18,094 research outputs found
Opinion dynamics with varying susceptibility to persuasion
A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates
Reciprocity-driven Sparse Network Formation
A resource exchange network is considered, where exchanges among nodes are
based on reciprocity. Peers receive from the network an amount of resources
commensurate with their contribution. We assume the network is fully connected,
and impose sparsity constraints on peer interactions. Finding the sparsest
exchanges that achieve a desired level of reciprocity is in general NP-hard. To
capture near-optimal allocations, we introduce variants of the Eisenberg-Gale
convex program with sparsity penalties. We derive decentralized algorithms,
whereby peers approximately compute the sparsest allocations, by reweighted l1
minimization. The algorithms implement new proportional-response dynamics, with
nonlinear pricing. The trade-off between sparsity and reciprocity and the
properties of graphs induced by sparse exchanges are examined.Comment: 19 page
Optimum Statistical Estimation with Strategic Data Sources
We propose an optimum mechanism for providing monetary incentives to the data
sources of a statistical estimator such as linear regression, so that high
quality data is provided at low cost, in the sense that the sum of payments and
estimation error is minimized. The mechanism applies to a broad range of
estimators, including linear and polynomial regression, kernel regression, and,
under some additional assumptions, ridge regression. It also generalizes to
several objectives, including minimizing estimation error subject to budget
constraints. Besides our concrete results for regression problems, we
contribute a mechanism design framework through which to design and analyze
statistical estimators whose examples are supplied by workers with cost for
labeling said examples
What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks
In this paper, we analyze the quality of a large class of simple dynamic
resource allocation (DRA) strategies which we name priority planning. Their aim
is to control an undesired diffusion process by distributing resources to the
contagious nodes of the network according to a predefined priority-order. In
our analysis, we reduce the DRA problem to the linear arrangement of the nodes
of the network. Under this perspective, we shed light on the role of a
fundamental characteristic of this arrangement, the maximum cutwidth, for
assessing the quality of any priority planning strategy. Our theoretical
analysis validates the role of the maximum cutwidth by deriving bounds for the
extinction time of the diffusion process. Finally, using the results of our
analysis, we propose a novel and efficient DRA strategy, called Maximum
Cutwidth Minimization, that outperforms other competing strategies in our
simulations.Comment: 18 pages, 3 figure
Observer Placement for Source Localization: The Effect of Budgets and Transmission Variance
When an epidemic spreads in a network, a key question is where was its
source, i.e., the node that started the epidemic. If we know the time at which
various nodes were infected, we can attempt to use this information in order to
identify the source. However, maintaining observer nodes that can provide their
infection time may be costly, and we may have a budget on the number of
observer nodes we can maintain. Moreover, some nodes are more informative than
others due to their location in the network. Hence, a pertinent question
arises: Which nodes should we select as observers in order to maximize the
probability that we can accurately identify the source? Inspired by the simple
setting in which the node-to-node delays in the transmission of the epidemic
are deterministic, we develop a principled approach for addressing the problem
even when transmission delays are random. We show that the optimal
observer-placement differs depending on the variance of the transmission delays
and propose approaches in both low- and high-variance settings. We validate our
methods by comparing them against state-of-the-art observer-placements and show
that, in both settings, our approach identifies the source with higher
accuracy.Comment: Accepted for presentation at the 54th Annual Allerton Conference on
Communication, Control, and Computin
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