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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 ef205f4..0c1cc3b 100644 --- a/paper/sections/results.tex +++ b/paper/sections/results.tex @@ -304,7 +304,7 @@ too collinear with each other. In the specific case of ``logistic cascades'' (where $f$ 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 $[x^1 \ldots -x^\mathca{|T|}]$. The restricted eigenvalue condition is equivalent in this +x^\mathcal{|T|}]$. The restricted eigenvalue condition is equivalent in this case to the assumption made in the Lasso analysis of \cite{bickel:2009}. \paragraph{(RE) with high probability} @@ -326,7 +326,7 @@ eigenvalue property, then the finite sample hessian also verifies the restricted eigenvalue property with overwhelming probability. It is straightforward to show this holds when $n \geq C s^2 \log m$ \cite{vandegeer:2009}, where $C$ is an absolute constant. By adapting Theorem -8 \cite{rudelson:13}}, this +8 \cite{rudelson:13}, this can be reduced to: \begin{displaymath} n \geq C s \log m \log^3 \left( \frac{s \log m}{C'} \right) |