Matlab Curve Fitting Algorithm
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I was trying to solve a surface fitting problem where I had two inputs [X1 X2] used to predict a third quantity Y that occupied the range [1,0). I initially created a very simple gradient descent script from scratch in Python. It was a traditional gradient descent with RMSE as the cost function. After playing aorund with different learning rates and starting guesses (learning along the way that the problem/solution seemed to be extrmeley sensitive to the learning rate and would easily diverge) the best result I was able to get was .05 RMSE.
I tried the matlab fit function next, with 'poly11' fit type and it found a surface with .0045 RMSE (1 order magnitude better than I achieved). It's not surprising to me that Matlab has a more sophisticated curve fitting algorithm than the rudamentary one I wrote up, but does anyone have an idea of what additional tricks fit() may be using that I'm not?
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Matt J
2019-9-5
编辑:Matt J
2019-9-5
If you didn't specify any lower/upper bounds in the fitoptions, then the 'poly11' fitting task has the form of an unconstrained linear-least squares problem and has a closed-form, linear algebraic solution. It is likely that no iterations were done by fit() it all, but rather it probably just solved an appropriate system of linear equations.
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