iccss2015 talk: null model for meme popularity
TRANSCRIPT
Effects of Memory and Network Structure on Memes Competing for Popularity
James P. Gleeson1, Kevin P. O’Sullivan1, Raquel A. Baños2, Yamir Moreno2
1 MACSI, Department of Mathematics and Statistics,
University of Limerick, Ireland 2 Instituto de Biocomputación y Física de Sistemas Complejos (BIFI),
Universidad de Zaragoza, Spain
www.ul.ie/gleeson [email protected] @gleesonj
International Conference on Computational Social Science, Helsinki, 10 Jun 2015
Yamir Moreno, Zaragoza Raquel A Baños, Zaragoza Kevin O’Sullivan, UL
William Lee, UL Jonathan Ward, Leeds
Davide Cellai, UL Mason Porter, Oxford J-P Onnela, Harvard Felix Reed-Tsochas, Oxford
Science Foundation Ireland FP7 FET Proactive PLEXMATH SFI/HEA Irish Centre for High-End
Computing (ICHEC)
Collaborators, funding, references
• arXiv:1501.05956 • Phys. Rev. Lett., 112, 048701 (2014); arXiv:1305.4328 • PNAS, 111, 10411 (2014); arXiv :1305.7440
Motivating examples from empirical work on Twitter
From Bakshy et al., 2011 “Everyone’s an influencer: Quantifying influence on Twitter”, Proc. 4th ACM Conf. Web Search and Data Mining
From Lerman et al., 2012 “Social contagion: An empirical study of information spread on Digg and Twitter follower graphs”, arXiv:1202.3162
𝜏 = 1.5
𝜏 = 2
𝜏 = 1.5
𝜏 = 2
Modelling and analysis of meme popularity
• L Weng, A Flammini, A Vespignani, and F Menczer. Competition among memes in a world with limited attention. Scientific Reports, 2:335, 2012.
• J. Cheng, L. Adamic, P. A. Dow, J. M. Kleinberg, and J. Leskovec. Can cascades be predicted? Proc. WWW23, 925–936, 2014.
• L. Weng, F. Menczer, and Y.-Y. Ahn. Virality prediction and community structure in social networks. Scientific Reports, 3:2522, 2013.
• R. A. Bentley, P. Ormerod, and M. Batty. Evolving social influence in large populations. Behavioral Ecology and Sociobiology, 65(3):537–546, 2011.
• T. Kuhn, M. Perc, D. Helbing. Inheritance patterns in citation networks reveal scientific memes. Physical Review X, 4, 041036, 2014.
• M. Coscia. Average is boring: how similarity kills a meme’s success. Scientific Reports, 4:6477, 2014.
• D. J. Watts, Everything is obvious: How common sense fails us. Random House, 2012.
• ….
• ….
• but: no null model for effects of network structure and human memory timescales
What is a null model?
• A baseline against which more complicated hypotheses or models can be tested
• Simple enough to be analytically tractable
• Realistic enough to capture features of empirical data
• Effects of network structure
• Memory effects
arXiv:1501.05956
When active, either: • retweet (prob 1 − 𝜇) or • innovate (prob 𝜇)
𝝀
𝝀
𝝀
𝝀
𝝀
network structure
memory time distribution
innovation probability
interestingness
Examples of popularity histories from model
