C - SNAP - Stanford University

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12/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 27
Goal: Find a graph G that best explains the observed information times Given a graph G, define the likelihood P(C|G): Define a model of information diffusion over a graph P c(u,v) … prob. that u infects v in cascade c P(c|T) … prob. that c spread in particular pattern T P(c|G) … prob. that cascade c occurred in G P(G|C) … prob. that a set of cascades C occurred in G Questions: How to efficiently compute P(G|C)? (given a single G) How to efficiently find G * that maximizes P(G|C)? (over O(2 N*N ) graphs) 12/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 28
Page 1 and 2: CS224W: Social and Information Netw
Page 3 and 4: Predict links in a evolving collabo
Page 5 and 6: For every pair of nodes (x,y) compu
Page 7 and 8: Improvement over #common neighbors
Page 9 and 10: Recommend a list of possible friend
Page 11 and 12: Let s be the center node Let f w(u
Page 13 and 14: a uv …. Strength of edge (u,v,)
Page 15 and 16: Want to minimize: Loss: h(x)=0 if
Page 17 and 18: How to minimize F? Take the deriva
Page 19 and 20: Facebook Iceland network 174,000 n
Page 21: Facebook: predict future friends A
Page 24 and 25: There is a hidden diffusion network
Page 28 and 29: Continuous time cascade diffusion m
Page 30 and 31: Given node infection times and patt
Page 32 and 33: Score of a graph G for a set of cas
Page 34 and 35: Theorem: F c(G) is monotonic, and s
Page 36 and 37: Synthetic data: Take a graph G on
Page 38 and 39: With 2x as many infections as edges
Page 40 and 41: 5,000 news sites: Blogs Mainstream

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