Putting DATA in Hilbert Spaces: Proving the Riesz Theorem (Theory of Machine Learning)
In this video we introduce and prove the Riesz representation theorem for Hilbert spaces. This is the fundamental theorem that enables much of machine learning and data science, since it allows us to embed information and measurements from the real world into a Hilbert function space.
//Watch Next
The Real Analysis Survival Guide • The Real Analysis Surv...
The Analyticity of the Laplace transform • Morera's Theorem in Pr...
Introduction to Control Theory • Introduction to Contro...
//Music Provided by Epidemic Sound
Use this referral link to get a 30 day free trial with Epidemic Sound for your KZread channel:
www.epidemicsound.com/referra...
//Recording Equipment
Canon SL3: amzn.to/3nZ11KU
Canon T6i: amzn.to/3FUpkQh
Rode VideoMic: amzn.to/3lhldGa
Blue Yeti Microphone: amzn.to/3I1y88N
Yeti Nano Microphone: amzn.to/3I1mriA
SanDisc 256GB SD Card: amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: amzn.to/3xvB9cN
Neewer 18 inch Ring Light: amzn.to/2ZvgCsc
Camera Power Adapter: amzn.to/3D3upUu
This content is partially supported by National Science Foundation - Award ID 2027976, Air Force Office Of Scientific Research - Award FA9550-20-1-0127 and FA9550-21-1-0134. I am responsible for all opinions and content, and what I say does not necessarily reflect the sponsoring organizations.
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 What are functionals?
2:54 Functionals over R^n
3:55 Who proved this theorem?
5:00 Recapping the Projection Theorem
6:09 How do you prove this anyway?
16:25 Wrapping up
Пікірлер: 14
Absolute perfection! Would be great to see the Hann Banach theorem next, perhaps applied to proving the universal approximation theorem?
@JoelRosenfeld
2 ай бұрын
That is in the plans, but I’ll need to do some work developing measure theory and that version of the Riesz theorem. I’ll probably cover universal approximation with kernels first and later neural networks
Great! btw, Hilbert wrote mostly during the end of the 19th century and the begining of the 20th
Found out your channel from algorithm rec. Thank you so much for higher math content, Sir! ❤❤
@JoelRosenfeld
2 ай бұрын
I'm glad you like it! Welcome!
This is brilliant stuff! Thank you!
@JoelRosenfeld
2 ай бұрын
I’m glad you like it!
this is great, thank you. i'm interested in a lot of things learning-related and functional-analysis-related (deep learning theory, operator learning, continuous optimization, etc. etc.), so i will definitely be keeping up with this series! but, i am only (almost) through one semester of analysis... will hopefully get to this fun stuff formally by the end of undergrad :P
@JoelRosenfeld
2 ай бұрын
Sounds great! I will eventually touch on all of those topics down the line. What would you like to know about operator learning in particular? I also have an analysis sequence on my channel, if you haven’t seen it yet.
Getting this video in suggestions having Walter Rudin's Functional Analysis right next to me, I wonder if it's destiny or if ML is using my laptop's camera to give me well-tailored suggestions :D regardless - a very informative and well-produced video!
@JoelRosenfeld
2 ай бұрын
Thank you! I'm glad you liked it. I hope I can deliver more timely content lol!
the rizz theorem??
@JoelRosenfeld
2 ай бұрын
I hear that Riesz went by Dr Rizz at parties lol jk