The Hilbert Projection Theorem - Full Proof! (Theory behind Machine Learning)

[@stretch8390]

Man, what a channel. Awesome to find videos not shying away from technical topics.

[@vtrandal]

The video does a great job of covering the Hilbert Projection Theorem and its proof but falls short of explicitly connecting this theory to machine learning, as the title suggests.

[@JoelRosenfeld]

@@vtrandal is fundamental to machine learning and establishing the connection is the point of the series of videos. More is coming.

[@davidg6324]

That proof was very nice, I didn't know something so seemingly simple as the parallelogram law could be used this way!

[@JoelRosenfeld]

It really is an unsung hero of functional analysis

[@fanalysis6734]

What about the role of hilbert spaces in machine learning?

[@JoelRosenfeld]

This is a buildup to answer that question. Essentially, projections are all over the place in Machine Learning, and that's where your approximations are ultimately coming from. The implementation of projections in finite dimensional spaces turn out to be equivalent to gradient descent problems on loss functions. Where you are guaranteed to achieve the best approximation in a Hilbert space on finding that minimum. Moreover, the representer theorem, which is at the core of things like support vector machines relies on the representer theorem, which is a direct consequence of the Hilbert Projection Theorem. We will talk about that in the next several videos. Sorry for the wait :)

[@route66math77]

Exquisite content -- thanks 🙂

[@JoelRosenfeld]

I’m glad you like it! It means a lot to me.