4,848 research outputs found
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
Perron-based algorithms for the multilinear pagerank
We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu,
Multilinear Pagerank, 2015], which is a system of quadratic equations with
stochasticity and nonnegativity constraints. We use the theory of quadratic
vector equations to prove several properties of its solutions and suggest new
numerical algorithms. In particular, we prove the existence of a certain
minimal solution, which does not always coincide with the stochastic one that
is required by the problem. We use an interpretation of the solution as a
Perron eigenvector to devise new fixed-point algorithms for its computation,
and pair them with a homotopy continuation strategy. The resulting numerical
method is more reliable than the existing alternatives, being able to solve a
larger number of problems
Stochastic Data Clustering
In 1961 Herbert Simon and Albert Ando published the theory behind the
long-term behavior of a dynamical system that can be described by a nearly
uncoupled matrix. Over the past fifty years this theory has been used in a
variety of contexts, including queueing theory, brain organization, and
ecology. In all these applications, the structure of the system is known and
the point of interest is the various stages the system passes through on its
way to some long-term equilibrium.
This paper looks at this problem from the other direction. That is, we
develop a technique for using the evolution of the system to tell us about its
initial structure, and we use this technique to develop a new algorithm for
data clustering.Comment: 23 page
- …