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diff --git a/paper/sections/discussion.tex b/paper/sections/discussion.tex index 9d7f491..10aa50b 100644 --- a/paper/sections/discussion.tex +++ b/paper/sections/discussion.tex @@ -1,6 +1,3 @@ - - -\paragraph{Future Work} Solving the Graph Inference problem with sparse recovery techniques opens new venues for future work. Firstly, the sparse recovery literature has already studied regularization patterns beyond the $\ell_1$-norm, notably the @@ -12,16 +9,14 @@ has been obtained for the Lasso in the recent series of papers Finally, the linear threshold model is a commonly studied diffusion process and can also be cast as a \emph{generalized linear cascade} with inverse link function $z \mapsto \mathbbm{1}_{z > 0}$: $ \label{eq:lt} - \tag{LT} X^{t+1}_j = \text{sign} \left(\inprod{\theta_j}{X^t} - t_j \right) - $ - -This model therefore falls into the 1-bit compressed sensing model -\cite{Boufounos:2008} framework. Several recent papers study the theoretical + $. +This model therefore falls into the 1-bit compressed sensing framework +\cite{Boufounos:2008}. Several recent papers study the theoretical guarantees obtained for 1-bit compressed sensing with specific measurements \cite{Gupta:2010, Plan:2014}. Whilst they obtained bounds of the order ${\cal O}(n \log \frac{n}{s}$), no current theory exists for recovering -positive bounded signals from bernoulli hyperplanes. This research direction +positive bounded signals from biniary measurememts. This research direction may provide the first clues to solve the ``adaptive learning'' problem: if we are allowed to adaptively \emph{choose} the source nodes at the beginning of each cascade, how much can we improve the current results? |