Related papers: Bound Propagation
This paper presents a linear prioritized local algorithm that computes large independent sets on a random $d$-regular graph with small and fixed degree $d$. We studied experimentally the independence ratio obtained by the algorithm when $ d…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…
We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…
We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…
We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form S_pi(N) := sum_{j_1, ..., j_2m = 1}^N t^1_{j_1 j_2} t^2_{j_3 j_4} ... t^m_{j_2m-1 j_2m} where some of the summation indices…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding…
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…