What is a BEST approximation? (Theory of Machine Learning)

Here we start our foray into Machine Learning, where we learn how to use the Hilbert Projection Theorem to give a best approximation of a function. This way we learn a function using an optimization procedure. To do this, we use the moments of a function. //Watch Next The Real Analysis Survival Guide https://youtu.be/v5rD0B-zfXw The Analyticity of the Laplace transform https://youtu.be/FIMkbFQL6XM Introduction to Control Theory https://youtu.be/0v4WFmOm764 //Music Provided by Epidemic Sound Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referral/644nao //Code https://bitbucket.org/joelrosenfeld/best-approximation-in-l2/src/main/ Or open it directly in MATLAB Online: https://matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/best-approximation-in-l2&project=bestapproximation.m //Recording Equipment Canon SL3: https://amzn.to/3nZ11KU Canon T6i: https://amzn.to/3FUpkQh Rode VideoMic: https://amzn.to/3lhldGa Blue Yeti Microphone: https://amzn.to/3I1y88N Yeti Nano Microphone: https://amzn.to/3I1mriA SanDisc 256GB SD Card: https://amzn.to/3E3LOOr Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc Camera Power Adapter: https://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!