tex

15.md

@@ -364,7 +364,7 @@ array([ 0.59610766, -0.19065363])
 
 我们如何实现呢？ 在二维空间中，这非常简单。 如果我们在坐标`(x0, y0)`处有一个点，而在`(x1, y1)`处有另一个点，则它们之间的距离是：
 
-![](http://latex.codecogs.com/gif.latex?D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%7D)
+![](https://www.zhihu.com/equation?tex=D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%7D)
 
 （这是从哪里来的？它来自勾股定理：我们有一个直角三角形，边长为`x0 - x1`和`y0 - y1`，我们想要求出斜边的长度。）
 
@@ -607,11 +607,11 @@ ax.scatter(banknotes.column('WaveletSkew'),
 
 我们知道如何在二维空间中计算距离。 如果我们在坐标`(x0, y0)`处有一个点，而在`(x1, y1)`处有另一个点，则它们之间的距离是：
 
-![](http://latex.codecogs.com/gif.latex?D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%7D)
+![](https://www.zhihu.com/equation?tex=D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%7D)
 
 在三维空间中，点是`(x0, y0, z0)`和`(x1, y1, z1)`，它们之间的距离公式为：
 
-![](http://latex.codecogs.com/gif.latex?D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%20+%20%28z_0-z_1%29%5E2%7D)
+![](https://www.zhihu.com/equation?tex=D%20%3D%20%5Csqrt%7B%28x_0-x_1%29%5E2%20+%20%28y_0-y_1%29%5E2%20+%20%28z_0-z_1%29%5E2%7D)
 
 在 N 维空间中，东西有点难以可视化，但我想你可以看到公式是如何推广的：我们总结每个独立坐标差的平方，然后取平方根。
 

17.md

@@ -129,13 +129,13 @@ students.pivot('Major', 'Year')
 
 后验概率。这些是考虑专业声明状态的信息后，二年级的概率。我们计算了其中的一个：
 
-假设学生已经声明，学生是三年级的后验概率表示为 ![](http://latex.codecogs.com/gif.latex?P%28%5Cmbox%7BThird%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29)，计算如下。
+假设学生已经声明，学生是三年级的后验概率表示为 ![](https://www.zhihu.com/equation?tex=P%28%5Cmbox%7BThird%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29)，计算如下。
 
-![](http://latex.codecogs.com/gif.latex?%5Cbegin%7Balign*%7D%20P%28%5Cmbox%7BThird%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29%20%7E%20%26%3D%7E%20%5Cfrac%7B%200.4%20%5Ctimes%200.8%7D%7B0.6%20%5Ctimes%200.5%20%7E+%7E%200.4%20%5Ctimes%200.8%7D%20%5C%5C%20%5C%5C%20%26%3D%7E%20%5Cfrac%7B%5Cmbox%7B%28prior%20probability%20of%20Third%20Year%29%7D%20%5Ctimes%20%5Cmbox%7B%28likelihood%20of%20Declared%20given%20Third%20Year%29%7D%7D%20%7B%5Cmbox%7Btotal%20probability%20of%20Declared%7D%7D%20%5Cend%7Balign*%7D)
+![](https://www.zhihu.com/equation?tex=%5Cbegin%7Balign*%7D%20P%28%5Cmbox%7BThird%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29%20%7E%20%26%3D%7E%20%5Cfrac%7B%200.4%20%5Ctimes%200.8%7D%7B0.6%20%5Ctimes%200.5%20%7E+%7E%200.4%20%5Ctimes%200.8%7D%20%5C%5C%20%5C%5C%20%26%3D%7E%20%5Cfrac%7B%5Cmbox%7B%28prior%20probability%20of%20Third%20Year%29%7D%20%5Ctimes%20%5Cmbox%7B%28likelihood%20of%20Declared%20given%20Third%20Year%29%7D%7D%20%7B%5Cmbox%7Btotal%20probability%20of%20Declared%7D%7D%20%5Cend%7Balign*%7D)
 
 另一个后验概率是：
 
-![](http://latex.codecogs.com/gif.latex?%5Cbegin%7Balign*%7D%20P%28%5Cmbox%7BSecond%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29%20%7E%20%26%3D%7E%20%5Cfrac%7B%200.6%20%5Ctimes%200.5%7D%7B0.6%20%5Ctimes%200.5%20%7E+%7E%200.4%20%5Ctimes%200.8%7D%20%5C%5C%20%5C%5C%20%26%3D%7E%20%5Cfrac%7B%5Cmbox%7B%28prior%20probability%20of%20Second%20Year%29%7D%20%5Ctimes%20%5Cmbox%7B%28likelihood%20of%20Declared%20given%20Second%20Year%29%7D%7D%20%7B%5Cmbox%7Btotal%20probability%20of%20Declared%7D%7D%20%5Cend%7Balign*%7D)
+![](https://www.zhihu.com/equation?tex=%5Cbegin%7Balign*%7D%20P%28%5Cmbox%7BSecond%20Year%7D%20%7E%5Cbig%7B%7C%7D%7E%20%5Cmbox%7BDeclared%7D%29%20%7E%20%26%3D%7E%20%5Cfrac%7B%200.6%20%5Ctimes%200.5%7D%7B0.6%20%5Ctimes%200.5%20%7E+%7E%200.4%20%5Ctimes%200.8%7D%20%5C%5C%20%5C%5C%20%26%3D%7E%20%5Cfrac%7B%5Cmbox%7B%28prior%20probability%20of%20Second%20Year%29%7D%20%5Ctimes%20%5Cmbox%7B%28likelihood%20of%20Declared%20given%20Second%20Year%29%7D%7D%20%7B%5Cmbox%7Btotal%20probability%20of%20Declared%7D%7D%20%5Cend%7Balign*%7D)
 
 ```py
 (0.6 * 0.5)/(0.6 * 0.5  +  0.4 * 0.8)
@@ -148,7 +148,7 @@ students.pivot('Major', 'Year')
 
 正因为如此，贝叶斯方法有时被归纳为比例陈述：
 
-![](http://latex.codecogs.com/gif.latex?%5Cmbox%7Bposterior%7D%20%7E%20%5Cpropto%20%7E%20%5Cmbox%7Bprior%7D%20%5Ctimes%20%5Cmbox%7Blikelihood%7D)
+![](https://www.zhihu.com/equation?tex=%5Cmbox%7Bposterior%7D%20%7E%20%5Cpropto%20%7E%20%5Cmbox%7Bprior%7D%20%5Ctimes%20%5Cmbox%7Blikelihood%7D)
 
 公式非常便于高效地描述计算。 但是在我们的学生示例这样的情况中，不用公式来思考更简单。 我们仅仅使用树形图。