104,335 research outputs found
Sublinear algorithms for local graph centrality estimation
We study the complexity of local graph centrality estimation, with the goal
of approximating the centrality score of a given target node while exploring
only a sublinear number of nodes/arcs of the graph and performing a sublinear
number of elementary operations. We develop a technique, that we apply to the
PageRank and Heat Kernel centralities, for building a low-variance score
estimator through a local exploration of the graph. We obtain an algorithm
that, given any node in any graph of arcs, with probability
computes a multiplicative -approximation of its score by
examining only nodes/arcs, where and are respectively the maximum and
average outdegree of the graph (omitting for readability
and
factors). A similar bound holds for computational complexity. We also prove a
lower bound of for both query complexity and computational complexity. Moreover,
our technique yields a query complexity algorithm for the
graph access model of [Brautbar et al., 2010], widely used in social network
mining; we show this algorithm is optimal up to a sublogarithmic factor. These
are the first algorithms yielding worst-case sublinear bounds for general
directed graphs and any choice of the target node.Comment: 29 pages, 1 figur
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights (possibly) dependent on the radio channels and we pose
special attention to the effect of the propagation delay occurring in the
exchange of data among sensors, as a function of the network geometry. We
derive necessary and sufficient conditions for the proposed system to reach a
consensus on globally optimal decision statistics. One of the major results
proved in this work is that a consensus is reached with exponential convergence
speed for any bounded delay condition if and only if the directed graph is
quasi-strongly connected. We provide a closed form expression for the global
consensus, showing that the effect of delays is, in general, the introduction
of a bias in the final decision. Finally, we exploit our closed form expression
to devise a double-step consensus mechanism able to provide an unbiased
estimate with minimum extra complexity, without the need to know or estimate
the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin
Estimation of Discrete Partially Directed Acyclic Graphical Models in Multitype Branching Processes
International audienceWe address the inference of discrete-state models for tree-structured data. Our aim is to introduce parametric multitype branching processes that can be efficiently estimated on the basis of data of limited size. Each generation distribution within this macroscopic model is modeled by a partially directed acyclic graphical model. The estimation of each graphical model relies on a greedy algorithm for graph selection. We present an algorithm for discrete graphical model which is applied on multivariate count data. The proposed modeling approach is illustrated on plant architecture datasets
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
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