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authorThibaut Horel <thibaut.horel@gmail.com>2015-02-01 20:09:55 -0500
committerThibaut Horel <thibaut.horel@gmail.com>2015-02-01 20:09:55 -0500
commit9cb8844a3c976258d88fab72a8f65ec415526530 (patch)
treed477750ed32ae9672de0ad72b46393ef6b2e4235
parenta4397760f744840005fd66dc87395493c521376b (diff)
downloadcascades-9cb8844a3c976258d88fab72a8f65ec415526530.tar.gz
Intro: add TODO
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@@ -72,6 +72,8 @@ function. Their work has the merit of studying a general framework of
continuous functions. Similarly to \cite{Abrahao:13}, they place themselves in
the restrictive single-source context.
+TODO: add related works on lower bounds.
+
\begin{comment}
\paragraph{Our contributions}
Though our work follows closely the spirit of \cite{Netrapalli:2012} and \cite{Daneshmand:2014}, we believe we provide several significant improvements to their work. We study sparse recovery under less restrictive assumptions and obtain the first ${\cal O}(\Delta \log m)$ algorithm for graph inference from cascades. We also study the seemingly overlooked problem of weight recovery as well as the setting of the relaxed sparsity setting. Finally, we show these results are almost tight, by proving in section~\ref{sec:lowerbound} the first lower bound on the number of observations required to recover the edges and the edge weights of a graph in the general case. We study the case of the two best known diffusion processes for simplicity as outlined in \cite{Kempe:03}, but many arguments can be extended to more general diffusion processes.