\subsection{Proof for different lemmas}

\subsubsection{Bounded gradient}
\subsubsection{Approximate sparsity proof}
\subsubsection{RE with high probability}

\subsection{Other continuous time processes binned to ours: prop. hazards model}

\subsection{Irrepresentability vs. Restricted Eigenvalue Condition}
In the words and notation of Theorem 9.1 in \cite{vandegeer:2009}:
\begin{lemma}
\label{lemm:irrepresentability_proof}
Let $\phi^2_{\text{compatible}}(L,S) \defeq \min \{ \frac{s
\|f_\beta\|^2_2}{\|\beta_S\|^2_1} \ : \ \beta \in {\cal R}(L, S) \}$, where
$\|f_\beta\|^2_2 \defeq \{ \beta^T \Sigma \beta \}$ and ${\cal R}(L,S) \defeq
\{\beta : \|\beta_{S^c}\|_1 \leq L \|\beta_S\|_1 \neq 0\}$. If
$\nu_{\text{irrepresentable}(S,s)} < 1/L$, then $\phi^2_{\text{compatible}}(L,S)
\geq (1 - L \nu_{\text{irrepresentable}(S,s)})^2 \lambda_{\min}^2$.
\end{lemma}

Since ${\cal R}(3, S) = {\cal C}$, $\|\beta_S\|_1 \geq \|\beta_S\|_2$, and
$\|\beta_S\|_1 \geq \frac{1}{3} \|\beta_{S^c}\|_1$ it is easy to see that
$\|\beta_S\|_1 \geq \frac{1}{4} \|\beta\|_2$ and therefore that: $\gamma_n \geq
\frac{n}{4s}\phi^2_{\text{compatible}}(3,S)$

Consequently, if $\epsilon > \frac{2}{3}$, then
$\nu_{\text{irrepresentable}(S,s)} < 1/3$ and the conditions of
Lemma~\ref{lemm:irrepresentability_proof} hold.



\subsection{Lower bound for restricted eigenvalues (expected hessian) for
different graphs}

\subsection{Better asymptotic w.r.t expected hessian}

\subsection{Confidence intervals?}

\subsection{Active learning}