19,582 research outputs found
Sketch-based Influence Maximization and Computation: Scaling up with Guarantees
Propagation of contagion through networks is a fundamental process. It is
used to model the spread of information, influence, or a viral infection.
Diffusion patterns can be specified by a probabilistic model, such as
Independent Cascade (IC), or captured by a set of representative traces.
Basic computational problems in the study of diffusion are influence queries
(determining the potency of a specified seed set of nodes) and Influence
Maximization (identifying the most influential seed set of a given size).
Answering each influence query involves many edge traversals, and does not
scale when there are many queries on very large graphs. The gold standard for
Influence Maximization is the greedy algorithm, which iteratively adds to the
seed set a node maximizing the marginal gain in influence. Greedy has a
guaranteed approximation ratio of at least (1-1/e) and actually produces a
sequence of nodes, with each prefix having approximation guarantee with respect
to the same-size optimum. Since Greedy does not scale well beyond a few million
edges, for larger inputs one must currently use either heuristics or
alternative algorithms designed for a pre-specified small seed set size.
We develop a novel sketch-based design for influence computation. Our greedy
Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with
billions of edges, with one to two orders of magnitude speedup over the best
greedy methods. It still has a guaranteed approximation ratio, and in practice
its quality nearly matches that of exact greedy. We also present influence
oracles, which use linear-time preprocessing to generate a small sketch for
each node, allowing the influence of any seed set to be quickly answered from
the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information
and Knowledge Management (CIKM 2014) in Shanghai, Chin
Seeding with Costly Network Information
We study the task of selecting nodes in a social network of size , to
seed a diffusion with maximum expected spread size, under the independent
cascade model with cascade probability . Most of the previous work on this
problem (known as influence maximization) focuses on efficient algorithms to
approximate the optimal seed set with provable guarantees, given the knowledge
of the entire network. However, in practice, obtaining full knowledge of the
network is very costly. To address this gap, we first study the achievable
guarantees using influence samples. We provide an approximation
algorithm with a tight (1-1/e){\mbox{OPT}}-\epsilon n guarantee, using
influence samples and show that this dependence on
is asymptotically optimal. We then propose a probing algorithm that queries
edges from the graph and use them to find a seed set with the
same almost tight approximation guarantee. We also provide a matching (up to
logarithmic factors) lower-bound on the required number of edges. To address
the dependence of our probing algorithm on the independent cascade probability
, we show that it is impossible to maintain the same approximation
guarantees by controlling the discrepancy between the probing and seeding
cascade probabilities. Instead, we propose to down-sample the probed edges to
match the seeding cascade probability, provided that it does not exceed that of
probing. Finally, we test our algorithms on real world data to quantify the
trade-off between the cost of obtaining more refined network information and
the benefit of the added information for guiding improved seeding strategies
Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency
Given a social network G and a constant k, the influence maximization problem
asks for k nodes in G that (directly and indirectly) influence the largest
number of nodes under a pre-defined diffusion model. This problem finds
important applications in viral marketing, and has been extensively studied in
the literature. Existing algorithms for influence maximization, however, either
trade approximation guarantees for practical efficiency, or vice versa. In
particular, among the algorithms that achieve constant factor approximations
under the prominent independent cascade (IC) model or linear threshold (LT)
model, none can handle a million-node graph without incurring prohibitive
overheads.
This paper presents TIM, an algorithm that aims to bridge the theory and
practice in influence maximization. On the theory side, we show that TIM runs
in O((k+\ell) (n+m) \log n / \epsilon^2) expected time and returns a
(1-1/e-\epsilon)-approximate solution with at least 1 - n^{-\ell} probability.
The time complexity of TIM is near-optimal under the IC model, as it is only a
\log n factor larger than the \Omega(m + n) lower-bound established in previous
work (for fixed k, \ell, and \epsilon). Moreover, TIM supports the triggering
model, which is a general diffusion model that includes both IC and LT as
special cases. On the practice side, TIM incorporates novel heuristics that
significantly improve its empirical efficiency without compromising its
asymptotic performance. We experimentally evaluate TIM with the largest
datasets ever tested in the literature, and show that it outperforms the
state-of-the-art solutions (with approximation guarantees) by up to four orders
of magnitude in terms of running time. In particular, when k = 50, \epsilon =
0.2, and \ell = 1, TIM requires less than one hour on a commodity machine to
process a network with 41.6 million nodes and 1.4 billion edges.Comment: Revised Sections 1, 2.3, and 5 to remove incorrect claims about
reference [3]. Updated experiments accordingly. A shorter version of the
paper will appear in SIGMOD 201
Contrasting Multiple Social Network Autocorrelations for Binary Outcomes, With Applications To Technology Adoption
The rise of socially targeted marketing suggests that decisions made by
consumers can be predicted not only from their personal tastes and
characteristics, but also from the decisions of people who are close to them in
their networks. One obstacle to consider is that there may be several different
measures for "closeness" that are appropriate, either through different types
of friendships, or different functions of distance on one kind of friendship,
where only a subset of these networks may actually be relevant. Another is that
these decisions are often binary and more difficult to model with conventional
approaches, both conceptually and computationally. To address these issues, we
present a hierarchical model for individual binary outcomes that uses and
extends the machinery of the auto-probit method for binary data. We demonstrate
the behavior of the parameters estimated by the multiple network-regime
auto-probit model (m-NAP) under various sensitivity conditions, such as the
impact of the prior distribution and the nature of the structure of the
network, and demonstrate on several examples of correlated binary data in
networks of interest to Information Systems, including the adoption of Caller
Ring-Back Tones, whose use is governed by direct connection but explained by
additional network topologies
Sample Complexity Bounds for Influence Maximization
Influence maximization (IM) is the problem of finding for a given s ? 1 a set S of |S|=s nodes in a network with maximum influence. With stochastic diffusion models, the influence of a set S of seed nodes is defined as the expectation of its reachability over simulations, where each simulation specifies a deterministic reachability function. Two well-studied special cases are the Independent Cascade (IC) and the Linear Threshold (LT) models of Kempe, Kleinberg, and Tardos [Kempe et al., 2003]. The influence function in stochastic diffusion is unbiasedly estimated by averaging reachability values over i.i.d. simulations. We study the IM sample complexity: the number of simulations needed to determine a (1-?)-approximate maximizer with confidence 1-?. Our main result is a surprising upper bound of O(s ? ?^{-2} ln (n/?)) for a broad class of models that includes IC and LT models and their mixtures, where n is the number of nodes and ? is the number of diffusion steps. Generally ? ? n, so this significantly improves over the generic upper bound of O(s n ?^{-2} ln (n/?)). Our sample complexity bounds are derived from novel upper bounds on the variance of the reachability that allow for small relative error for influential sets and additive error when influence is small. Moreover, we provide a data-adaptive method that can detect and utilize fewer simulations on models where it suffices. Finally, we provide an efficient greedy design that computes an (1-1/e-?)-approximate maximizer from simulations and applies to any submodular stochastic diffusion model that satisfies the variance bounds
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