deletions | additions       diff --git a/section_Fitting_Multivariate_Hawkes_Process__.tex b/section_Fitting_Multivariate_Hawkes_Process__.tex  index 90a5cfd..fe00ffb 100644  --- a/section_Fitting_Multivariate_Hawkes_Process__.tex  +++ b/section_Fitting_Multivariate_Hawkes_Process__.tex 
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In the following, we visualize the the directed weighted network as a matrix. $W(i,j)$ measures the excitatory jump exerted from $i$ to $j$, where $i$ corresponds to row and $j$ corresponds to column.   The result is still preliminary and looks hard to interpret. Some of the relations found do not semantically match the meaning expected. For example, in the first plot below, the nuanced relation $\#\text{ff} \rightarrow \#\text{bullying}$ is bogus since $\#\text{ff}$ is hashtag that simply recurs every Friday. The weekly trend is an obvious confounding factor. As another example, the big entry $\#\text{cyberbullying} \rightarrow \#\text{ripboybeliebermartin}$ also does not make sense, since the latter is an incidental event. To illustrate the issue, we also show the time series for these two pairs of hashtags. hashtags (properly scaled).