From d1596ae6e0f0f26b6e60f7a0b9d56faf4463fc4e Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 11 Dec 2015 22:09:05 -0500
Subject: Add discussion

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 finale/sections/discussion.tex | 22 ++++++++++++++++++++++
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+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}
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