diff --git a/15.md b/15.md index bc380576cc19db43b494412000971e6229812004..940a5c0ec36a935a5bb746b4427e3a68f3caeca0 100644 --- a/15.md +++ b/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。 diff --git a/17.md b/17.md index 4c1de680ab13b156542082ee972b0c3e31041a96..5151a6c96a96b7f8c1082581625cb779a03af2f1 100644 --- a/17.md +++ b/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。