network structure innovation
probability activity rate memory time
distribution
𝐺 𝑎, 𝑥 = 𝑝𝒋𝑘 𝑑ℓ 𝑗𝛽𝜆 + 𝜇𝛽𝑗𝑘 𝑒− 𝑗 𝛽 𝜆+𝜇𝛽𝑗𝑘 ℓ ×∞
0 𝒋,𝑘
× exp − 1 − 𝜇 𝛽𝑗𝑘 𝑑𝑟
min ℓ,𝑎
0
𝑑𝜏𝑎−𝑟
0
Φ 𝑎 − 𝑟 − 𝜏 1 − 𝑥 1 − 𝜆 + 𝜆𝐺 𝜏, 𝑥 𝑘
interestingness
𝐻 𝑎, 𝑥 = 𝑞𝑛 𝑎 𝑥𝑛∞
𝑛=0
Competition-induced criticality (CIC) in the model
• The copying-with-memory model gives a critical branching process in the limit of vanishing innovation, 𝜇 → 0
• The memes have equal “fitness” – a type of “neutral model” [Pinto and Muñoz, 2011, Bentley et al. 2004 ]
• Does not have the “early-mover advantage” property of cumulative advantage (preferential attachment) models
• Distinct from sandpile self-organized criticality (SOC)
Phys. Rev. Lett., 112, 048701 (2014); arXiv:1305.4328
𝑝𝑘 ∼ 𝐷 𝑘−𝛾; 𝛾 = 2.5 𝑝𝑘 Poisson
𝑞𝑛 ∞ ∼ 𝐶1 𝑛−
𝛾𝛾−1 𝑞𝑛 ∞ ∼ 𝐶2 𝑛
− 32 𝑒−
𝑛𝜅
𝑝𝑘 ∼ 𝐷 𝑘−𝛾; 𝛾 = 2.5 𝑝𝑘 Poisson
𝑚 𝑠 = 1
𝑠+1 − 𝜇
𝑠
(𝜆𝑧 + 1)Φ (𝑠)
𝜆𝑧 + 𝜇 + 𝑠 − 1 − 𝜇 𝜆𝑧 Φ (𝑠)
𝑝𝑘 ∼ 𝐷 𝑘−𝛾; 𝛾 = 2.5 𝑝𝑘 Poisson
𝑚 𝑎 ∼ 𝜆𝑧 + 1
𝑇𝜆𝑧 + 1𝑎
𝑝𝑘 ∼ 𝐷 𝑘−𝛾; 𝛾 = 2.5 𝑝𝑘 Poisson
𝑞1 𝑎 ∼ 𝛽𝑗𝑘𝑝𝑗𝑘𝑗𝛽 𝜆 + 𝜇𝛽𝑗𝑘
𝑗𝛽 𝜆 + 𝜇𝛽𝑗𝑘 + 1 − 𝜇 𝛽𝑗𝑘𝐶(𝑎)1 − 𝜆 + 𝜆 𝐺 𝑎, 0 𝑘
𝑗,𝑘
𝑝𝑘 ∼ 𝐷 𝑘−𝛾; 𝛾 = 2.5 𝑝𝑘 Poisson
𝑞1 𝑎 − 𝑞1(∞) ∼ 𝐵 Φ 𝑡 𝑑𝑡∞
𝑎
What is a null model?
• A baseline against which more complicated hypotheses or models can be tested
• Simple enough to be analytically tractable
• Realistic enough to capture features of empirical data
Comparing the model to data
𝑚 𝑠 = 1
𝑠+1 − 𝜇
𝑠
(𝜆𝑧 + 1)Φ (𝑠)
𝜆𝑧 + 𝜇 + 𝑠 − 1 − 𝜇 𝜆𝑧 Φ (𝑠)
Φ 𝜏 = Gamma(𝑘, 𝜃)
=1
Γ 𝑘 𝜃𝑘𝜏𝑘−1𝑒−𝜏/𝜃
𝑘 = 0.25; 𝜃 = 500
Comparing the model to data
𝜇 = 0.033
𝑚 𝑠 = 1
𝑠+1 − 𝜇
𝑠
(𝜆𝑧 + 1)Φ (𝑠)
𝜆𝑧 + 𝜇 + 𝑠 − 1 − 𝜇 𝜆𝑧 Φ (𝑠)
Comparing the model to data
Data Model
Comparing the model to data
Data Model
Distributions scaled by their mean show a collapse
Comparing the model to data
• A model where competition between memes for the limited resource of user attention induces criticality in the 𝜇 → 0 limit
– Power-law popularity distributions
– Linear-in-age mean popularity growth
• Simple enough to be analytically tractable
• Realistic enough to capture features of empirical data
Conclusions
⇒ a useful null model to help understand how memory, network structure and competition affect meme popularity
• arXiv:1501.05956 • Phys. Rev. Lett., 112, 048701 (2014); arXiv:1305.4328 • PNAS, 111, 10411 (2014); arXiv :1305.7440
www.ul.ie/gleeson [email protected] @gleesonj
Effects of Memory and Network Structure on Memes Competing for Popularity
James P. Gleeson1, Kevin P. O’Sullivan1, Raquel A. Baños2, Yamir Moreno2
1 MACSI, Department of Mathematics and Statistics,
University of Limerick, Ireland 2 Instituto de Biocomputación y Física de Sistemas Complejos (BIFI),
Universidad de Zaragoza, Spain
www.ul.ie/gleeson [email protected] @gleesonj
International Conference on Computational Social Science, Helsinki, 10 Jun 2015