96,809 research outputs found
Exact Computation of Influence Spread by Binary Decision Diagrams
Evaluating influence spread in social networks is a fundamental procedure to
estimate the word-of-mouth effect in viral marketing. There are enormous
studies about this topic; however, under the standard stochastic cascade
models, the exact computation of influence spread is known to be #P-hard. Thus,
the existing studies have used Monte-Carlo simulation-based approximations to
avoid exact computation.
We propose the first algorithm to compute influence spread exactly under the
independent cascade model. The algorithm first constructs binary decision
diagrams (BDDs) for all possible realizations of influence spread, then
computes influence spread by dynamic programming on the constructed BDDs. To
construct the BDDs efficiently, we designed a new frontier-based search-type
procedure. The constructed BDDs can also be used to solve other
influence-spread related problems, such as random sampling without rejection,
conditional influence spread evaluation, dynamic probability update, and
gradient computation for probability optimization problems.
We conducted computational experiments to evaluate the proposed algorithm.
The algorithm successfully computed influence spread on real-world networks
with a hundred edges in a reasonable time, which is quite impossible by the
naive algorithm. We also conducted an experiment to evaluate the accuracy of
the Monte-Carlo simulation-based approximation by comparing exact influence
spread obtained by the proposed algorithm.Comment: WWW'1
Data-driven satisficing measure and ranking
We propose an computational framework for real-time risk assessment and
prioritizing for random outcomes without prior information on probability
distributions. The basic model is built based on satisficing measure (SM) which
yields a single index for risk comparison. Since SM is a dual representation
for a family of risk measures, we consider problems constrained by general
convex risk measures and specifically by Conditional value-at-risk. Starting
from offline optimization, we apply sample average approximation technique and
argue the convergence rate and validation of optimal solutions. In online
stochastic optimization case, we develop primal-dual stochastic approximation
algorithms respectively for general risk constrained problems, and derive their
regret bounds. For both offline and online cases, we illustrate the
relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure
Newton based Stochastic Optimization using q-Gaussian Smoothed Functional Algorithms
We present the first q-Gaussian smoothed functional (SF) estimator of the
Hessian and the first Newton-based stochastic optimization algorithm that
estimates both the Hessian and the gradient of the objective function using
q-Gaussian perturbations. Our algorithm requires only two system simulations
(regardless of the parameter dimension) and estimates both the gradient and the
Hessian at each update epoch using these. We also present a proof of
convergence of the proposed algorithm. In a related recent work (Ghoshdastidar
et al., 2013), we presented gradient SF algorithms based on the q-Gaussian
perturbations. Our work extends prior work on smoothed functional algorithms by
generalizing the class of perturbation distributions as most distributions
reported in the literature for which SF algorithms are known to work and turn
out to be special cases of the q-Gaussian distribution. Besides studying the
convergence properties of our algorithm analytically, we also show the results
of several numerical simulations on a model of a queuing network, that
illustrate the significance of the proposed method. In particular, we observe
that our algorithm performs better in most cases, over a wide range of
q-values, in comparison to Newton SF algorithms with the Gaussian (Bhatnagar,
2007) and Cauchy perturbations, as well as the gradient q-Gaussian SF
algorithms (Ghoshdastidar et al., 2013).Comment: This is a longer of version of the paper with the same title accepted
in Automatic
- …