Transcript Lecture 1 - Manuel Gomez Rodriguez

Machine learning for
Dynamic Social Network Analysis
Manuel Gomez Rodriguez
Max Planck Institute for Software Systems
UNIVERSITY OF SYDNEY, JANUARY 2017
Interconnected World
SOCIAL
NETWORKS
TRANSPORTATION
NETWORKS
WORLD WIDE
WEB
PROTEIN
INTERACTIONS
INFORMATION
NETWORKS
INTERNET OF
THINGS
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Many discrete events in continuous time
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Qmee, 2013
Variety of processes behind these events
Events are (noisy) observations of a
variety of complex dynamic processes…
News spread
in Twitter
Product reviews
and sales in
Amazon
Video
becomes viral
in Youtube
FAST
A user gains
recognition in
Quora
Article
creation in
Wikipedia
SLOW
…in a wide range of temporal scales.
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Example I: Idea adoption/viral marketing
S means D
Christine
D follows S
Bob
3.00pm
3.25pm
Beth
3.27pm
Joe
David
4.15pm
Friggeri et al., 2014
They can have an impact
in the off-line world
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Example II: Information creation & curation
✗
Addition
Refutation
Question
Answer
Upvote
Example III: Learning trajectories
1st year computer science student
Introduction to programming
Discrete math
Project presentation
For/do-while
loops
Define
Set theory
functions
Powerpoint
Graph Theory
Class
vs. Keynote
inheritance
Export
Geometrypptx to pdf
t
If … else
How to write
switch
Logic
Private
functions
PP
templates
Class
destructor
Plot
library
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DETAILED TRACES OF ACTIVITY
Detailed event traces
The availability of event traces
boosts a new generation of
data-driven models and
algorithms
#greece
retweet
s
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Previously: discrete-time models & algorithms
Epoch 1
Epoch 2
Epoch 3
Epoch 4
Discrete-time models artificially introduce epochs:
1. How long is each epoch? Data is very heterogeneous.
2. How to aggregate events within an epoch?
3. What if no event within an epoch?
4. Time is treated as index or conditioning variable, not easy
to deal with time-related queries.
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Outline of the Seminar
REPRESENTATION: TEMPORAL POINT PROCESSES
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
APPLICATIONS: MODELS
1. Information propagation
2. Opinion dynamics
3. Information reliability
4. Knowledge acquisition
APPLICATIONS: CONTROL
1. Influence maximization
2. Activity shaping
3. When-to-post
Slides/references: learning.mpi-sws.org/sydney-seminar
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Representation:
Temporal Point Processes
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
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Temporal point processes
Temporal point process:
A random process whose realization consists of
discrete events localized in time
Discrete events
time
History,
Dirac delta function
Formally:
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Model time as a random variable
density
Prob. between [t, t+dt)
time
History,
Likelihood of a timeline:
Prob. not before t
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Problem of parametrizing density
time
Likelihood is not concave in w:
It is difficult for model design and interpretability:
1. Densities need to integrate to 1
2. Combination of timelines results in density convolutions
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Intensity function
density
Prob. between [t, t+dt)
time
History,
Prob. not before t
Intensity:
Probability between [t, t+dt) but not before t
Observation:
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Advantages of parametrizing intensity
time
Likelihood is concave in w:
Suitable for model design and interpretable:
1. Intensities only need to be nonnegative
2. Combination of timelines results in intensity additions
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Relation between f*, F*, S*, λ*
Central quantity
we will use!
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Representation:
Temporal Point Processes
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
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Poisson process
time
Intensity of a Poisson process
Observations:
1. Intensity independent of history
2. Uniformly random occurrence
3. Time interval follows exponential distribution
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Inhomogeneous Poisson process
time
Intensity of an inhomogeneous Poisson process
Observations:
1. Intensity independent of history
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Nonparametric inhomogeneous Poisson process
Positive combination of (Gaussian) RFB kernels:
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Terminating (or survival) process
time
Intensity of a terminating (or survival) process
Observations:
1. Limited number of occurrences
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Self-exciting (or Hawkes) process
time
History,
Triggering kernel
Intensity of self-exciting
(or Hawkes) process:
Observations:
1. Clustered (or bursty) occurrence of events
2. Intensity is stochastic and history dependent
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How do we sample from a Hawkes process?
time
Thinning procedure (similar to rejection sampling):
1. Sample
from Poisson process with intensity
2. Keep the sample with probability
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Summary
Building blocks to represent different dynamic processes:
Poisson processes:
Inhomogeneous Poisson processes:
Terminating point processes:
Self-exciting point processes:
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Representation:
Temporal Point Processes
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
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Superposition of processes
time
Sample each intensity + take minimum = Additive intensity
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Mutually exciting process
time
Bob
History
Christine
time
History
Clustered occurrence affected by neighbors
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Mutually exciting terminating process
time
Bob
Christine
time
History
Clustered occurrence affected by neighbors
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Representation:
Temporal Point Processes
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
30
Marked temporal point processes
Marked temporal point process:
A random process whose realization consists of discrete
marked events localized in time
time
time
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History,
Independent identically distributed marks
time
Distribution for the marks:
Observations:
1. Marks independent of the temporal dynamics
2. Independent identically distributed (I.I.D.)
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Dependent marks: SDEs with jumps
time
History,
Marks given by stochastic differential equation with jumps:
Observations:
Drift
Event influence
1. Marks dependent of the temporal dynamics
2. Defined for all values of t
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Dependent marks: distribution + SDE with jumps
time
History,
Distribution for the marks:
Drift
Event influence
Observations:
1. Marks dependent on the temporal dynamics
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2. Distribution represents additional source of uncertainty
Mutually exciting + marks
Bob
time
Christine
Marks affected by neighbors
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Drift
Neighbor influence
REPRESENTATION: TEMPORAL POINT PROCESSES
1. Intensity function
2. Basic building blocks
3. Superposition
4. Marks and SDEs with jumps
This
lecture
APPLICATIONS: MODELS
1. Information propagation
2. Opinion dynamics
3. Information reliability
4. Knowledge acquisition
Next
lecture
APPLICATIONS: CONTROL
1. Influence maximization
2. Activity shaping
3. When-to-post
Slides/references: learning.mpi-sws.org/sydney-seminar
36