Pros and cons of multivariate interpolation techniques for scattered data?
$begingroup$
I have a numerical simulation $f$ that takes 6 input parameters $mathbf x = x_1, x_2, ldots x_6$. I have randomly selected $25,000$ random combinations of these inputs and calculated $f(mathbf x)$. The output of the simulation is about 25 numbers $mathbf y = y_1, y_2, ldots y_{25}$ (although for the sake of simplicity we could pretend I am only computing $y_1$).
I am now trying to interpolate this function 6-dimensional function. I hold out a model, train on the remaining models, and test on the held-out model.
I have tried various schemes:
Linear interpolation (scipy.interpolate.griddata)
Artificial neural network (sklearn.neural_network.MLPRegressor)
Kriging / Gaussian Process Regression (sklearn.gaussian_process.gaussianProcessRegressor)
Polynomial ridge regression (e.g., polynomial features)
Distance-weighted nearest neighbors (K Nearest Neighbors)
To my surprise, linear interpolation has outperformed the rest. (To be clear, I have tried various data preprocessing steps to ensure the data are normalized, etc., as well as several hours changing the parameters of each method.)
Is this what I should have expected? Is there another technique that may work better?
I would like to note that I have apparently failed to find a method that can do cubic interpolation with high dimensional input, which I would imagine to be a promising route. (SciPy at least is limited to 2D functions.)
numerical-methods regression interpolation simulation
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
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add a comment |
$begingroup$
I have a numerical simulation $f$ that takes 6 input parameters $mathbf x = x_1, x_2, ldots x_6$. I have randomly selected $25,000$ random combinations of these inputs and calculated $f(mathbf x)$. The output of the simulation is about 25 numbers $mathbf y = y_1, y_2, ldots y_{25}$ (although for the sake of simplicity we could pretend I am only computing $y_1$).
I am now trying to interpolate this function 6-dimensional function. I hold out a model, train on the remaining models, and test on the held-out model.
I have tried various schemes:
Linear interpolation (scipy.interpolate.griddata)
Artificial neural network (sklearn.neural_network.MLPRegressor)
Kriging / Gaussian Process Regression (sklearn.gaussian_process.gaussianProcessRegressor)
Polynomial ridge regression (e.g., polynomial features)
Distance-weighted nearest neighbors (K Nearest Neighbors)
To my surprise, linear interpolation has outperformed the rest. (To be clear, I have tried various data preprocessing steps to ensure the data are normalized, etc., as well as several hours changing the parameters of each method.)
Is this what I should have expected? Is there another technique that may work better?
I would like to note that I have apparently failed to find a method that can do cubic interpolation with high dimensional input, which I would imagine to be a promising route. (SciPy at least is limited to 2D functions.)
numerical-methods regression interpolation simulation
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
$endgroup$
add a comment |
$begingroup$
I have a numerical simulation $f$ that takes 6 input parameters $mathbf x = x_1, x_2, ldots x_6$. I have randomly selected $25,000$ random combinations of these inputs and calculated $f(mathbf x)$. The output of the simulation is about 25 numbers $mathbf y = y_1, y_2, ldots y_{25}$ (although for the sake of simplicity we could pretend I am only computing $y_1$).
I am now trying to interpolate this function 6-dimensional function. I hold out a model, train on the remaining models, and test on the held-out model.
I have tried various schemes:
Linear interpolation (scipy.interpolate.griddata)
Artificial neural network (sklearn.neural_network.MLPRegressor)
Kriging / Gaussian Process Regression (sklearn.gaussian_process.gaussianProcessRegressor)
Polynomial ridge regression (e.g., polynomial features)
Distance-weighted nearest neighbors (K Nearest Neighbors)
To my surprise, linear interpolation has outperformed the rest. (To be clear, I have tried various data preprocessing steps to ensure the data are normalized, etc., as well as several hours changing the parameters of each method.)
Is this what I should have expected? Is there another technique that may work better?
I would like to note that I have apparently failed to find a method that can do cubic interpolation with high dimensional input, which I would imagine to be a promising route. (SciPy at least is limited to 2D functions.)
numerical-methods regression interpolation simulation
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
$endgroup$
I have a numerical simulation $f$ that takes 6 input parameters $mathbf x = x_1, x_2, ldots x_6$. I have randomly selected $25,000$ random combinations of these inputs and calculated $f(mathbf x)$. The output of the simulation is about 25 numbers $mathbf y = y_1, y_2, ldots y_{25}$ (although for the sake of simplicity we could pretend I am only computing $y_1$).
I am now trying to interpolate this function 6-dimensional function. I hold out a model, train on the remaining models, and test on the held-out model.
I have tried various schemes:
Linear interpolation (scipy.interpolate.griddata)
Artificial neural network (sklearn.neural_network.MLPRegressor)
Kriging / Gaussian Process Regression (sklearn.gaussian_process.gaussianProcessRegressor)
Polynomial ridge regression (e.g., polynomial features)
Distance-weighted nearest neighbors (K Nearest Neighbors)
To my surprise, linear interpolation has outperformed the rest. (To be clear, I have tried various data preprocessing steps to ensure the data are normalized, etc., as well as several hours changing the parameters of each method.)
Is this what I should have expected? Is there another technique that may work better?
I would like to note that I have apparently failed to find a method that can do cubic interpolation with high dimensional input, which I would imagine to be a promising route. (SciPy at least is limited to 2D functions.)
numerical-methods regression interpolation simulation
numerical-methods regression interpolation simulation
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
asked Dec 16 '18 at 12:14
rhombidodecahedronrhombidodecahedron
6281619
6281619
add a comment |
add a comment |
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