Reproducing Kernels and Functionals (Theory of Machine Learning)

In this video we give the functional analysis definition of a Reproducing Kernel Hilbert space, and then we investigate approximations within this space using moments as data. We draw a comparison with polynomial best approximations over L^2, and get comparable results with a new basis function made from kernels. //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 //Books Steve Brunton and J. Nathan Kutz - Data Driven Science and Engineering https://amzn.to/4daHtem Holger Wendland - Scattered Data Approximation https://amzn.to/4daHtem Gregory Fasshauer - Meshfree Approximation Methods with MATLAB https://amzn.to/3U1KMeM Gregory Fasshauer - Kernel Based Approximation Methods using MATLAB https://amzn.to/4d1CwEx Ingo Steinwart and Andreas Christmann - Support Vector Machines https://amzn.to/4d5C7km // Code BitBucket https://bitbucket.org/joelrosenfeld/rkhs-moments-approximation/src/main/ Try Through MATLAB Online for free (20 hours free use per month) https://matlab.mathworks.com/open/github/v1?host=bitbucket.org&repo=joelrosenfeld/rkhs-moments-approximation //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 //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! 0:00 Start 1:11 Reproducing Kernel Hilbert Spaces 5:01 Two Examples 12:01 Customizing Bases for Approximation 14:22 Comparing Best Approximations 21:03 Wrap up and Watch Next