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

[–] hank-particles-pym@alien.top 1 points 11 months ago

Curious about this answer, I use AI to help me understand a lot of what happens with questions like these, but as its not my expertise, I am always suspect of the answers i get. So I sent your question to Phind:

A good example of a function that is difficult to optimize by setting its first derivative to zero, but can be easily optimized using gradient descent, is the function f(x) = x*ln(x) - sqrt(x)

The derivative of this function is f'(x) = ln(x) + 1 - 1/(2*sqrt(x)). Setting this equal to zero does not yield a solution that can be expressed in terms of elementary functions. However, we can easily apply the gradient descent method to find a numerical solution.

*********************************

it also generated a bunch of example code in Python. Curious as to the validity of the response.