1,543 research outputs found
Sensor Networks with Random Links: Topology Design for Distributed Consensus
In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.Comment: Submitted to IEEE Transaction
ChoiceRank: Identifying Preferences from Node Traffic in Networks
Understanding how users navigate in a network is of high interest in many
applications. We consider a setting where only aggregate node-level traffic is
observed and tackle the task of learning edge transition probabilities. We cast
it as a preference learning problem, and we study a model where choices follow
Luce's axiom. In this case, the marginal counts of node visits are a
sufficient statistic for the transition probabilities. We show how to
make the inference problem well-posed regardless of the network's structure,
and we present ChoiceRank, an iterative algorithm that scales to networks that
contains billions of nodes and edges. We apply the model to two clickstream
datasets and show that it successfully recovers the transition probabilities
using only the network structure and marginal (node-level) traffic data.
Finally, we also consider an application to mobility networks and apply the
model to one year of rides on New York City's bicycle-sharing system.Comment: Accepted at ICML 201
kLog: A Language for Logical and Relational Learning with Kernels
We introduce kLog, a novel approach to statistical relational learning.
Unlike standard approaches, kLog does not represent a probability distribution
directly. It is rather a language to perform kernel-based learning on
expressive logical and relational representations. kLog allows users to specify
learning problems declaratively. It builds on simple but powerful concepts:
learning from interpretations, entity/relationship data modeling, logic
programming, and deductive databases. Access by the kernel to the rich
representation is mediated by a technique we call graphicalization: the
relational representation is first transformed into a graph --- in particular,
a grounded entity/relationship diagram. Subsequently, a choice of graph kernel
defines the feature space. kLog supports mixed numerical and symbolic data, as
well as background knowledge in the form of Prolog or Datalog programs as in
inductive logic programming systems. The kLog framework can be applied to
tackle the same range of tasks that has made statistical relational learning so
popular, including classification, regression, multitask learning, and
collective classification. We also report about empirical comparisons, showing
that kLog can be either more accurate, or much faster at the same level of
accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at
http://klog.dinfo.unifi.it along with tutorials
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