fixed typos

4 files changed, 5 insertions, 5 deletions

diff --git a/paper/sections/appendix.tex b/paper/sections/appendix.tex
index 22b87c2..a72114d 100644
--- a/paper/sections/appendix.tex
+++ b/paper/sections/appendix.tex
@@ -159,7 +159,7 @@ convex optimization, the MLE algorithm is faster. This is due to the overhead
 caused by the $\ell_1$-regularisation in~\eqref{eq:pre-mle}.
 
 The dependency of the running time on the number of cascades increases is
-linear, as expected. The slope is largest for our algorithm, which is against
+linear, as expected. The slope is largest for our algorithm, which is again
 caused by the overhead induced by the $\ell_1$-regularization.
 
 
diff --git a/paper/sections/intro.tex b/paper/sections/intro.tex
index cc29ed7..206fbf6 100644
--- a/paper/sections/intro.tex
+++ b/paper/sections/intro.tex
@@ -62,7 +62,7 @@ required number of observed cascades is $\O(poly(s)\log m)$
 \cite{Netrapalli:2012, Abrahao:13}.
 
 A more recent line of research~\cite{Daneshmand:2014} has focused on applying
-advances in sparse recovery to the graph inference problem. Indeed, the graph
+advances in sparse recovery to the network inference problem. Indeed, the graph
 can be interpreted as a ``sparse signal'' measured through influence cascades
 and then recovered.  The challenge is that influence cascade models typically
 lead to non-linear inverse problems and the measurements (the state of the
diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index ecf5ad6..ec2da8b 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -253,7 +253,7 @@ problem:
     \hat{\Theta} \in \argmax_{\Theta} \frac{1}{n}
     \mathcal{L}(\Theta\,|\,x^1,\ldots,x^n) - \lambda\|\Theta\|_1
 \end{displaymath}
-where $\lambda$ is the regularization factor which helps preventing
+where $\lambda$ is the regularization factor which helps prevent
 overfitting and controls the sparsity of the solution.
 
 The generalized linear cascade model is decomposable in the following sense:
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