stmorse / hawkes Goto Github PK

Hello,

You appear to have forgotten to link the blog post in the README.

Current markdown is [this blog post]()

Thanks,
David

Hi Steve, I have been using hawkes library, and I found an issue regarding an availability of time horizon in EM method.

For generating a sequence, we need to give a horizon parameter (e.g., P.generate_seq(10)), so that we can obtain the simulated data up to t=10. However, the EM method does not get any information from the last event, which does not produce the right parameter estimation.

In below example, I share a case when the event happens in the early beginning of the time horizon, thus the EM method fails by estimating parameter by only using the information until the last event.

### A single case 
m = np.array([0.1])
a = np.array([[0]])
w = 1

P = MHP(mu=m, alpha=a, omega=w)
### In this example, an event appeared in a very early stage of the time horizon.
P.generate_seq(10)

Out[1]: array([[1.69135373, 0. ]])

# Since the input of the EM method is only P.data, 
# it does not have any information that no event happens from [1.69, 10]
# So the predicted 'mu' value is very big (0.59124238 = 1/1.69135373)
P.EM(a, m, w, verbose=False)

Out[2]: (array([[0.]]), array([0.59124238]))

Is there any walkaround that I can put extra time_horizon parameter to make a right parameter estimation? I think the right solution might look like this.

# Add or have a time horizon in P, so that EM algorithm can utilize a timeline after the last event.
P.time_horizon = [10]
P.EM(a, m, w, verbose=False)    # or P.EM(a, m, w, time_horizon=[10], verbose=False)

Out[2]: (array([[0.]]), array([0.1]))

Thanks for effort on publicizing your work, I think your library is much more intuitive than tick.

Just running the example:

from MHP import MHP
P = MHP()
P.generate_seq(60)

fails with:

.../hawkes/MHP.py", line 102, in generate_seq
    self.data = np.array(self.data)
ValueError: setting an array element with a sequence. The requested array has an inhomogeneous shape after 2 dimensions. The detected shape was (14, 2) + inhomogeneous part.

Hello,

Thank you for posting this code.

I have a doubt regarding this line of code : (line 71 of MHP.py)
Istar = np.sum(lastrates) + self.omega * np.sum(self.alpha[:,uj])
, why is there the self.omega ? I'm not sure of your notation but the use would be only the np.sum(lastrates) + np.sum(self.alpha[:,uj]) , no ?

Kind regards,