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Diffstat (limited to 'paper')
| -rw-r--r-- | paper/sections/intro.tex | 1 | ||||
| -rw-r--r-- | paper/sections/results.tex | 7 |
2 files changed, 4 insertions, 4 deletions
diff --git a/paper/sections/intro.tex b/paper/sections/intro.tex index 4c18faf..c89c641 100644 --- a/paper/sections/intro.tex +++ b/paper/sections/intro.tex @@ -72,7 +72,6 @@ be sufficient to recover the graph~\cite{donoho2006compressed, candes2006near}. However, the best known upper bound to this day is $\O(s^2\log m)$~\cite{Netrapalli:2012, Daneshmand:2014} - The contributions of this paper are the following: \begin{itemize} \item we formulate the Graph Inference problem in the context of diff --git a/paper/sections/results.tex b/paper/sections/results.tex index 7eb3973..7fca661 100644 --- a/paper/sections/results.tex +++ b/paper/sections/results.tex @@ -43,8 +43,9 @@ by~\cite{bickel2009simultaneous}. A discussion of the $(S,\gamma)$-{\bf(RE)} assumption in the context of generalized linear cascade models can be found in Section~\ref{sec:re}. In our setting we require that the {\bf(RE)}-condition holds for the Hessian of the -log-likelihood function $\mathcal{L}$: it essentially captures the fact that the -binary vectors of the set of active nodes are not \emph{too} collinear. +log-likelihood function $\mathcal{L}$: it essentially captures the fact that +the binary vectors of the set of active nodes (\emph{i.e} the measurement) are +not \emph{too} collinear. {\color{red} Rewrite the minimal assumptions necessary} We will also need the following assumption on the inverse link function $f$ of @@ -318,7 +319,7 @@ again non restrictive in the (IC) model and (V) model. Observe that the number of measurements required in Proposition~\ref{prop:fi} is now quadratic in $s$. If we only keep the first measurement from each -cascade which are independent, we can apply Theorem 1.8 from +cascade, which are independent, we can apply Theorem 1.8 from \cite{rudelson:13}, lowering the number of required cascades to $s\log m \log^3( s\log m)$. |