bayeso.covariance

bayeso.covariance.choose_fun_cov(str_cov, is_grad=False)

It is for choosing a covariance function or a function for computing gradients of covariance function.

Parameters:
  • str_cov (str.) – the name of covariance function.
  • is_grad (bool., optional) – flag for returning a function for the gradients
Returns:

covariance function, or function for computing gradients of covariance function.
Return type:

function
Raises:

AssertionError
bayeso.covariance.cov_main(str_cov, X, Xs, hyps, same_X_Xs, jitter=1e-05)

It computes kernel matrix over X and Xs, where hyps is given.

Parameters:
  • str_cov (str.) – the name of covariance function.
  • X (numpy.ndarray) – one inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • hyps (dict.) – dictionary of hyperparameters for covariance function.
  • same_X_Xs (bool.) – flag for checking X and Xs are same.
  • jitter (float, optional) – jitter for diagonal entries.
Returns:

kernel matrix over X and Xs. Shape: (n, m).
Return type:

numpy.ndarray
Raises:

AssertionError, ValueError
bayeso.covariance.cov_matern32(X, Xs, lengthscales, signal)

It computes Matern 3/2 kernel over X and Xs, where lengthscales and signal are given.

Parameters:
  • X (numpy.ndarray) – inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • lengthscales (numpy.ndarray, or float) – length scales. Shape: (d, ) or ().
  • signal (float) – coefficient for signal.
Returns:

kernel values over X and Xs. Shape: (n, m).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.cov_matern52(X, Xs, lengthscales, signal)

It computes Matern 5/2 kernel over X and Xs, where lengthscales and signal are given.

Parameters:
  • X (numpy.ndarray) – inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • lengthscales (numpy.ndarray, or float) – length scales. Shape: (d, ) or ().
  • signal (float) – coefficient for signal.
Returns:

kernel values over X and Xs. Shape: (n, m).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.cov_se(X, Xs, lengthscales, signal)

It computes squared exponential kernel over X and Xs, where lengthscales and signal are given.

Parameters:
  • X (numpy.ndarray) – inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • lengthscales (numpy.ndarray, or float) – length scales. Shape: (d, ) or ().
  • signal (float) – coefficient for signal.
Returns:

kernel values over X and Xs. Shape: (n, m).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.cov_set(str_cov, X, Xs, lengthscales, signal)

It computes set kernel matrix over X and Xs, where lengthscales and signal are given.

Parameters:
  • str_cov (str.) – the name of covariance function.
  • X (numpy.ndarray) – one inputs. Shape: (n, m, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (l, m, d).
  • lengthscales (numpy.ndarray, or float) – length scales. Shape: (d, ) or ().
  • signal (float) – coefficient for signal.
Returns:

set kernel matrix over X and Xs. Shape: (n, l).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.grad_cov_main(str_cov, X, Xs, hyps, is_fixed_noise, same_X_Xs=True, jitter=1e-05)

It computes gradients of kernel matrix over hyperparameters, where hyps is given.

Parameters:
  • str_cov (str.) – the name of covariance function.
  • X (numpy.ndarray) – one inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • hyps (dict.) – dictionary of hyperparameters for covariance function.
  • is_fixed_noise (bool.) – flag for fixing a noise.
  • same_X_Xs (bool., optional) – flag for checking X and Xs are same.
  • jitter (float, optional) – jitter for diagonal entries.
Returns:

gradient matrix over hyperparameters. Shape: (n, m, l) where l is the number of hyperparameters.
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.grad_cov_matern32(cov_, X, Xs, hyps, num_hyps, is_fixed_noise)

It computes gradients of Matern 3/2 kernel over X and Xs, where hyps is given.

Parameters:
  • cov (numpy.ndarray) – covariance matrix. Shape: (n, m).
  • X (numpy.ndarray) – one inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • hyps (dict.) – dictionary of hyperparameters for covariance function.
  • num_hyps (int.) – the number of hyperparameters == l.
  • is_fixed_noise (bool.) – flag for fixing a noise.
Returns:

gradient matrix over hyperparameters. Shape: (n, m, l).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.grad_cov_matern52(cov_, X, Xs, hyps, num_hyps, is_fixed_noise)

It computes gradients of Matern 5/2 kernel over X and Xs, where hyps is given.

Parameters:
  • cov (numpy.ndarray) – covariance matrix. Shape: (n, m).
  • X (numpy.ndarray) – one inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • hyps (dict.) – dictionary of hyperparameters for covariance function.
  • num_hyps (int.) – the number of hyperparameters == l.
  • is_fixed_noise (bool.) – flag for fixing a noise.
Returns:

gradient matrix over hyperparameters. Shape: (n, m, l).
Return type:

numpy.ndarray
Raises:

AssertionError
bayeso.covariance.grad_cov_se(cov_, X, Xs, hyps, num_hyps, is_fixed_noise)

It computes gradients of squared exponential kernel over X and Xs, where hyps is given.

Parameters:
  • cov (numpy.ndarray) – covariance matrix. Shape: (n, m).
  • X (numpy.ndarray) – one inputs. Shape: (n, d).
  • Xs (numpy.ndarray) – another inputs. Shape: (m, d).
  • hyps (dict.) – dictionary of hyperparameters for covariance function.
  • num_hyps (int.) – the number of hyperparameters == l.
  • is_fixed_noise (bool.) – flag for fixing a noise.
Returns:

gradient matrix over hyperparameters. Shape: (n, m, l).
Return type:

numpy.ndarray
Raises:

AssertionError