相关论文: A New Construction of the Vietoris-Rips Complex

We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…

Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the…

We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…

We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages…

Deploying machine learning systems in the real world requires both high accuracy on clean data and robustness to naturally occurring corruptions. While architectural advances have led to improved accuracy, building robust models remains…

We describe a combinatorial algorithm which, given a monotone and consistent symmetric set function d on a finite set V in the sense of Rizzi, constructs a non trivial set S minimizing d(S,V-S). This includes the possibility for the…

Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. We continue this line of work focusing on space. Our first result is a…

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior…

This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far…

Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…

Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…

In this paper we represent a new framework for integrated distributed and reliable systems. In the proposed framework we have used three parts to increase Satisfaction and Performance of this framework. At first we analyze previous…

This paper presents \pandora, a novel parallel algorithm for efficiently constructing dendrograms for single-linkage hierarchical clustering, including \hdbscan. Traditional dendrogram construction methods from a minimum spanning tree…

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…

We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The $n$ input points are drawn from a hidden mixture of product distributions; we are only…

We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…

Gaussian Processes (GPs) provide a powerful framework for making predictions and understanding uncertainty for classification with kernels and Bayesian non-parametric learning. Building such models typically requires strong prior knowledge…

It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also…

Fast matrix multiplication algorithms are asymptotically faster than the classical cubic-time algorithm, but they are often slower in practice. One important obstacle is the use of complex coefficients, which increases arithmetic overhead…