Does "MLE: Gaussian example" video have a conceptual mistake?

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
1

Hello, prof. Serrano!

The video “MLE: Gaussian Example” from 5:33 consider the Variance of a Sample formula dividing the sum of squares (x-mu) by n, which according to the week 2 video “Sample Variance” we must divide by “n-1”.

So, the conclusions of the best distribution are the same, but they “whys” change a little bit and I think it forces rebuild the video, maybe…

I also noticed that the video at that same part (from 5:33) talks about Variance, but shows the Standard Deviation formula. And the following part just repeats everything saying “Std Dev.” but showing “Variance” on the screen. It is doubled and with many flaws.

2

Hi @Joao_Carlos_Lima_Sel!

Thanks again for your careful look into the lectures!

Regarding the division by n-1, it is a bit tricky here. The point is, if you want an unbiased estimation for the variance, then you should indeed divide it by n-1. However, Luis is trying to motivate the Maximum Likelihood Estimator for the variance, which is a biased estimator! This is why it is being divided by n. Note that there is no right or wrong answer when dealing with estimatiors. Every estimator has advantages and disadvantages, the point is to know them!

Regarding the Variance, it is indeed a mistake and I have informed our team to fix it.

Thanks,
Lucas

1 Like
3

Hey @lucas.coutinho,
Please ask the team to add a reading item or some pop up in the lecture video, indicating that the MLE is a biased estimator with appropriate context, and the fact that it uses n to calculate the variance, instead of n-1, unlike the sample variance formula told to us in Week 2, otherwise, it can get easily confusing as you pointed out for a lot of learners.

Cheers,
Elemento

4

Thanks @Elemento!

I have forwarded it to our team, probably an IVQ will suffice for a while but it is not the best option. We are considering recording again the MLE example for the variance to explain this further, so the learners don’t get confused.

Thanks,
Lucas

5

Hey Lucas,
Sounds great. Looking forward to the updated lecture video.

Cheers,
Elemento

6

Hi guys,

I have added the IVQ by now, once the team finishes with the re-recording I will let you guys know.

Thanks,
Lucas