The goodness of fit of Hawkes processes (or D-dimentional Hawkes processes)

[rudanie89]

Good morning,

I read the paper that tick.HawkesADM4 was developed: 'Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes.' For my understanding, this paper focused on optimisation problem, and they use "loglike" metric score to compare with baseline. So, I am wondering that which function from 'tick' provide me to test whether Hawkes processes fit with my data ( I mean the goodness of fit). Thank you.

[Mbompr]

Hi,

Have you tried objective : that is the function to be minimized, or score : that is the goodness of fit function, to test whether Hawkes processes fit with your data but that does not include the penalty terms.

[rudanie89]

Hi, Thank you. Yes I have tried. But I don't think it is as we usually do in statistics like, we will test how well Hawkes processes can fit with the data. And, I am just wondering that is it weird if I got some coefficient values of adjacency matrix are greater than 1? I though the coefficient values of adjacency matrix are in (0,1). Can you help me to correct me please? Thank you.

[stephanegaiffas]

Hi, what is computed through the score method is precisely the negative log likelihood of the model, so yes it is what we usually do in statistics. However, tick does not provide statistical tests for now, with p-value computations.

The entries of the adjacency matrix can perfectly be larger than 1, note that it is not an adjacency matrix per se from graph theory, but something that plays a similar role for a Hawkes model. The only theoretical constraint about it (but not required in the procedures used in tick) is that it’s spectral radius is < 1 to ensure stationnarity

Best

Le 26 sept. 2019 à 07:31, rudascience [email protected] a écrit :

 Hi, Thank you. Yes I have tried. But I don't think it is as we usually do in statistics like, we will test how well Hawkes processes can fit with the data. And, I am just wondering that is it weird if I got some coefficient values of adjacency matrix are greater than 1? I though the coefficient values of adjacency matrix are in (0,1). Can you help me to correct me please? Thank you.

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[rudanie89]

Hi, Thank you. Yes, I mean p-value. Re: The entries of the adjacency matrix. So, it doesn't mean the influence probabilities of users in HawkesADM4? I thought the adjacency matrix as the following paper mentioned: Zhou, K., Zha, H., & Song, L. (2013, May). Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes.

I am so sorry to ask a lot. But, I am confused now. Might you help me to clarify, please? Thank you.