How to sample from a dataset using a normal distribution as a sampling scheme?

Hi,

Suppose we have a dataset of images of size n, and I would like to sample from this dataset using a normal distribution with known mean and variance, How this could be achieved?

Thank you.

Answer 1

[Walter Roberson]

You cannot. A normal distribution is inherently a continuous distribution with infinite tails in both directions. You are trying to sample from a finite population. Regardless if you are trying to sample from the pool of (all pixels in all images) or the pool of (all images) or something in-between such as "randomly selected 227 x 227 patches from randonly selected images", that is sampling from a finite discrete population not an infinite continuous population.

You could, of course, round() the randn() and min() and max() to truncate it to the integer bounds, but the result will not be a normal distribution.

You may wish to consider something like https://en.wikipedia.org/wiki/Beta-binomial_distribution which is designed for sampling from a finite population in ways influenced by Beta distribution.

[Akram Awad]

Thanks for your reply!!

But I have read in a paper in which they were trying to sample from a training data and used a normal distribution as a sampling scheme. I am referring to section 4.2.2 of Huang et al (2006), read line 6-10. I am not sure what they are referring to by "as a sampling scheme".

Huang, Jiayuan, et al. "Correcting sample selection bias by unlabeled data." Advances in neural information processing systems 19 (2006).