Maximum Likelihood Estimation of Power-law Degree Distributions via Friendship Paradox based Sampling

Nettasinghe, Buddhika; Krishnamurthy, Vikram

doi:10.48550/arxiv.1908.00310

Cited by 3 publications

(4 citation statements)

References 43 publications

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“…Future directions of this work include further improving the accuracy of the proposed method using different sampling methods based on friendship paradox (e.g. [24], [25], [26]); enriching this framework to handle more sophisticated network topologies such as heterogeneous graphs; incorporating the hidden Markov bridge model with generation models to forecast opinion dynamics (e.g. [20], [31], [32]).…”

Section: Discussionmentioning

confidence: 99%

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Echo Chambers and Segregation in Social Networks: Markov Bridge Models and Estimation

Luo¹,

Nettasinghe²,

Krishnamurthy³

2020

Preprint

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This paper deals with the modeling and estimation of the sociological phenomena called echo chambers and segregation in social networks. Specifically, we present a novel community-based graph model that represents the emergence of segregated echo chambers as a Markov bridge process. A Markov bridge is a one-dimensional Markov random field that facilitates modeling the formation and disassociation of communities at deterministic times which is important in social networks with known timed events. We justify the proposed model with six real world examples and examine its performance on a recent Twitter dataset. We provide model parameter estimation algorithm based on maximum likelihood and, a Bayesian filtering algorithm for recursively estimating the level of segregation using noisy samples obtained from the network. Numerical results indicate that the proposed filtering algorithm outperforms the conventional hidden Markov modeling in terms of the mean-squared error. The proposed filtering method is useful in computational social science where data-driven estimation of the level of segregation from noisy data is required.

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Section: Discussionmentioning

confidence: 99%

“…We assume that γN of the total N edges are uniformly sampled and observed at each time t (random sampling of edges has been used widely in literature in statistical estimation tasks e.g. [24], [25], [26]). γ is a fixed ratio in (0, 1].…”

Section: Measuring Conductance Via Sampled Edgesmentioning

confidence: 99%

Echo Chambers and Segregation in Social Networks: Markov Bridge Models and Estimation

Luo¹,

Nettasinghe²,

Krishnamurthy³

2020

Preprint

Self Cite

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“…1) The edge formation protocol proposed in this paper assumes homogeneity among users in one community, i.e., users' community information solely determines their edge formation probabilities. An interesting future direction is to incorporate heterogeneity (e.g., preferential attachment with fitness) into the network model and apply methods such as friendship paradox sampling [34], [35], [36] to assign different weights to the 2 hop connections between different pairs of users. 2) Another interesting direction is to consider ARM's parameter (e.g., the recommendation acceptance probability) depends on users' actions and incorporates a feedback law, i.e., ARM raises the acceptance probability when users become more segregated in network.…”

Section: Limitations and Extensionsmentioning

confidence: 99%

Controlling Segregation in Social Network Dynamics as an Edge Formation Game

Luo¹,

Nettasinghe²,

Krishnamurthy³

2021

Preprint

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This paper studies controlling segregation in social networks via exogenous incentives. We construct an edge formation game on a directed graph. A user (node) chooses the probability with which it forms an inter-or intra-community edge based on a utility function that reflects the tradeoff between homophily (preference to connect with individuals that belong to the same group) and the preference to obtain an exogenous incentive. Decisions made by the users to connect with each other determine the evolution of the social network. We explore an algorithmic recommendation mechanism where the exogenous incentive in the utility function is based on weak ties which incentivizes users to connect across communities and mitigates the segregation. This setting leads to a submodular game with a unique Nash equilibrium. In numerical simulations, we explore how the proposed model can be useful in controlling segregation and echo chambers in social networks under various settings.

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“…Friendship paradox has recently gained attention in several applications related to networks under the broad theme "how network biases can be used effectively for estimation problems?". For example, [14], [15] show how friendship paradox can be utilized for accurate estimation of a heavy tailed degree distribution, [16], [17] show how friendship paradox can be used for quickly detecting a disease outbreak. Our results for the case 1 and case 2 also fall under this broad theme.…”

Section: Related Workmentioning

confidence: 99%

"What Do Your Friends Think?": Efficient Polling Methods for Networks Using Friendship Paradox

Nettasinghe

Krishnamurthy

2019

IEEE Trans. Knowl. Data Eng.

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This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose three NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph (ii) the social network graph is unknown. For both cases, algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.

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Maximum Likelihood Estimation of Power-law Degree Distributions via Friendship Paradox based Sampling

Cited by 3 publications

References 43 publications

Echo Chambers and Segregation in Social Networks: Markov Bridge Models and Estimation

Echo Chambers and Segregation in Social Networks: Markov Bridge Models and Estimation

Controlling Segregation in Social Network Dynamics as an Edge Formation Game

"What Do Your Friends Think?": Efficient Polling Methods for Networks Using Friendship Paradox

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