approximate_gaussian_process¶
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pyapprox.approximate.approximate_gaussian_process(train_samples, train_vals, nu=inf, n_restarts_optimizer=5, verbosity=0)[source]¶ Compute a Gaussian process approximation of a function from a fixed data set using the Matern kernel
\[k(z_i, z_j) = \frac{1}{\Gamma(\nu)2^{\nu-1}}\Bigg( \frac{\sqrt{2\nu}}{l} \lVert z_i - z_j \rVert_2\Bigg)^\nu K_\nu\Bigg( \frac{\sqrt{2\nu}}{l} \lVert z_i - z_j \rVert_2\Bigg)\]where \(\lVert \cdot \rVert_2\) is the Euclidean distance, \(\Gamma(\cdot)\) is the gamma function, \(K_\nu(\cdot)\) is the modified Bessel function.
- Parameters
- train_samplesnp.ndarray (nvars,nsamples)
The inputs of the function used to train the approximation
- train_valsnp.ndarray (nvars,nsamples)
The values of the function at
train_samples- kernel_nustring
The parameter \(\nu\) of the Matern kernel. When \(\nu\to\inf\) the Matern kernel is equivalent to the squared-exponential kernel.
- n_restarts_optimizerint
The number of local optimizeation problems solved to find the GP hyper-parameters
- verbosityinteger
Controls the amount of information printed to screen
- Returns
- result
pyapprox.approximate.ApproximateResult Result object with the following attributes
- approx
pyapprox.gaussian_process.GaussianProcess The Gaussian process
- result