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| author | Thibaut Horel <thibaut.horel@gmail.com> | 2015-02-01 20:09:55 -0500 |
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| committer | Thibaut Horel <thibaut.horel@gmail.com> | 2015-02-01 20:09:55 -0500 |
| commit | 9cb8844a3c976258d88fab72a8f65ec415526530 (patch) | |
| tree | d477750ed32ae9672de0ad72b46393ef6b2e4235 | |
| parent | a4397760f744840005fd66dc87395493c521376b (diff) | |
| download | cascades-9cb8844a3c976258d88fab72a8f65ec415526530.tar.gz | |
Intro: add TODO
| -rw-r--r-- | paper/sections/intro.tex | 2 |
1 files changed, 2 insertions, 0 deletions
diff --git a/paper/sections/intro.tex b/paper/sections/intro.tex index 695c084..0f42855 100644 --- a/paper/sections/intro.tex +++ b/paper/sections/intro.tex @@ -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. |
