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authorYuchen Pei <me@ypei.me>2019-02-18 10:57:31 +0100
committerYuchen Pei <me@ypei.me>2019-02-18 10:57:31 +0100
commit132a8c8858dbf635f2b0060e41a61add55c89387 (patch)
treedace592d57d5376bd7de87cf774fff8f23aeba7e
parentcf3a03b0e4ecd7c5f0ba92693be732b676061642 (diff)
minor change
-rw-r--r--posts/2019-02-14-raise-your-elbo.md6
1 files changed, 3 insertions, 3 deletions
diff --git a/posts/2019-02-14-raise-your-elbo.md b/posts/2019-02-14-raise-your-elbo.md
index 5700899..5249445 100644
--- a/posts/2019-02-14-raise-your-elbo.md
+++ b/posts/2019-02-14-raise-your-elbo.md
@@ -272,8 +272,8 @@ ocurrance of word $x$ in document $d$.
For each datapoint $(d_{i}, x_{i})$,
$$\begin{aligned}
-p(d_i, x_i; \theta) &= \sum_{z_i} p(z; \theta) p(d_i | z_i; \theta) p(x_i | z_i; \theta) \qquad (2.91)\\
-&= p(d_i; \theta) \sum_{z_i} p(x_i | z_i; \theta) p (z_i | d_i; \theta) \qquad (2.92).
+p(d_i, x_i; \theta) &= \sum_z p(z; \theta) p(d_i | z; \theta) p(x_i | z; \theta) \qquad (2.91)\\
+&= p(d_i; \theta) \sum_z p(x_i | z; \theta) p (z | d_i; \theta) \qquad (2.92).
\end{aligned}$$
Of the two formulations, (2.91) corresponds to pLSA type 1, and (2.92)
@@ -285,7 +285,7 @@ The pLSA1 model (Hoffman 2000) is basically SMM with $x_i$ substituted
with $(d_i, x_i)$, which conditioned on $z$ are independently
categorically distributed:
-$$p(d_i = u, x_i = w | z_i = k) = p(d_i | \xi_k) p(x_i; \eta_k) = \xi_{ku} \eta_{kw}.$$
+$$p(d_i = u, x_i = w | z = k) = p(d_i | \xi_k) p(x_i; \eta_k) = \xi_{ku} \eta_{kw}.$$
The model can be illustrated in the plate notations: