Add discussion

2 files changed, 23 insertions, 0 deletions

diff --git a/finale/final_report.tex b/finale/final_report.tex
index 113a637..f2c7fbb 100644
--- a/finale/final_report.tex
+++ b/finale/final_report.tex
@@ -89,6 +89,7 @@ Diffusion Processes}
 \input{sections/experiments.tex}
 
 \section{Discussion}
+\input{sections/discussion.tex}
 
 \bibliography{sparse}
 \bibliographystyle{icml2015}
diff --git a/finale/sections/discussion.tex b/finale/sections/discussion.tex
new file mode 100644
index 0000000..b04b6dc
--- /dev/null
+++ b/finale/sections/discussion.tex
@@ -0,0 +1,22 @@
+The experimental results obtained in Section 5 look impressive and confirm the
+relevance of using a Bayesian approach for the Network Inference problem.
+However, we believe that many other aspects of Bayesian Inference could and
+should be exploited in the context of Network Inference. We wish to explore
+this in future work and only highlight a few possible directions here:
+\begin{itemize}
+    \item obtain formal guarantees on the convergence of measure of the
+    Bayesian posterior. Similarly to convergence rate results obtained with MLE
+    estimation, we believe that convergence results could also be obtained in
+    the Bayesian setting, at least in restricted settings or by making certain
+    assumptions about the network being learned.
+    \item strengthening the experimental results by systematically studying how
+    different network properties impact the speedup induced by active learning.
+    \item finish formally deriving the update equations when using Bohning
+    approximations for Variational Inference.
+    \item extend the combined Variational Inference and Bohning approximation
+    to Hawkes processes to obtain a unified Bayesian framework for both
+    discrete-time and continuous-time models.
+    \item explore the impact of using more expressive (in particular
+    non-factorized) on the speed of convergence, both in offline and active
+    online learning.
+\end{itemize}