Skip to content

Commit de0b799

Browse files
authored
p instead of q (ermongroup#197)
I think it should be "support of p" because we estimate p by q.
1 parent dfc7456 commit de0b799

File tree

1 file changed

+2
-2
lines changed

1 file changed

+2
-2
lines changed

inference/variational/index.md

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -93,9 +93,9 @@ $$
9393
KL(q\|p) = \sum_x q(x) \log \frac{q(x)}{p(x)}.
9494
$$
9595

96-
This means that if $$p(x) = 0$$ we must have $$q(x) = 0$$. We say that $$KL(q\|p)$$ is zero-forcing for $$q$$ and it will typically under-estimate the support of $$q$$.
96+
This means that if $$p(x) = 0$$ we must have $$q(x) = 0$$. We say that $$KL(q\|p)$$ is zero-forcing for $$q$$ and it will typically under-estimate the support of $$p$$.
9797

98-
On the other hand, $$KL(p\|q)$$ --- known as the M-projection or the moment projection --- is infinite if $$q(x) = 0$$ and $$p(x) > 0$$. Thus, if $$p(x) > 0$$ we must have $$q(x) > 0$$. We say that $$KL(p\|q)$$ is zero-avoiding for $$q$$ and it will typically over-estimate the support of $$q$$.
98+
On the other hand, $$KL(p\|q)$$ --- known as the M-projection or the moment projection --- is infinite if $$q(x) = 0$$ and $$p(x) > 0$$. Thus, if $$p(x) > 0$$ we must have $$q(x) > 0$$. We say that $$KL(p\|q)$$ is zero-avoiding for $$q$$ and it will typically over-estimate the support of $$p$$.
9999

100100
The figure below illustrates this phenomenon graphically.
101101

0 commit comments

Comments
 (0)