Lipschitz Functions: Intro and Simple Explanation for Usefulness in Machine Learning

In a nutshell, saying a function is Lipschitz means there exists a constant K such that the distance between two outputs is at most K times the distance between the inputs, and this K must work for all inputs in the domain. We look at the single variable case with an example, and then the multi variable case. In machine learning context, we want similar inputs to be classified as similar. Lipschitz functions provide a reliable way to do that.

[@tnuts92]

Thanks for the explanation of its interest for machine learning algorithms !! Thats all I'd like to understand about any math concept ! Cheers 🙏🙏

[@DrMcCrady]

Glad it was helpful, give math a chance though :)

[@Mulkek]

Thanks, and it's so easy & simple!

[@meghbhalerao5208]

Great intuitive explanation! Thank you!

[@DrMcCrady]

Glad it was helpful!

[@inerammeloo7915]

Thank you for making this! It was really well explained and helped a lot for me to grasp the concept

[@DrMcCrady]

Glad it was helpful!

[@hazema.6150]

Very nice breakdown, thank you so much for it.

[@DrMcCrady]

Glad it was helpful!

[@troisiemeoeil3651]

Thank you for the clear insight. I've been struggling with the underpinnings of statistical learning theory and videos such as yours are godsends.

[@sukritkapil9816]

Thanks for the clear explanation!!

[@DrMcCrady]

Glad it was helpful!

[@harperbye]

Thank you, this was really helpful.

[@DrMcCrady]

Glad it was helpful!

[@Niki99fun]

This really helped me! Thank you

[@DrMcCrady]

Glad to hear it!

[@CodeEmporium]

Loved this

[@DrMcCrady]

Thank you! And you make great ML content, too!

[@hamzamohiuddin973]

Thank you, very easy to follow.

[@DrMcCrady]

Glad it was helpful!

[@jasonrichards5192]

Great Explanation!

[@DrMcCrady]

Thank you!

[@soroushmehraban]

Awesome explanation. Keep going!

[@DrMcCrady]

Thanks for your kindness!

[@SinghTheMaster]

You got a new subscriber ❤

[@sam_joshua_s]

its the best video explaination

[@DrMcCrady]

Thank you!

[@karthikeyakethamakka]

I would say lipschitz is mostly used as a regularization technique for a machine learning problem.

[@QmiStudying]

do you have any idea on how to prove lotka-volterra equations is locally lipschitz

[@DrMcCrady]

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.

[@victorezekiel5374]

Great video! Please what do you mean by between -K and K. Is the slope of the secant supposed to be K?

[@DrMcCrady]

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.

[@antonioruizvillasenor5258]

gracias

[@DrMcCrady]

Glad it was helpful!

[@tuongnguyen9391]

Damn it this is so good !!!!!, May I ask what playlist this video belong to

[@DrMcCrady]

Thank you! I think it belongs to this one Real Analysis/Advanced Calculus
ruclips.net/p/PLrvK1zCpb85AtQZjin-IJLRK4uOMX0Hji

[@tuongnguyen9391]

@@DrMcCrady not really the one in that playlist is only ""Lipschitz Functions"

[@anirudhthatipelli8765]

Thanks a lot, this was very clear!

[@DrMcCrady]

Glad it was helpful!