178 research outputs found
A Web Aggregation Approach for Distributed Randomized PageRank Algorithms
The PageRank algorithm employed at Google assigns a measure of importance to
each web page for rankings in search results. In our recent papers, we have
proposed a distributed randomized approach for this algorithm, where web pages
are treated as agents computing their own PageRank by communicating with linked
pages. This paper builds upon this approach to reduce the computation and
communication loads for the algorithms. In particular, we develop a method to
systematically aggregate the web pages into groups by exploiting the sparsity
inherent in the web. For each group, an aggregated PageRank value is computed,
which can then be distributed among the group members. We provide a distributed
update scheme for the aggregated PageRank along with an analysis on its
convergence properties. The method is especially motivated by results on
singular perturbation techniques for large-scale Markov chains and multi-agent
consensus.Comment: To appear in the IEEE Transactions on Automatic Control, 201
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank
In this paper, we propose three methods to solve the PageRank problem for the
transition matrices with both row and column sparsity. Our methods reduce the
PageRank problem to the convex optimization problem over the simplex. The first
algorithm is based on the gradient descent in L1 norm instead of the Euclidean
one. The second algorithm extends the Frank-Wolfe to support sparse gradient
updates. The third algorithm stands for the mirror descent algorithm with a
randomized projection. We proof converges rates for these methods for sparse
problems as well as numerical experiments support their effectiveness.Comment: 26 page
Ergodic Control and Polyhedral approaches to PageRank Optimization
We study a general class of PageRank optimization problems which consist in
finding an optimal outlink strategy for a web site subject to design
constraints. We consider both a continuous problem, in which one can choose the
intensity of a link, and a discrete one, in which in each page, there are
obligatory links, facultative links and forbidden links. We show that the
continuous problem, as well as its discrete variant when there are no
constraints coupling different pages, can both be modeled by constrained Markov
decision processes with ergodic reward, in which the webmaster determines the
transition probabilities of websurfers. Although the number of actions turns
out to be exponential, we show that an associated polytope of transition
measures has a concise representation, from which we deduce that the continuous
problem is solvable in polynomial time, and that the same is true for the
discrete problem when there are no coupling constraints. We also provide
efficient algorithms, adapted to very large networks. Then, we investigate the
qualitative features of optimal outlink strategies, and identify in particular
assumptions under which there exists a "master" page to which all controlled
pages should point. We report numerical results on fragments of the real web
graph.Comment: 39 page
Surfing a genetic association interaction network to identify modulators of antibody response to smallpox vaccine
The variation in antibody response to vaccination likely involves small contributions of numerous genetic variants, such as single-nucleotide polymorphisms (SNPs), which interact in gene networks and pathways. To accumulate the bits of genetic information relevant to the phenotype that are distributed throughout the interaction network, we develop a network eigenvector centrality algorithm (SNPrank) that is sensitive to the weak main effects, gene–gene interactions and small higher-order interactions through hub effects. Analogous to Google PageRank, we interpret the algorithm as the simulation of a random SNP surfer (RSS) that accumulates bits of information in the network through a dynamic probabilistic Markov chain. The transition matrix for the RSS is based on a data-driven genetic association interaction network (GAIN), the nodes of which are SNPs weighted by the main-effect strength and edges weighted by the gene–gene interaction strength. We apply SNPrank to a GAIN analysis of a candidate-gene association study on human immune response to smallpox vaccine. SNPrank implicates a SNP in the retinoid X receptor α (RXRA) gene through a network interaction effect on antibody response. This vitamin A- and D-signaling mediator has been previously implicated in human immune responses, although it would be neglected in a standard analysis because its significance is unremarkable outside the context of its network centrality. This work suggests SNPrank to be a powerful method for identifying network effects in genetic association data and reveals a potential vitamin regulation network association with antibody response
The use of multilayer network analysis in animal behaviour
Network analysis has driven key developments in research on animal behaviour
by providing quantitative methods to study the social structures of animal
groups and populations. A recent formalism, known as \emph{multilayer network
analysis}, has advanced the study of multifaceted networked systems in many
disciplines. It offers novel ways to study and quantify animal behaviour as
connected 'layers' of interactions. In this article, we review common questions
in animal behaviour that can be studied using a multilayer approach, and we
link these questions to specific analyses. We outline the types of behavioural
data and questions that may be suitable to study using multilayer network
analysis. We detail several multilayer methods, which can provide new insights
into questions about animal sociality at individual, group, population, and
evolutionary levels of organisation. We give examples for how to implement
multilayer methods to demonstrate how taking a multilayer approach can alter
inferences about social structure and the positions of individuals within such
a structure. Finally, we discuss caveats to undertaking multilayer network
analysis in the study of animal social networks, and we call attention to
methodological challenges for the application of these approaches. Our aim is
to instigate the study of new questions about animal sociality using the new
toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl
- …