In two dimensions, the two expressions for the changes in population are products of linear functions. Linear functions are Lipschitz. Use that to show the product is locally Lipschitz.
The slope of the secant line would be between -K and K. So the difference between any two outputs is at most K times the difference between the corresponding inputs.
Great intuitive explanation! Thank you!
Glad it was helpful!
Thank you for making this! It was really well explained and helped a lot for me to grasp the concept
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Very nice breakdown, thank you so much for it.
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Loved this
Thank you! And you make great ML content, too!
I would say lipschitz is mostly used as a regularization technique for a machine learning problem.
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Thanks for the explanation of its interest for machine learning algorithms !! Thats all I'd like to understand about any math concept ! Cheers 🙏🙏
Glad it was helpful, give math a chance though :)
Awesome explanation. Keep going!
Thanks for your kindness!
Thanks, and it's so easy & simple!
do you have any idea on how to prove lotka-volterra equations is locally lipschitz
In two dimensions, the two expressions for the changes in population are products of linear functions. Linear functions are Lipschitz. Use that to show the product is locally Lipschitz.
Thanks for the clear explanation!!
Glad it was helpful!
Great video! Please what do you mean by between -K and K. Is the slope of the secant supposed to be K?
The slope of the secant line would be between -K and K. So the difference between any two outputs is at most K times the difference between the corresponding inputs.
its the best video explaination
Thank you!
Thank you, very easy to follow.
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Thank you, this was really helpful.
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Great Explanation!
Thank you!
Thanks a lot, this was very clear!
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This really helped me! Thank you
Glad to hear it!
Damn it this is so good !!!!!, May I ask what playlist this video belong to
Thank you! I think it belongs to this one Real Analysis/Advanced Calculus
ua-cam.com/play/PLrvK1zCpb85AtQZjin-IJLRK4uOMX0Hji.html
@@DrMcCrady not really the one in that playlist is only ""Lipschitz Functions"
gracias
Glad it was helpful!
Thank you for the clear insight. I've been struggling with the underpinnings of statistical learning theory and videos such as yours are godsends.