds for the {\em dynamic} set cover problem. First, we give a $(1+\epsilon) f$-approximation for fully dynamic set cover in $O(f^2\log n /\epsilon^5)$ (amortized) update time, for any $\epsilon > 0$, where $f$…
In this paper we study the kernel change-point algorithm (KCP) proposed by Arlot, Celisse and Harchaoui (2012), which aims at locating an unknown number of change-points in the distribution of a sequence of independent data taking values in…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This separation hides a simple geometric fact: all three act on…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
A popular model to measure network stability is the $k$-core, that is the maximal induced subgraph in which every vertex has degree at least $k$. For example, $k$-cores are commonly used to model the unraveling phenomena in social networks.…
A function approximation method is developed that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on the theory of universal reproducing kernel Hilbert spaces…
A geometric $t$-spanner for a set $S$ of $n$ point sites is an edge-weighted graph for which the (weighted) distance between any two sites $p,q \in S$ is at most $t$ times the original distance between $p$ and~$q$. We study geometric…
In the Tree Deletion Set problem the input is a graph G together with an integer k. The objective is to determine whether there exists a set S of at most k vertices such that G-S is a tree. The problem is NP-complete and even NP-hard to…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
In this paper, we revisit the Minimum Enclosing Ball (MEB) problem and its robust version, MEB with outliers, in Euclidean space $\mathbb{R}^d$. Though the problem has been extensively studied before, most of the existing algorithms need at…
Change-points in time series data are usually defined as the time instants at which changes in their properties occur. Detecting change-points is critical in a number of applications as diverse as detecting credit card and insurance frauds,…
Given a set $P$ of $n$ points in $\mathbf{R}^d$, and a positive integer $k \leq n$, the $k$-dispersion problem is that of selecting $k$ of the given points so that the minimum inter-point distance among them is maximized (under Euclidean…
We consider the problem of maintaining the Euclidean Delaunay triangulation $\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the…
The core numbers of vertices in a graph are one of the most well-studied cohesive subgraph models because of the linear running time. In practice, many data graphs are dynamic graphs that are continuously changing by inserting or removing…