从二元高斯分布产生均值 [英] Generating means from a bivariate gaussian distribution

问题描述

我正在阅读 ESLII 的统计学习内容，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.为了生成此数据集，他们首先从二元高斯分布N((1,0)'，I)中生成10个均值.我不确定它们是什么意思?

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?

如何从均值(1,0)的双变量分布中生成10个均值?

How can you generate 10 means from a bivariate distribution having mean(1,0)?

推荐答案

从二元高斯分布生成的均值中的每一个均是单点采样，其采样方式与可从均方根生成的任何其他随机点完全相同.分配.他们使用这些生成的点作为新分布的手段这一事实是无关紧要的.

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.

假设10个均值中的每一个均用于构造新的二元高斯变量.

Let's say that each of the 10 means is then used to construct a new bivariate Gaussian.

意味着〜N((1,0)，I)

means ~ 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二元高斯分布，因此采样的每个数据点都是二维点(x1，y1).

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).

从原始分布中采样的每个点都可以用于创建新分布.

Each of these points sampled from the original distribution can then be used to make a new distribution.

示例:

means = [ (x1,y1), (x2,y2), ..., (x10,y10) ]

要建立新的二元高斯变量:

To build new bivariate Gaussians:

N1((x1,x2), I), N2((x2,y2), I), ..., N10((x10,y10), I)

他们只是使用初始二元高斯分布N((1,0)，I)作为选择10个正态分布的随机均值的简便方法.

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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