逻辑回归的向量化实现样例

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【原文】:
【原文】:
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where (following the notational convention from the OpenClassroom videos and from CS229) we let <math>x_{0}=1</math> , so that <math>x\in R^{n+1}</math> and  <math>\theta \in R^{n+1}</math>, and <math>\theta _{0}</math> is our intercept term. We have a training set{(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) } of m examples, and the batch gradient ascent update rule is <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> , where <math>l\left( \theta \right) </math>  is the log likelihood and  <math>\nabla _{\theta }l\left( \theta \right) </math> is its derivative.
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where (following the notational convention from the OpenClassroom videos and from CS229) we let <math>\textstyle x_0=1</math>, so that <math>x\in R^{n+1}</math> and  <math>\theta \in R^{n+1}</math>, and <math>\textstyle \theta_0</math> is our intercept term. We have a training set{(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) } of m examples, and the batch gradient ascent update rule is <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> , where <math>l\left( \theta \right) </math>  is the log likelihood and  <math>\nabla _{\theta }l\left( \theta \right) </math> is its derivative.
【初译】:
【初译】:
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设 <math>x_{0}=1</math>(符号规范遵从公开课程视频与CS229教学讲义),于是 <math>x\in R^{n+1}</math> , <math>\theta \in R^{n+1}</math>, <math>\theta _{0}</math>为截距。现在,我们有m组样本数据集 {(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) },而批量梯度上升法的规则是: <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> ,这里的<math>l\left( \theta \right) </math> 是对数似然函数,<math>\nabla _{\theta }l\left( \theta \right) </math> 它的导函数。
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设 <math>\textstyle x_0=1</math>(符号规范遵从公开课程视频与CS229教学讲义),于是 <math>x\in R^{n+1}</math> , <math>\theta \in R^{n+1}</math>, <math>\textstyle \theta_0</math>为截距。现在,我们有m组样本数据集 {(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) },而批量梯度上升法的规则是: <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> ,这里的<math>l\left( \theta \right) </math> 是对数似然函数,<math>\nabla _{\theta }l\left( \theta \right) </math> 它的导函数。
【一校】:
【一校】:
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设 <math>x_{0}=1</math> (符号规范遵从公开课程视频与CS229教学讲义),于是<math>x\in R^{n+1}</math> ,<math>\theta \in R^{n+1}</math>, <math>\theta _{0} </math> 为截距。我们有m个训练样本{(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) },而批量梯度上升法的更新法则是: <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> ,这里的 <math>l\left( \theta \right) </math> 是对数似然函数,<math>\nabla _{\theta }l\left( \theta \right) </math> 是其导函数。
+
设 <math>\textstyle x_0=1</math>(符号规范遵从公开课程视频与CS229教学讲义),于是<math>x\in R^{n+1}</math> ,<math>\theta \in R^{n+1}</math>, <math>\textstyle \theta_0</math> 为截距。我们有m个训练样本{(<math>x^\left( 1\right) </math>,<math>y^\left( 1\right)</math> ) ,...,(<math>x^\left( m\right)</math> ,<math>y^\left( m\right)</math> ) },而批量梯度上升法的更新法则是: <math>\theta :=\theta +\alpha \nabla _{\theta }l\left( \theta \right) </math> ,这里的 <math>l\left( \theta \right) </math> 是对数似然函数,<math>\nabla _{\theta }l\left( \theta \right) </math> 是其导函数。
【原文】:
【原文】:

Revision as of 05:17, 8 March 2013

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