blairzheng commited on
Commit
e6088ac
1 Parent(s): d365954

add log in equation 6.4; change order of condition variable in figure 1(a)

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Files changed (4) hide show
  1. RenderMarkdownEn.py +1 -1
  2. RenderMarkdownZh.py +1 -1
  3. data.json +0 -0
  4. fig1.png +0 -0
RenderMarkdownEn.py CHANGED
@@ -235,7 +235,7 @@ def md_fit_posterior_en():
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  KL divergence can also be optimized as the objective function. KL divergence and cross-entropy are equivalent[\\[10\\]](#ce_kl)
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  <span id="en_fit_0">
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  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
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- &= \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
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  &= -\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}
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  </span>
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  KL divergence can also be optimized as the objective function. KL divergence and cross-entropy are equivalent[\\[10\\]](#ce_kl)
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  <span id="en_fit_0">
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  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
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+ &= \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
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  &= -\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}
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  </span>
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RenderMarkdownZh.py CHANGED
@@ -227,7 +227,7 @@ def md_fit_posterior_zh():
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  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)。
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  <span id="zh_fit_0">
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  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
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- &= \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
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  &= -\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}
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  </span>
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  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)。
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  <span id="zh_fit_0">
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  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
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+ &= \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
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  &= -\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}
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  </span>
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data.json CHANGED
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fig1.png CHANGED