Timeline for How can I fit rational function to data?
Current License: CC BY-SA 4.0
16 events
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| Jan 26 at 5:36 | history | edited | Pabitra Tripathy | CC BY-SA 4.0 |
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| Jan 26 at 5:29 | comment | added | Pabitra Tripathy | Now, I understand the issues. Thank you very much for your insightful comments. @JimB | |
| Jan 26 at 5:07 | comment | added | JimB | I don't think anyone can regenerate the results of that paper without using the exact data and software the authors used. Why? Their model is so overparameterized that iterative fitting algorithms will stop at different places in the parameter space. And their model is overparameterized for 2 reasons: (1) too many coefficients for a simple curve (and the number of data points is irrelevant), and (2) one of the parameters needs to be set to a constant such as 1. For example, fitting $(1+c_1 x+\cdots+c_5 x^5)/(d_0+d_1 x+\cdots+d_6 x^6)$ gives exactly the same predictions. | |
| Jan 26 at 4:42 | comment | added | Pabitra Tripathy | I see. All I was trying to do was regenerate the results of that paper, @JimB. My apologies to @DanielHuber; in my previous comment, I mistakenly referred to your answer as Domen's. | |
| Jan 25 at 19:09 | comment | added | JimB | Ooops! Sorry @DanielHuber. I earlier mistakenly attributed your answer to Domen. | |
| Jan 25 at 19:08 | comment | added | JimB |
In short, there are gazillions of parameter combinations from rational functions that will produce nearly identical predictions for this data because there's not much complexity in the shape of the underlying curve. So @DanielHuber 's results are all that you need (although I would use n=1; m=2).
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| Jan 25 at 19:05 | comment | added | JimB |
If the 300 data points provide just a "denser" set of points, then I would say that the paper should have had a statistical review (from a statistician and not a physicist). A rational function with $n=5$ and $n=6$ can result in a lot bumpier shape than what appears from a plot of the function you present. What one sees is a relatively smooth curve with no need for lots of parameters. Looking at the estimated correlation matrix (fit("CorrelationMatrix")//TableForm) shows many, many entries near 1 or -1 which implies (or actually yells out) overparameterization.
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| Jan 25 at 18:11 | comment | added | Pabitra Tripathy | You are correct; I only provided a few data points here. However, I have worked with a total of 300 data points, and the results do not align with @Domen's answer. I am uncertain about where I may have made a mistake. The reference for my work is arxiv.org/abs/1603.08694v1. In this paper, the data points are generated by solving equations (30) and (31), and the functions I have written correspond to equation (35). | |
| Jan 25 at 17:22 | comment | added | JimB |
Thank you for adding that. I'd also be curious about the reference because the question you should have is why anyone would attempt to fit 13 parameters with 24 data points. @Domen ' s answer with n=1; m=2 (5 parameters) gives an almost perfect fit (and nearly identical predictions as with n=2; m=2).
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| Jan 25 at 16:17 | comment | added | Pabitra Tripathy | @JimB I have updated the answer. Thank you. | |
| Jan 25 at 16:15 | history | edited | Pabitra Tripathy | CC BY-SA 4.0 |
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| Jan 25 at 15:17 | comment | added | JimB | It would be helpful if you could give the full answer. | |
| Jan 25 at 11:38 | vote | accept | Pabitra Tripathy | ||
| Jan 25 at 11:22 | history | edited | Domen | CC BY-SA 4.0 |
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| Jan 25 at 11:14 | answer | added | Daniel Huber | timeline score: 7 | |
| Jan 25 at 10:40 | history | asked | Pabitra Tripathy | CC BY-SA 4.0 |