From 0ff14f56819acfc7be77f9237e18417d465b2266 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 6 Feb 2015 15:48:24 -0500
Subject: Compression

---
 paper/sections/experiments.tex | 13 +++++++++++--
 1 file changed, 11 insertions(+), 2 deletions(-)

(limited to 'paper/sections/experiments.tex')

diff --git a/paper/sections/experiments.tex b/paper/sections/experiments.tex
index 1b72753..2369b11 100644
--- a/paper/sections/experiments.tex
+++ b/paper/sections/experiments.tex
@@ -45,10 +45,19 @@ We did not benchmark against other known algorithms (\textsc{netrate} \cite{gome
 In the case of the \textsc{lasso}, \textsc{mle} and \textsc{sparse mle} algorithms, we construct the edges of $\hat {\cal G} : \cup_{j \in V} \{i : \Theta_{ij} > 0.1\}$, \emph{i.e} by thresholding. The true positives are the edges which appear both in ${\cal G}$ and $\hat {\cal G}$ and the true negatives are the edges which appear in neither. Finally, we report the F1-score$=2 \text{precision}\cdot\text{recall}/(\text{precision}+\text{recall})$, which considers the number of true edges recovered by the algorithm over the total number of edges returned by the algorithm (\emph{precision}) with the number of true edges recovered by the algorithm over the total number of edges it should have recovered (\emph{recall}).
 
 Over all experiments, \textsc{sparse mle} achieves higher rates of precision,
-recall, and f1-score. Interestingly, both \textsc{mle} and \textsc{sparse mle} perform exceptionally well on the Watts-Strogatz graph. The recovery rate converges at
+recall, and F1-score. Interestingly, both \textsc{mle} and \textsc{sparse mle} perform exceptionally well on the Watts-Strogatz graph.
+\begin{comment}
+    The recovery rate converges at
 around $5000$ cascades, which is more than $15$ times the number of nodes. By
 contrast, \textsc{sparse mle} achieves a reasonable F$1$-score of $.75$ for roughly $500$ observed cascades. 
+\end{comment}
 
 \paragraph{Quantifying robustness}
 
-The previous experiments only considered graphs with strong edges. To test the algorithms in the approximately sparse case, we add sparse edges to the previous graphs according to a bernoulli variable of parameter $1/3$ for every non-edge, and drawing a weight uniformly from $[0,0.1]$. The results are reported in Figure~\ref{fig:four_figs} (d)-(e) by plotting the convergence of the $\ell2$-norm error, and show that both the \textsc{lasso}, followed by \textsc{sparse mle} are the most robust to noise.
+The previous experiments only considered graphs with strong edges. To test the
+algorithms in the approximately sparse case, we add sparse edges to the
+previous graphs according to a bernoulli variable of parameter $1/3$ for every
+non-edge, and drawing a weight uniformly from $[0,0.1]$. The non-sparse case is
+compared to the sparse case in Figure~\ref{fig:four_figs} (d)--(e) for the $\ell_2$
+norm showing that both the \textsc{lasso}, followed by \textsc{sparse mle} are
+the most robust to noise. 
-- 
cgit v1.2.3-70-g09d2

