Spaces:
Running
Running
blairzheng
commited on
Commit
•
e6088ac
1
Parent(s):
d365954
add log in equation 6.4; change order of condition variable in figure 1(a)
Browse files- RenderMarkdownEn.py +1 -1
- RenderMarkdownZh.py +1 -1
- data.json +0 -0
- fig1.png +0 -0
RenderMarkdownEn.py
CHANGED
@@ -235,7 +235,7 @@ def md_fit_posterior_en():
|
|
235 |
KL divergence can also be optimized as the objective function. KL divergence and cross-entropy are equivalent[\\[10\\]](#ce_kl)
|
236 |
<span id="en_fit_0">
|
237 |
loss &= \int q(z_t) KL(q(z_{t-1}|z_t) \Vert \textcolor{blue}{p(z_{t-1}|z_t)})dz_t \tag{6.3} \newline
|
238 |
-
&= \int q(z_t) \int q(z_{t-1}|z_t) \frac{q(z_{t-1}|z_t)}{\textcolor{blue}{p(z_{t-1}|z_t)}} dz_{t-1} dz_t \tag{6.4} \newline
|
239 |
&= -\int q(z_t)\ \underbrace{\int q(z_{t-1}|z_t) \log \textcolor{blue}{p(z_{t-1}|z_t)}dz_{t-1}}{underline}{\text{Cross Entropy}}\ dz_t + \underbrace{\int q(z_t) \int q(z_{t-1}|z_t) \log q(z_{t-1}|z_t)}{underline}{\text{Is Constant}} dz \tag{6.5}
|
240 |
</span>
|
241 |
|
|
|
235 |
KL divergence can also be optimized as the objective function. KL divergence and cross-entropy are equivalent[\\[10\\]](#ce_kl)
|
236 |
<span id="en_fit_0">
|
237 |
loss &= \int q(z_t) KL(q(z_{t-1}|z_t) \Vert \textcolor{blue}{p(z_{t-1}|z_t)})dz_t \tag{6.3} \newline
|
238 |
+
&= \int q(z_t) \int q(z_{t-1}|z_t) \log \frac{q(z_{t-1}|z_t)}{\textcolor{blue}{p(z_{t-1}|z_t)}} dz_{t-1} dz_t \tag{6.4} \newline
|
239 |
&= -\int q(z_t)\ \underbrace{\int q(z_{t-1}|z_t) \log \textcolor{blue}{p(z_{t-1}|z_t)}dz_{t-1}}{underline}{\text{Cross Entropy}}\ dz_t + \underbrace{\int q(z_t) \int q(z_{t-1}|z_t) \log q(z_{t-1}|z_t)}{underline}{\text{Is Constant}} dz \tag{6.5}
|
240 |
</span>
|
241 |
|
RenderMarkdownZh.py
CHANGED
@@ -227,7 +227,7 @@ def md_fit_posterior_zh():
|
|
227 |
也可以KL散度作为目标函数进行优化,KL散度与交叉熵是等价的[\[10\]](#ce_kl)。
|
228 |
<span id="zh_fit_0">
|
229 |
loss &= \int q(z_t) KL(q(z_{t-1}|z_t) \Vert \textcolor{blue}{p(z_{t-1}|z_t)})dz_t \tag{6.3} \newline
|
230 |
-
&= \int q(z_t) \int q(z_{t-1}|z_t) \frac{q(z_{t-1}|z_t)}{\textcolor{blue}{p(z_{t-1}|z_t)}} dz_{t-1} dz_t
|
231 |
&= -\int q(z_t)\ \underbrace{\int q(z_{t-1}|z_t) \log \textcolor{blue}{p(z_{t-1}|z_t)}dz_{t-1}}{underline}{\text{Cross Entropy}}\ dz_t + \underbrace{\int q(z_t) \int q(z_{t-1}|z_t) \log q(z_{t-1}|z_t)}{underline}{\text{Is Constant}} dz \tag{6.5}
|
232 |
</span>
|
233 |
|
|
|
227 |
也可以KL散度作为目标函数进行优化,KL散度与交叉熵是等价的[\[10\]](#ce_kl)。
|
228 |
<span id="zh_fit_0">
|
229 |
loss &= \int q(z_t) KL(q(z_{t-1}|z_t) \Vert \textcolor{blue}{p(z_{t-1}|z_t)})dz_t \tag{6.3} \newline
|
230 |
+
&= \int q(z_t) \int q(z_{t-1}|z_t) \log \frac{q(z_{t-1}|z_t)}{\textcolor{blue}{p(z_{t-1}|z_t)}} dz_{t-1} dz_t \tag{6.4} \newline
|
231 |
&= -\int q(z_t)\ \underbrace{\int q(z_{t-1}|z_t) \log \textcolor{blue}{p(z_{t-1}|z_t)}dz_{t-1}}{underline}{\text{Cross Entropy}}\ dz_t + \underbrace{\int q(z_t) \int q(z_{t-1}|z_t) \log q(z_{t-1}|z_t)}{underline}{\text{Is Constant}} dz \tag{6.5}
|
232 |
</span>
|
233 |
|
data.json
CHANGED
The diff for this file is too large to render.
See raw diff
|
|
fig1.png
CHANGED