gemseo.mlearning.regression.algos.ot_gpr module

Gaussian process regression.

class OTGaussianProcessRegressor(data, settings_model=None, **settings)

Bases: BaseRandomProcessRegressor

Gaussian process regression.

Initialize self. See help(type(self)) for accurate signature.

Parameters:

• data (Dataset) -- The training dataset.

• settings_model (BaseMLAlgoSettings | None) -- The machine learning algorithm settings as a Pydantic model. If None, use **settings.

• **settings (Any) -- The machine learning algorithm settings. These arguments are ignored when settings_model is not None.

Raises:

ValueError -- When both the variable and the group it belongs to have a transformer.

Settings

alias of OTGaussianProcessRegressor_Settings

compute_samples(input_data, n_samples, seed=None)

Sample a random vector from the conditioned Gaussian process.

Parameters:

• input_data (RealArray) -- The \(N\) input points of dimension \(d\) at which to observe the conditioned Gaussian process; shaped as \((N, d)\).

• n_samples (int) -- The number of samples \(M\).

• seed (int | None) -- The seed for reproducible results.

Returns:

The output samples shaped as \((M, N, p)\) where \(p\) is the output dimension.

Return type:

RealArray

predict_covariance(input_data)

Predict the covariance matrix from input data.

Parameters:

input_data (RealArray) -- The \(N\) input points of dimension \(d\) at which to observe the conditioned Gaussian process; shaped as \((N, d)\).

Returns:

The posterior covariance matrix at the input points

of shape \((Np, Np)\) with \(p\) the output dimension. The covariance between the \(k\)-th output at the \(i\)-th input point and the \(l\)-th output at the \(j\)-th input point is located at the \(m\)-th line and \(n\)-th column with \(m=ip+k\), \(n=jp+l\), \(i,j\in\{0,\ldots,N-1\}\) and \(k,l\in\{0,\ldots,p-1\}\).

Warning

This statistic is expressed in relation to the transformed output space. You can sample the predict() method to estimate it in relation to the original output space if it is different from the transformed output space.

Return type:

RealArray

predict_std(input_data)

Predict the standard deviation from input data.

Parameters:

input_data (DataType) -- The input data with shape (n_samples, n_inputs).

Returns:

The output data with shape (n_samples, n_outputs).

Return type:

output_data

HMATRIX_ASSEMBLY_EPSILON: ClassVar[float] = 1e-05

The epsilon for the assembly of the H-matrix.

Used when use_hmat is True.

HMATRIX_RECOMPRESSION_EPSILON: ClassVar[float] = 0.0001

The epsilon for the recompression of the H-matrix.

Used when use_hmat is True.

LIBRARY: ClassVar[str] = 'OpenTURNS'

The name of the library of the wrapped machine learning algorithm.

MAX_SIZE_FOR_LAPACK: ClassVar[int] = 100

The maximum size of the training dataset to use LAPACK as linear algebra library.

Use HMAT otherwise.

SHORT_ALGO_NAME: ClassVar[str] = 'GPR'

The short name of the machine learning algorithm, often an acronym.

Typically used for composite names, e.g. f"{algo.SHORT_ALGO_NAME}_{dataset.name}" or f"{algo.SHORT_ALGO_NAME}_{discipline.name}".

property use_hmat: bool

Whether to use the HMAT linear algebra method or LAPACK.