Bessel’s Correction
Saw this in an #ee16b note relating to PCA calculation: https://www.eecs16b.org/discussion/dis4C.pdf
Following this math makes the most sense to me — if you follow it carefully, it actually works out, and the rest you can rely on intuition about one less degree of freedom, and the actual sample variance always being slightly higher than the population variance (and needing to correct for that).
image-20200715123142978
Where we have that $_Y^2$ is just the normal formula for variance (squared distance from the mean for each point). This is saying that using the normal formula for variance on a sample is going to underestimate the variance, so we have to correct it by $$.
uid: 202007151213 tags: #ML