Curve fitting

Hello /prog/
I've been talking to Xarn about curve fitting and I wanted to know your opinions on this as well.
Is anyone here familiar with curve fitting?
http://bbs.readsicp.org/kareha.pl/1468337795/

Are you doing this in MATLAB or R?

There are several methods, like splines (linear splines, cubic splines), polynomial interpolation, least squares

These are notes from a course I took on the subject

http://www.cs.mcgill.ca/~chang/teaching/cs350/slides/ls.pdf - least squares
http://www.cs.mcgill.ca/~chang/teaching/cs350/slides/pi.pdf - polynomial interpolation
http://www.cs.mcgill.ca/~chang/teaching/cs350/slides/spline.pdf - splines

>>2

I already know R and MATLAB, but I can learn any tool needed.
The problem I face is to choose a method to fit a curve to certain data. Most methods require you to know the distribution of the data, something I rarely know with real world data. And then there are the non-parametric algorithms. But which one to choose is a mystery...

And then it comes the issue with extrapolation. Which method will better predict the future if you set the curve for a time that has not been yet observed?

>>3
I'll read those slides, thanks a lot for sharing. I hope it brings some light to my doubts.

>>4
If your signal is band-limited then use selective deconvolution.

>>3
I read the paper and they are pretty interesting. I didn't have know how those methods worked in such detail.
But I'm still lost when it comes to which method I should use in each situation.

For example, let's say we have a time series with random data. We don't know the probability distribution of this data or if it should form a line, sine, tangent, polynomial or something else.
It's just a bunch of (x,y) values for which we don't know the behavior. But we want to fit a curve to it so we can -
I. get a visual idea of the behavior of the data
II. extrapolate data (to predict how the data will behave in the future).
My question is which method should be used. Since we have no idea of the probability distribution it must be a non-parametric method. But that's as far as I figured out. There are many non-parametric methods.

>>5
I don't know what you mean by that. Can you be a bit more specific?

>>6
Do you even know what frequency analysis is? Band-limited means it has a restricted frequency range.

>>7
I know about frequency analysis and how it can be used to break caesar cipher, but I don't know what's selective deconvolution or how this all relates to the topic of fitting a curve to some general data.

Wait!
There's more than 1 thing called frequency analysis.
https://en.wikipedia.org/wiki/Frequency_analysis_%28disambiguation%29
Which one are you talking about?

And no, I don't know what it is.
Can you explain how it's useful for curve fitting?

>>8,9
I'm talking about the Fourier transform kind, and selective deconvolution is more for extrapolation from limited data, since you were asking about that sort of thing as well. Take a couple semesters of calc and then we can continue this conversation.

>>10
Do you have a good introduction to the topic of using frequency analysis and fourier transform to curve fitting? I couldn't find much online.

I never heard of this method to fit a curve to data.
Would you say it's better than splines, least squares, polynomial interpolation, etc? If so why?

Symbolic regression looks cool.

xarn is a SJW