SLIDE 1
Learning Hawkes Processes Under Synchronization Noise
William Trouleau
Presented at ICML’19
- n Tue Jun 11th 2019
Jalal Etesami Negar Kiyavash Matthias Grossglauser Patrick Thiran
Learning Hawkes Processes Under Synchronization Noise William - - PowerPoint PPT Presentation
Learning Hawkes Processes Under Synchronization Noise William - - PowerPoint PPT Presentation
Learning Hawkes Processes Under Synchronization Noise William Trouleau Jalal Etesami Negar Kiyavash Matthias Grossglauser Patrick Thiran Presented at ICML19 on Tue Jun 11th 2019 Question of interest Learning the causal structure of
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?
Don’t listen to @Bob, it’s FAKE NEWS!
Charly @TruthSeeker
This candidate will stop global warming! Vote for him!
Bob @Bob
Example1: Information Diffusion
- Consider a network of users
- We observe a a sequence of
discrete events in continuous time: tweets, Facebook posts…
SLIDE 4
Don’t listen to @Bob, it’s FAKE NEWS!
Charly @TruthSeeker
This candidate will stop global warming! Vote for him!
Bob @Bob
Example1: Information Diffusion
?
- Consider a network of users
- We observe a a sequence of
discrete events in continuous time: tweets, Facebook posts…
- Questions of interest:
Who influences whom? How does fake news spread?
SLIDE 5
Don’t listen to @Bob, it’s FAKE NEWS!
Charly @TruthSeeker
This candidate will stop global warming! Vote for him!
Bob @Bob
Example1: Information Diffusion
?
- Consider a network of users
- We observe a a sequence of
discrete events in continuous time: tweets, Facebook posts…
- Questions of interest:
Who influences whom? How does fake news spread?
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Example 2: Disease Dynamics
?
- Consider a network of hospitals
- We observe a a sequence of
discrete events in continuous time: interactions, infections, recoveries…
- Questions of interest:
Who infected whom? How does the disease spread? How to control it?
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Example 2: Disease Dynamics
?
- Consider a network of hospitals
- We observe a a sequence of
discrete events in continuous time: interactions, infections, recoveries…
- Questions of interest:
Who infected whom? How does the disease spread? How to control it?
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How do we usually solve it?
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Method: Multivariate Hawkes Process (MHP)
- Temporal Point Process
- Widely used model to learn causal
structure between time series
- Captures mutually exciting patterns
- f influence between dimensions
λi(t|Ht) = µi +
d
- j=1
- τ∈Hj
t
κij(t − τ)
αij
λi(t|Ht) λj(t|Ht)
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Method: Multivariate Hawkes Process (MHP)
- Temporal Point Process
- Widely used model to learn causal
structure between time series
- Captures mutually exciting patterns
- f influence between dimensions
λi(t|Ht) = µi +
d
- j=1
- τ∈Hj
t
κij(t − τ)
Exogenous intensity: constant, independent
- f the past
Endogenous intensity: due to excitation from past events, with excitation kernel
κij(t) = αije−βt1{t > 0}
αij
λi(t|Ht) λj(t|Ht)
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Method: Multivariate Hawkes Process (MHP)
- Prior work assume perfect traces
without noise
- What if the observed stream of events
is subject to a random and unknown time shift?
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How to learn MHPs under noisy observations?
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- What it events have systematic measurement errors?
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t0 Multivariate Hawkes Process under Synchronization Noise
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- What it events have systematic measurement errors?
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Order of events can be switched
Multivariate Hawkes Process under Synchronization Noise
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- What it events have systematic measurement errors?
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Events can enter the
- bservation
window… …or escape it
Multivariate Hawkes Process under Synchronization Noise
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- What it events have systematic measurement errors?
- Edges learnt by maximum likelihood estimation can be
significantly affected by even small delays
−6 −4 −2 2 4 6 0.0 0.5 1.0 Kernel coefficients
NA NB NA NB NA NB NA NB NA NB NA NB
Learnt Network
AB BA A B A B
) )
A B
NA NB
Ground truth Network
Multivariate Hawkes Process under Synchronization Noise
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New approach DESYNC-MHP
- Idea:
- Consider the noise as parameters
- Maximize the joint log-likelihood over
both MHP parameters and noise
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New approach DESYNC-MHP
- Idea:
- Consider the noise as parameters
- Maximize the joint log-likelihood over
both MHP parameters and noise
- Challenges: resulting objective is
- Non-smooth
- Non-convex
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New approach DESYNC-MHP
- Idea:
- Consider the noise as parameters
- Maximize the joint log-likelihood over
both MHP parameters and noise
- Challenges: resulting objective is
- Non-smooth
- Non-convex
- Solution:
- Approximate the objective with a
smooth approximation
- Use SGD to escape local minima
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Experimental Results
- Noise variance
- Average accuracy ( std)
Classic MLE DESYNC-MHP MLE
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Learning Hawkes Processes Under Synchronization Noise
William Trouleau Jalal Etesami Negar Kiyavash Matthias Grossglauser Patrick Thiran