Graphs have been extensively studied for their propagative abilities:
connectivity, routing, gossip algorithms, etc.  A diffusion process taking
place over a graph provides valuable information about the presence and weights
of its edges. \emph{Cascades} are a specific type of diffusion processes in
which a particular infectious behavior spreads over the nodes of the graph.  By
only observing the ``infection times'' of the nodes in the graph, one might
hope to recover the underlying graph and the parameters of the cascade model.
This problem is known in the literature as the \emph{Network Inference problem}.

\begin{itemize}
    \item graph inference: what is the proble? what is an observation,
        contagion model
    \item prior work: sample complexity with MLE
    \item here: bayesian approach
        \begin{itemize}
            \item natural framework for active learning wwith significant
                speedup over passive
        \end{itemize}
\end{itemize}

\input{sections/related.tex}