Sampling the univariate Normal by Box-Müller Transform | Example in Python

[@abhishekarora4007]

Thank you. This is exactly i was looking for !

[@MachineLearningSimulation]

Glad I could help! You're welcome.

[@johnnyg3007]

Very helpful, thank you!

[@MachineLearningSimulation]

You're welcome :). Thanks for the kind comment!

[@samaradossantos9192]

Thank you so much for this video. Really helped me!

[@MachineLearningSimulation]

You're very welcome :)

[@andywang1950]

Not sure if I'm mistaken or not. In your explanation, the formula is wrong since it's actually suppose to use "ln" rather than "log" For others looking at the math part of the explanation np.log is actually doing ln or Log base e got me confused for a while.

[@MachineLearningSimulation]

Good catch. 👍 Indeed, it has to be "ln" for the correct box-muller transform. CS people tend to always just write log 😅

[@YT-yt-yt-3]

but how does box muller method output normal distribution? i think that's important to understand.

[@adetayoeyelade3912]

Can the Box-Muller model BE USED to make initial guess of a fitting parameters?

[@MachineLearningSimulation]

Hi, thanks for the question. :) Sure, the Box-Mueller transform is a valid way to produce normally distributed samples. If you want to initialize parameters according to a Normal distribution, this is one way to obtain these initial estimates. For example, in neural networks, one often uses a glorot normal initializer (a specially scaled normal distribution): www.tensorflow.org/api_docs/python/tf/keras/initializers/GlorotNormal I am unsure how it is implemented internally in TensorFlow, but a Box-Mueller transform would be my way to obtain these normal samples. Hope that helps :).

[@jakebrowning2373]

Was the splitting up the 1000 uniform values into 2 500 length vectors a necessary step? Or was it just showcasing that both ways create a standard normal?

[@MachineLearningSimulation]

Alternatively, you could have also drawn two vectors of size 500. That would lead to a similar result. Hope that helped, let me know if that was not clear :).

[@lidiatjr]

Thank you!!

[@MachineLearningSimulation]

You're welcome :)

[@palpadhading8245]

What environment is this for ipy , I use google colab it's just not putting two plt.hist(X , bins=100) or plt(Y, bins=100) same time and not seeing two 2 colors

[@MachineLearningSimulation]

Do you want two histograms in one figure? I think that you then have to put the two plot calls into one cell. :) Hope that helps 😊

[@SumriseHD]

Wie kriegt man so einen guten Akzent? :D

[@MachineLearningSimulation]

Übung ist wichtig und natürlich auch der Wille, nicht zu deutsch zu klingen. 😅 Ich habe auch auf Englisch studiert und habe internationale Freunde, dadurch muss ich zwangsläufig viel auf Englisch reden.

[@todianmishtaku6249]

Great!

[@MachineLearningSimulation]

Thanks for checking it out ;)

[@guoqiqi-h2t]

how to extend the box muller from 2 to n dimensions n>2

[@MachineLearningSimulation]

I think this is what you're looking for: kzbin.info/www/bejne/eoS6fmpjbsx-bdU :) In essence: you sample standard uniform normal in each dimension and then link the dimensions with the cholesky factor

[@姐z]

thanks，but i mean Devise a method of generating n iid standard normal random samples (n ≥ 3) when chi-square and uniform random samples are given. (Hint: Extend the Box-Muller method in the lecture note to the n-dimensional case.)

[@姐z]

@@MachineLearningSimulation thanks，but i mean Devise a method of generating n iid standard normal random samples (n ≥ 3) when chi-square and uniform random samples are given. (Hint: Extend the Box-Muller method in the lecture note to the n-dimensional case.)

[@MachineLearningSimulation]

Okay, I think I almost get what you would like to do. I'm afraid, this is beyond my expertise in this field.

[@omarbranquinho8531]

Ver good

[@MachineLearningSimulation]

Nice, thanks a lot ❤️

[@ccuuttww]

no way for u to copy the content from the wiki btw this is the source for the transformation function :)

[@MachineLearningSimulation]

What do you refer to?