1. Mixture of Mutually Exciting Processes for Viral Diffusion
Shuang-Hong Yang, Hongyuan Zhang
Mingqing Li
04/20/2017

2. CONTENTS 01 02 03 04 05 Introduction Models Inference Experiments
Conclusions

3. Viral Diffusion 01 INTRODUCTION
How does the viral signal (e.g., behavior, idea, disease) evolve over time and spread through social network?
Two lines: time / infect process

4. 02 01 01 INTRODUCTION Memes Tracking Network Inference
Entangling situation:
Hard to detect and identify among different but related viruses, especially when they simultaneously diffuse and entangle with each other.
Network Inference
Hidden network:
Cannot observe or identify the network structure directly during the diffusion process.
Correlated challenges => jointly tackled
Tracking the flow of memes: spatially over a network (network diffusion) and temporally over time (meme evolution)

5. 02 01 01 INTRODUCTION Memes Tracking Network Inference
Correlated to each other:
Tracking the flow of memes:
spatially over a network (network diffusion)
temporally over time (meme evolution)
Correlated challenges => jointly tackled
Tracking the flow of memes: spatially over a network (network diffusion) and temporally over time (meme evolution)
Goal:
Identify memes;
Uncover the structure;

6. Scenarios
02 Model
A set of memes {m|m = 1, , M} simultaneously evolve over time t and propagate among a set of nodes I = {i|i = 1, , I} through a hidden social network G. The typical observations are a sequence of N events {En|n = 1, , N}, where an event is denoted as En = (tn, in, Wn), i.e., a node i got infected at time t and was observed with behavior (e.g., the symptoms of an infected patient) W
TWO Network: one for memes (hidden) and one for event (observed)

7. Evolutionary point process
02 Model
Evolutionary point process
Number of points before t
History of events up to but not including t
A list of times t at which a sequence of event E occur
Conditional intensity function
For the occurrences of discrete events:
Conditional Intensity function

8. 02 Model
Hawkes process
Deterministic base intensity
The occurrence of an event increases the probability of future events
A kernel function expressing the time-decay effect
Imply dependence
Multivariate Hawkes process
Integrate

9. Mixture of Hawkes processes
02 Model
Mixture of Hawkes processes
Consider the diffusion of a single meme
How often node i gets infected spontaneously (Constant)
each element αij expresses the degree of social influence from a node i to another node j, i.e., how likely i infects j
The kernel κ is now node-independent and used only to capture the time-decay effect

10. 02 Model Assumptions 1 Intensity equivalent
where λm specifies the base rate of meme m’s propagation;
2 These M memes are spreading over the same social network; 3
how likely i infects j;
4 All the events have been chronologically ordered.
Intensity equivalent
If we have a set of M memes diffusing
Znm = 1 if and only if En belongs to the m-th meme
µi,m specifies how likely node i got infected spontaneously on meme m;
the topology of the network doesn’t change from meme to meme;

11. 02 Model Model factors: Time t
Extend the model to capture the content W: massages belonging to the same meme are usually semantically related.
who is spreading from whom
Model factors:
Time t
Node id (user) i
En = (tn, in, Wn)
Detect the mutation-from relationship by string matching algorithms and model such pairwise constraints
内容的相关性指向meme的相关性
Bag of word model / text representation models – classification model
who was mutated from whom

12. 03 Inference Inner loop: Outer loop: Addresses meme-tracking:
Network inference:
By inferring Z, it essentially segments the single successive event history into multiple cascades, one per meme.
Further find the optimal network configuration α and other parameters based on the cascades inferred.

13. 03 Inference
The algorithm resembles the mean-filed Boltzmann machine: starting from an initial meme configuration, it runs by cyclically updating each variational meme assignment φn while keeping other φ’s fixed until the equilibrium configuration is reached (i.e., all meme assignments are consistent with one another)

14. 04 Experiment On controlled synthetic data
Mixture of Multivariate Hawkes Process
to what extent the model can recover the structure of the underlying network by measuring the difference between the learned infectivity matrix ˆα and the true α.
If the meme tracking algorithm can segment memes from the mixture: comparing the inferred meme identities with the true labels
MMHP denotes the plain mixture of MHPs model (i.e., without viral content model);
MMHP-LM the one with language model;
MMHP-MC with mutation constraints;
MHP-True is the model with meme identities {Z} being known (upper bound performance);
MHP-One is the model assuming only one meme (M = 1) (lower bound performance);

15. 04 Experiment On Twitter & Blogosphere Applied MMHP-LM model
These memes reflect the top trending events that occurred between mid June and late November in 2009
(e.g., the Microsoft-Yahoo! search deal, the Obama healthcare reform and the outbreak of the swine flue).

16. 1 Presented a viral diffusion model involving a mixture of MHPs, which addresses diffusion network inference and meme-tracking simultaneously and requires no human annotation or prior meme segmentation.
2 Fast inference algorithms have been developed based on mean-filed method and experiments were conducted on both synthetic and real data.
05 Conclusions

17. THANK YOU!