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Diffstat (limited to 'paper/sections/results.tex')
| -rw-r--r-- | paper/sections/results.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/paper/sections/results.tex b/paper/sections/results.tex index 6b9fd7a..af0b076 100644 --- a/paper/sections/results.tex +++ b/paper/sections/results.tex @@ -30,7 +30,7 @@ by~\cite{bickel2009simultaneous}. \begin{definition} Let $\Sigma\in\mathcal{S}_m(\reals)$ be a real symmetric matrix and $S$ be a subset of $\{1,\ldots,m\}$. Defining $\mathcal{C}(S)\defeq - \{X\in\reals^m\,:\,\|X\|_1\leq 1\text{ and } \|X_{S^c}\|_1\leq + \{X\in\reals^m\,:\,\|X_{S^c}\|_1\leq 3\|X_S\|_1\}$. We say that $\Sigma$ satisfies the $(S,\gamma)$-\emph{restricted eigenvalue condition} iff: \begin{equation} @@ -268,7 +268,7 @@ cascade, which are independent, we can apply Theorem 1.8 from s\log m)$. If $f$ and $(1-f)$ are strictly log-convex, then the previous observations show -that the quantity $\E[\nabla2\mathcal{L}(\theta^*)]$ in +that the quantity $\E[\nabla^2\mathcal{L}(\theta^*)]$ in Proposition~\ref{prop:fi} can be replaced by the expected \emph{Gram matrix}: $A \equiv \mathbb{E}[X^T X]$. This matrix $A$ has a natural interpretation: the entry $a_{i,j}$ is the probability that node $i$ and node $j$ are infected at |