相关论文: Computing Marginals Using MapReduce

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…

Searching for the $k$-nearest neighbors (KNN) in multimodal data retrieval is computationally expensive, particularly due to the inherent difficulty in comparing similarity measures across different modalities. Recent advances in multimodal…

The exponential growth of data in current times and the demand to gain information and knowledge from the data present new challenges for database researchers. Known database systems and algorithms are no longer capable of effectively…

We study the maximum set coverage problem in the massively parallel model. In this setting, $m$ sets that are subsets of a universe of $n$ elements are distributed among $m$ machines. In each round, these machines can communicate with each…

We tackle the problem of counting the number of $k$-cliques in large-scale graphs, for any constant $k \ge 3$. Clique counting is essential in a variety of applications, among which social network analysis. Due to its computationally…

Large datasets ("Big Data") are becoming ubiquitous because the potential value in deriving insights from data, across a wide range of business and scientific applications, is increasingly recognized. In particular, machine learning - one…

MapReduce is a popular programming model for data parallel computation. In MapReduce, the reducer produces an output from a list of inputs. Due to the scheduling policy of the platform, the inputs may arrive at the reducers in different…

Computations, where the number of results is much smaller than the input data and are produced through some sort of accumulation, are called Reductions. Reductions appear in many scientific applications. Usually, reductions admit an…

This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…

The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each…

Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the…

In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…

We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…

MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding…

We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower…

In the reordering buffer problem (RBP), a server is asked to process a sequence of requests lying in a metric space. To process a request the server must move to the corresponding point in the metric. The requests can be processed slightly…