Compression

1 files changed, 4 insertions, 4 deletions

diff --git a/paper/sections/results.tex b/paper/sections/results.tex
index 25f540a..86f4c32 100644
--- a/paper/sections/results.tex
+++ b/paper/sections/results.tex
@@ -296,16 +296,16 @@ In our case we have:
     \bigg[x_i^{t+1}\frac{f''f-f'^2}{f^2}(\inprod{\theta^*}{x^t})\\
     -(1-x_i^{t+1})\frac{f''(1-f) + f'^2}{(1-f)^2}(\inprod{\theta^*}{x^t})\bigg]
 \end{multline*}
-It is interesting to observe that the Hessian of $\mathcal{L}$ can be seen as
+Observe that the Hessian of $\mathcal{L}$ can be seen as
 a re-weighted Gram matrix of the observations. In other words, the restricted
 eigenvalue condition expresses that the observed set of active nodes are not
 too collinear with each other.
 
-In the specific case of ``logistic cascades'' (where $f$ is the logistic
+In the specific case of ``logistic cascades'' (when $f$ is the logistic
 function), the Hessian simplifies to $\nabla^2\mathcal{L}(\theta^*)
 = \frac{1}{|\mathcal{T}|}XX^T$ where $X$ is the design matrix $[x^1 \ldots
-x^\mathcal{|T|}]$. The restricted eigenvalue condition is equivalent in this
-case to the assumption made in the Lasso analysis of \cite{bickel:2009}.
+x^\mathcal{|T|}]$. The (RE) condition is then equivalent 
+to the assumption made in the Lasso analysis of \cite{bickel:2009}.
 
 \paragraph{(RE) with high probability}