From ed1f54061ce8cda0aa20adbad2c470758a91fa13 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Fri, 11 Dec 2015 18:01:28 -0500
Subject: experiments small updates, going for dinner:

---
 finale/sections/experiments.tex | 23 +++++++++++++++++++++--
 1 file changed, 21 insertions(+), 2 deletions(-)

diff --git a/finale/sections/experiments.tex b/finale/sections/experiments.tex
index 169554f..8e5a9eb 100644
--- a/finale/sections/experiments.tex
+++ b/finale/sections/experiments.tex
@@ -23,9 +23,28 @@ one for the susceptible nodes, the variational inference objective can be
 written as a sum of two matrix multiplications, which Theano optimizes for
 on GPU.
 
-baseline
+Since intuitively if nodes are exchangeable in our graph, the active learning
+policy will have little impact over the uniform-source policy, we decided to
+test our algorithms on an unbalanced graph $\mathcal{G}_A$ whose adjacency
+matrix $A$ is as follows:
+\begin{equation*}
+A = \left( \begin{array}{cccccc}
+0 & 1 & 1 & 1 & \dots & 1 \\
+0 & 0 & 1 & 0 & \dots & 0 \\
+0 & 0 & 0 & 1 & \dots & 0 \\
+\vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\
+0 & 1 & 0 &  0 & \dots & 0
+\end{array}
+\right)
+\end{equation*}
 
-fair comparison of online learning
+In other words, graph $\mathcal{G}_A$ is a star graph where every node, except
+for the center node, points to its (clock-wise) neighbor. In order for the
+baseline to be fair, we choose to create cascades starting from the source node
+on the fly both in the case of the uniform source and for the active learning
+policy. Each cascade is therefore `observed' only once. We plot the RMSE of the
+graph i.e. $RMSE^2 = \frac{1}{n^2} \|\hat \mathbf{\Theta} -
+\mathbf{\Theta}\|^2_2$.
 
 graphs/datasets
 
-- 
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