rfflearn.cpu.RFFGPR

Gaussian Process Regression with random Fourier features.

def rfflearn.cpu.RFFGPR(self, dim_kernel=128, std_kernel=0.1, std_error=0.1, W=None, b=None, a=None, S=None)

Parameters:

dim_kernel: int  (default=128)

Dimension of the random matrix.

std_kernel: float  (default=0.1)

Standard deviation of the random matrix.

std_error: float  (default=0.1)

Standard deviation of the measurement error.

W: np.ndarray  (default=None)

Random matrix for the input X. If None then generated automatically.

b: np.ndarray  (default=None)

Random bias for the input X. If None then generated automatically.

a: np.ndarray  (default=None)

Cache of the matrix a. If None then generated automatically.

S: np.ndarray  (default=None)

Cache of the matrix S. If None then generated automatically.

Attributes:

dim: int

Dimension of the random matrix.

s_k: float

Standard deviation of the random matrix.

mat: Callable

A function to generate the random matrix W.

W: np.ndarray

Random matrix for the input X.

b: np.ndarray

Random bias for the input X.

s_e: np.ndarray

Standard deviation of the measurement error.

a: np.ndarray

Cache of the matrix a. If None then generated automatically.

S: np.ndarray

Cache of the matrix S. If None then generated automatically.

Member functions

def fit(self, X, y, **args)

Trains the GPR model according to the given data.

Parameters:

X: np.ndarray

Input matrix with shape (n_samples, n_features_input).

y: np.ndarray

Output matrix with shape (n_samples, n_features_output).

args: dict  (default={})

Extra arguments. However, this arguments will be ignored. This argument exists only for keeping the same interface with scikit-learn.

Returns:

rfflearn.cpu.RFFGPR

Fitted estimator.

def predict(self, X, return_std=False, return_cov=False)

Performs regression on the input data.

Parameters:

X: np.ndarray

Input matrix with shape (n_samples, n_features_input).

return_std: bool  (default=False)

Returns standard deviation of the prediction if True.

return_cov: bool  (default=False)

Returns covariance of the prediction if True.

Returns:

np.ndarray, or tuple

Predicted vector, or tuple of prediction, standard deviation, and covariance of the prediction.

def std(self, F)

Returns standard deviation of the prediction.

Parameters:

F: np.ndarray

Matrix F (= self.conv(X).T).

Returns:

np.ndarray

Standard deviation of the prediction.

def cov(self, F)

Returns covariance of the prediction.

Parameters:

F: np.ndarray

Matrix F (= self.conv(X).T).

Returns:

np.ndarray

Covariance of the prediction.

def score(self, X, y, **args)

Returns the R2 score (coefficient of determination) of the prediction.

Parameters:

X: np.ndarray

Input matrix with shape (n_samples, n_features_input).

y: np.ndarray

True output matrix with shape (n_samples, n_features_output).

args: dict  (default={})

Extra arguments. However, this arguments will be ignored.

Returns:

float

R2 score of the prediction.

Minimal Example

>>> import numpy as np                                  # Import Numpy
>>> import rfflearn.cpu as rfflearn                     # Import module
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])  # Define input data
>>> y = np.array([0.5, 1, 1.5, 2])                      # Defile label data
>>> gpr = rfflearn.RFFGPR().fit(X, y)                   # Training (on CPU)
>>> gpr.score(X, y)                                     # Inference (on CPU)
0.982939182798136
>>> gpr.predict(np.array([[-0.8, -1]]))
array([0.52784025])