Suggested edit to message passing notation in junction tree notes

inference/jt/index.md

@@ -18,7 +18,7 @@ We will introduce two variants of this algorithm: belief propagation (BP), and t
 
 First, consider what happens if we run the VE algorithm on a tree in order to compute a marginal $$p(x_i)$$. We can easily find an optimal ordering for this problem by rooting the tree at $$x_i$$ and iterating through the nodes in post-order{% include sidenote.html id="note-postorder" note="A postorder traversal of a rooted tree is one that starts from the leaves and goes up the tree such that a node is always visited after all of its children. The root is visited last." %}.
 
-This ordering is optimal because the largest clique formed during VE will have size 2. At each step, we will eliminate $$x_j$$; this will involve computing the factor $$\tau_{jk}(x_k) = \sum_{x_j} \phi(x_k, x_j) \tau_j(x_j)$$, where $$x_k$$ is the parent of $$x_j$$ in the tree. At a later step, $$x_k$$ will be eliminated, and $$\tau_{jk}(x_k)$$ will be passed up the tree to the parent $$x_l$$ of $$x_k$$ in order to be multiplied by the factor $$\phi(x_l, x_k)$$ before being marginalized out. The factor $$\tau_j(x_j)$$ can be thought of as a message that $$x_j$$ sends to $$x_k$$ that summarizes all of the information from the subtree rooted at $$x_j$$. We can visualize this transfer of information using arrows on a tree.
+This ordering is optimal because the largest clique formed during VE will have size 2. At each step, we will eliminate $$x_j$$; this will involve computing the factor $$\tau_{jk}(x_k) = \sum_{x_j} \phi(x_k, x_j) \tau_j(x_j)$$, where $$x_k$$ is the parent of $$x_j$$ in the tree. At a later step, $$x_k$$ will be eliminated, and $$\tau_{jk}(x_k)$$ will be passed up the tree to the parent $$x_l$$ of $$x_k$$ in order to be multiplied by the factor $$\phi(x_l, x_k)$$ before being marginalized out. The factor $$\tau_{jk}(x_k)$$ can be thought of as a message that $$x_j$$ sends to $$x_k$$ that summarizes all of the information from the subtree rooted at $$x_j$$. We can visualize this transfer of information using arrows on a tree.
 {% include marginfigure.html id="mp1" url="assets/img/mp1.png" description="Message passing order when using VE to compute $$p(x_3)$$ on a small tree." %}
 
 At the end of VE, $$x_i$$ receives messages from all of its immediate children, marginalizes them out, and we obtain the final marginal.