Example with approximating sinc( x ) function.
This is a implementation of a small lib for RFF - Random Fourier Features Ridge Regressor, with an example of the aproximation of a sinc( x ) function.
Target :
sinc( x ) = sin( x ) / x, with sinc( 0 ) = 1 .
Approximate sinc( x ) on [ -10, 10 ] .
Universal-approximation-like via RBF-ish kernel using random Fourier features, trained with one linear solve.
Random Fourier Features Ridge Regressor ( approximating sinc( x ) function )
Target : sinc( x ) = sin( x ) / x, with sinc( 0 ) = 1
Approximate sinc( x ) on [ -10, 10 ].
Universal-approximation-like via RBF-ish kernel using random
Fourier features, trained with one linear solve.
Training RFF regressor on sinc...
Done.
x = -10.00 sinc( x ) = -00.054402 RFF(x) = -00.054262
x = -05.00 sinc( x ) = -00.191785 RFF(x) = -00.191805
x = -02.00 sinc( x ) = 000.454649 RFF(x) = 000.454844
x = -01.00 sinc( x ) = 000.841471 RFF(x) = 000.841588
x = 000.00 sinc( x ) = 001.000000 RFF(x) = 000.999822
x = 001.00 sinc( x ) = 000.841471 RFF(x) = 000.841236
x = 002.00 sinc( x ) = 000.454649 RFF(x) = 000.454716
x = 005.00 sinc( x ) = -00.191785 RFF(x) = -00.192080
x = 010.00 sinc( x ) = -00.054402 RFF(x) = -00.053250
Training MSE = 5.28264e-08
Training RMSE = 0.00022984
MIT Open Source License
Best regards,
Joao Carvalho