81 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
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Robust Estimation and Filtering in the Presence of Unknown but Bounded Noise
In this paper optimal algorithms for robust estimation and filtering are constructed.
No statistical assumption is supposed available or used and the noise is considered a deterministic variable unknown but bounded belonging to a set described by a norm. Previous results obtained for complete (one-to-one) and approximate information [1] are now extended to partial and approximate information. This information seems useful in dealing with dynamic systems not completely identifiable and/or with two different sources of noise, for example process and measurement noise. For different norms characterizing the noise, optimal algorithms (in a min-max sense) are shown. In particular for Hilbert norms a linear optimal algorithm is the well-known minimum variance estimator. For 1β β and 1β norms optimal algorithms, computable by linear programming, are presented. Applications to time series prediction and parameter estimation of nonidentifiable dynamic systems are shown. State estimation is formalized in the context of the general theory. Assuming an exponential smoothing of the bounds of the noise it is proved that, for stable systems, the uncertainty of the state is aymptotically bounded. Then the results of the previous sections provide computable algorithms for this problem. Two application examples are shown: Leontief models and Markov chains
Ergodic Randomized Algorithms and Dynamics over Networks
Algorithms and dynamics over networks often involve randomization, and
randomization may result in oscillating dynamics which fail to converge in a
deterministic sense. In this paper, we observe this undesired feature in three
applications, in which the dynamics is the randomized asynchronous counterpart
of a well-behaved synchronous one. These three applications are network
localization, PageRank computation, and opinion dynamics. Motivated by their
formal similarity, we show the following general fact, under the assumptions of
independence across time and linearities of the updates: if the expected
dynamics is stable and converges to the same limit of the original synchronous
dynamics, then the oscillations are ergodic and the desired limit can be
locally recovered via time-averaging.Comment: 11 pages; submitted for publication. revised version with fixed
technical flaw and updated reference
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