我正在阅读统计学习元素ESLII ，在第2章中，他们有一个高斯混合数据集来说明一些学习算法。 为了生成该数据集，它们首先从双变量高斯分布N（（1,0）'，I）生成10个均值。 我不确定他们是什么意思？
如何从具有均值（1,0）的双变量分布中生成10个均值？
I am reading Elements of Statistical Learning ESLII and in chapter 2, they have a gaussian mixture data set to illustrate some learning algorithms. To generate this data set, they first generate 10 means from a bivariate gaussian distribution N((1,0)', I). I am not sure what they mean?
How can you generate 10 means from a bivariate distribution having mean(1,0)?
最满意答案
从双变量高斯分布生成的每个均值是简单的单点，其采样方式与可从分布生成的任何其他随机点完全相同。 他们使用这些生成的点作为新分布的手段的事实是无关紧要的。
假设这10个均值中的每一个都用于构造一个新的双变量高斯。
表示~N（（1,0），I）
其中〜表示从分布中提取的值。 由于在这种情况下从中采样的分布是双变量高斯，所以采样的每个数据点将是二维点（x1，y1）。
然后，可以使用从原始分布中采样的这些点中的每一个来进行新的分布。
例：
means = [ (x1,y1), (x2,y2), ..., (x10,y10) ]建立新的双变量高斯：
N1((x1,x2), I), N2((x2,y2), I), ..., N10((x10,y10), I)他们只是使用初始的双变量高斯分布N（（1,0），I）作为一种简单的方法来挑选10个正态分布的随机方法。
Each of the means that are generated from the bivariate Gaussian distribution are simply single points sampled in exactly the same way as any other random points that could be generated from the distribution. The fact that they use these generated points to be the means of new distributions is irrelevant.
Let's say that each of the 10 means is then used to construct a new bivariate Gaussian.
means ~ N( (1,0), I)
Where ~ indicates a value being drawn from the distribution. Since the distribution being sampled from in this case is a bivariate Gaussian, each of the data points sampled will be a 2-dimensional point (x1, y1).
Each of these points sampled from the original distribution can then be used to make a new distribution.
Example:
means = [ (x1,y1), (x2,y2), ..., (x10,y10) ]To build new bivariate Gaussians:
N1((x1,x2), I), N2((x2,y2), I), ..., N10((x10,y10), I)They are just using the initial bivariate Gaussian distribution N((1,0), I) as an easy way to pick 10 random means that are distributed normally.
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