The Hilbert Projection Theorem - Full Proof! (Theory behind Machine Learning)
In this video we embark on the study of spaces of (potentially) infinite dimension, Hilbert spaces. Here we give the full proof the Hilbert Projection theorem, which is the most critical piece of their study.
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Пікірлер: 7
Man, what a channel. Awesome to find videos not shying away from technical topics.
What about the role of hilbert spaces in machine learning?
@JoelRosenfeld
3 ай бұрын
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 :)
That proof was very nice, I didn't know something so seemingly simple as the parallelogram law could be used this way!
@JoelRosenfeld
3 ай бұрын
It really is an unsung hero of functional analysis
Exquisite content -- thanks 🙂
@JoelRosenfeld
3 ай бұрын
I’m glad you like it! It means a lot to me.