Related papers: Fully-Dynamic Coresets

We give algorithms for computing coresets for $(1+\varepsilon)$-approximate $k$-median clustering of polygonal curves (under the discrete and continuous Fr\'{e}chet distance) and point sets (under the Hausdorff distance), when the cluster…

Continuous/Lifelong learning of high-dimensional data streams is a challenging research problem. In fact, fully retraining models each time new data become available is infeasible, due to computational and storage issues, while na\"ive…

Recent advances in coreset methods have shown that a selection of representative datapoints can replace massive volumes of data for Bayesian inference, preserving the relevant statistical information and significantly accelerating…

We consider the Euclidean $k$-means clustering problem in a dynamic setting, where we have to explicitly maintain a solution (a set of $k$ centers) $S \subseteq \mathbb{R}^d$ subject to point insertions/deletions in $\mathbb{R}^d$. We…

We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…

Randomised algorithms often employ methods that can fail and that are retried with independent randomness until they succeed. Randomised data structures therefore often store indices of successful attempts, called seeds. If $n$ such seeds…

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…

Consider the problem of maintaining a family $F$ of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given $S,S'\in F$, report every member of $S\cap S'$ in any order. We show that in the word RAM…

We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…

We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and…

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…

We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…

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),…

Computational cost of training state-of-the-art deep models in many learning problems is rapidly increasing due to more sophisticated models and larger datasets. A recent promising direction for reducing training cost is dataset…

We present algorithms that create coresets in an online setting for clustering problems according to a wide subset of Bregman divergences. Notably, our coresets have a small additive error, similar in magnitude to the lightweight coresets…

We develop and analyze data subsampling techniques for Poisson regression, the standard model for count data $y\in\mathbb{N}$. In particular, we consider the Poisson generalized linear model with ID- and square root-link functions. We…

Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…