Machine Learning

1 readers

1 users here now

Community Rules:

Be nice. No offensive behavior, insults or attacks: we encourage a diverse community in which members feel safe and have a voice.
Make your post clear and comprehensive: posts that lack insight or effort will be removed. (ex: questions which are easily googled)
Beginner or career related questions go elsewhere. This community is focused in discussion of research and new projects that advance the state-of-the-art.
Limit self-promotion. Comments and posts should be first and foremost about topics of interest to ML observers and practitioners. Limited self-promotion is tolerated, but the sub is not here as merely a source for free advertisement. Such posts will be removed at the discretion of the mods.

founded 1 year ago

MODERATORS

communick@academy.garden

[D] Simplest mathematical example of a function that can only be solved by gradient descent (alien.top)

submitted 11 months ago by EatMeMonster@alien.top to c/machinelearning@academy.garden

25 comments fedilink hide all child comments

I'm trying to teach a lesson on gradient descent from a more statistical and theoretical perspective, and need a good example to show its usefulness.

What is the simplest possible algebraic function that would be impossible or rather difficult to optimize for, by setting its 1st derivative to 0, but easily doable with gradient descent? I preferably want to demonstrate this in context linear regression or some extremely simple machine learning model.

you are viewing a single comment's thread
view the rest of the comments

[–] neyman-pearson@alien.top 1 points 11 months ago (1 children)

Except you could get stuck at an arbitary saddle point

[–] DoctorFuu@alien.top 1 points 11 months ago (1 children)

Isn't the probability of getting exactly on one 0 though?

[–] jamochasnake@alien.top 1 points 11 months ago

of course, every locally lipschitz function is differentiable almost everywhere, i.e., the set of points where it is not differentiable is a measure zero set. So if you drew a point randomly (with distribution absolutely continuous w.r.t. the lebesgue measure) then you avoid such points with probability. However, this has NOTHING to do with actually performing an algorithm like gradient descent - in these algorithms you are NOT simply drawing points randomly and you cannot guarantee you avoid these points a priori.