Many years ago I did my B.S thesis about functional regression. It was still a relatively new subject back then. Some of the professors (they're mathematicians after all, I'll give them that) had never heard of the concept, and tutorials were nowhere to find. I only recall that when handling the mathematics of the models, I was very grateful that an entire semester of Functional Analysis that had made everybody wanna kill themselves, finally paid off😂 Anyway, functional regression turned out to be very effective when I later worked in the R&D of an E-bike startup, optimizing the power according to slope and pedaling strength, both being functions for sure.
Haha somehow it always happens, I felt the same way about my math stat classes. A nightmare when I was taking it, but then it turns out it was all needed in the end. That’s cool to hear about it being used with E-bikes. That’s not something I would think of, but it totally makes sense with some thought. Thanks for sharing!
Hi :) I just discovered and subscribed to your interesting channel. In this video, two equations seem a bit strange to me. Firstly, why would we need an integral in the equation for function-on-scalar regression? Secondly, ik function-on-function regression, why is X_i not evaluated at s, over which we integrate? This would allow Y_i(t) to depend on all values X_i(s) and not just X_i(t). Wikipedia seems to agree with me ( eq. 4 in the article Functional Regression). Thanks for clarifying.
if someone wants to learn more about this field or perhaps even do research, would taking some higher level math like functional analysis be useful? when I was taking nonparametrics, there were some parts which made references to things like linear functionals and kernels etc
Based off my own experience, it’d be faster to work with a textbook that deals directly with the material. The math is still there but it’s all the things that are directly related to functional regression. I’d recommend Functional Data Analysis by Crainiceanu or the book by Ramsay
Many years ago I did my B.S thesis about functional regression. It was still a relatively new subject back then. Some of the professors (they're mathematicians after all, I'll give them that) had never heard of the concept, and tutorials were nowhere to find. I only recall that when handling the mathematics of the models, I was very grateful that an entire semester of Functional Analysis that had made everybody wanna kill themselves, finally paid off😂 Anyway, functional regression turned out to be very effective when I later worked in the R&D of an E-bike startup, optimizing the power according to slope and pedaling strength, both being functions for sure.
Haha somehow it always happens, I felt the same way about my math stat classes. A nightmare when I was taking it, but then it turns out it was all needed in the end.
That’s cool to hear about it being used with E-bikes. That’s not something I would think of, but it totally makes sense with some thought. Thanks for sharing!
very interesting, thank you for covering these unpopular concepts
The examples were amazing for understanding the concept
Hi :)
I just discovered and subscribed to your interesting channel.
In this video, two equations seem a bit strange to me. Firstly, why would we need an integral in the equation for function-on-scalar regression? Secondly, ik function-on-function regression, why is X_i not evaluated at s, over which we integrate? This would allow Y_i(t) to depend on all values X_i(s) and not just X_i(t). Wikipedia seems to agree with me ( eq. 4 in the article Functional Regression).
Thanks for clarifying.
if someone wants to learn more about this field or perhaps even do research, would taking some higher level math like functional analysis be useful? when I was taking nonparametrics, there were some parts which made references to things like linear functionals and kernels etc
Based off my own experience, it’d be faster to work with a textbook that deals directly with the material. The math is still there but it’s all the things that are directly related to functional regression. I’d recommend Functional Data Analysis by Crainiceanu or the book by Ramsay
Is this a short glimpse at the subject or what's your goal?
Excelent video ❤