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| author | jeanpouget-abadie <jean.pougetabadie@gmail.com> | 2015-02-01 21:13:06 -0500 |
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| committer | jeanpouget-abadie <jean.pougetabadie@gmail.com> | 2015-02-01 21:13:06 -0500 |
| commit | 3173920dc2e45ba7998d5cf0745e7de1a14eb68d (patch) | |
| tree | b695d405fcb2d6b896c1de1864eebdd1639c6e1f /paper/sections/model.tex | |
| parent | 30606c850bc585848aa7cb809590a4e920822197 (diff) | |
| download | cascades-3173920dc2e45ba7998d5cf0745e7de1a14eb68d.tar.gz | |
small touch ups to results
Diffstat (limited to 'paper/sections/model.tex')
| -rw-r--r-- | paper/sections/model.tex | 8 |
1 files changed, 3 insertions, 5 deletions
diff --git a/paper/sections/model.tex b/paper/sections/model.tex index 3bc8b20..e35aa4a 100644 --- a/paper/sections/model.tex +++ b/paper/sections/model.tex @@ -45,9 +45,7 @@ cascade model. \subsection{Examples} \label{subsec:examples} -In this section, we show that both the Independent Cascade Model and the Voter -model are Generalized Linear Cascades. The Linear Threshold model will be -discussed in Section~\ref{sec:linear_threshold}. +In this section, we show that the well-known Independent Cascade Model and the Voter model are Generalized Linear Cascades. The Linear Threshold model will be discussed in Section~\ref{sec:linear_threshold}. \subsubsection{Independent Cascade Model} @@ -75,7 +73,7 @@ Defining $\Theta_{i,j} \defeq \log(1-p_{i,j})$, this can be rewritten as: = 1 - e^{\inprod{\theta_j}{X^t}} \end{equation} which is a Generalized Linear Cascade model with inverse link function $f(z) -= z$. += 1 - e^z$. \subsubsection{The Voter Model} @@ -90,7 +88,7 @@ step $t$, then we have: \mathbb{P}\left[X^{t+1}_j = 1 | X^t \right] = \sum_{i=1}^m \Theta_{i,j} X_i^t = \inprod{\theta_j}{X^t} \tag{V} \end{equation} -which is again a Generalized Linear Cascade model with inverse link function +which is a Generalized Linear Cascade model with inverse link function $f(z) = z$. \subsection{Maximum Likelihood Estimation} |
