diff options
Diffstat (limited to 'paper/sections/model.tex')
| -rw-r--r-- | paper/sections/model.tex | 3 |
1 files changed, 2 insertions, 1 deletions
diff --git a/paper/sections/model.tex b/paper/sections/model.tex index 25f55e0..d3403ef 100644 --- a/paper/sections/model.tex +++ b/paper/sections/model.tex @@ -120,6 +120,7 @@ Therefore, the independent cascade model is a Generalized Linear Cascade model w \subsection{Maximum Likelihood Estimation} +\label{sec:mle} Recovering the model parameter $\Theta$ from observed influence cascades is the central question of the present work. Recovering the edges in $E$ from observed @@ -149,7 +150,7 @@ of $m$ terms, each term $i\in\{1,\ldots,m\}$ only depending on $\theta_i$. Since this is equally true for $\|\Theta\|_1$, each column $\theta_i$ of $\Theta$ can be estimated by a separate optimization program: \begin{equation}\label{eq:pre-mle} - \hat{\theta}_i \in \argmax_{\theta} \frac{1}{n}\mathcal{L}_i(\theta_i\,|\,x^1,\ldots,x^n) + \hat{\theta}_i \in \argmax_{\theta} \mathcal{L}_i(\theta_i\,|\,x^1,\ldots,x^n) - \lambda\|\theta_i\|_1 \end{equation} where we denote by ${\cal T}_i$ the time steps at which node $i$ is susceptible and: |