bayeso.covariance¶
It defines covariance functions and their associated functions.
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bayeso.covariance.
choose_fun_cov
(str_cov: str) → Callable¶ It chooses a covariance function.
Parameters: str_cov (str.) – the name of covariance function. Returns: covariance function. Return type: callable Raises: AssertionError
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bayeso.covariance.
choose_fun_grad_cov
(str_cov: str) → Callable¶ It chooses a function for computing gradients of covariance function.
Parameters: str_cov (str.) – the name of covariance function. Returns: function for computing gradients of covariance function. Return type: callable Raises: AssertionError
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bayeso.covariance.
cov_main
(str_cov: str, X: numpy.ndarray, Xp: numpy.ndarray, hyps: dict, same_X_Xp: bool, jitter: float = 1e-05) → numpy.ndarray¶ It computes kernel matrix over X and Xp, where hyps is given.
Parameters: - str_cov (str.) – the name of covariance function.
- X (numpy.ndarray) – one inputs. Shape: (n, d).
- Xp (numpy.ndarray) – another inputs. Shape: (m, d).
- hyps (dict.) – dictionary of hyperparameters for covariance function.
- same_X_Xp (bool.) – flag for checking X and Xp are same.
- jitter (float, optional) – jitter for diagonal entries.
Returns: kernel matrix over X and Xp. Shape: (n, m).
Return type: numpy.ndarray
Raises: AssertionError, ValueError
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bayeso.covariance.
cov_matern32
(X: numpy.ndarray, Xp: numpy.ndarray, lengthscales: Union[numpy.ndarray, float], signal: float) → numpy.ndarray¶ It computes Matern 3/2 kernel over X and Xp, where lengthscales and signal are given.
Parameters: - X (numpy.ndarray) – inputs. Shape: (n, d).
- Xp (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 Xp. Shape: (n, m).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
cov_matern52
(X: numpy.ndarray, Xp: numpy.ndarray, lengthscales: Union[numpy.ndarray, float], signal: float) → numpy.ndarray¶ It computes Matern 5/2 kernel over X and Xp, where lengthscales and signal are given.
Parameters: - X (numpy.ndarray) – inputs. Shape: (n, d).
- Xp (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 Xp. Shape: (n, m).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
cov_se
(X: numpy.ndarray, Xp: numpy.ndarray, lengthscales: Union[numpy.ndarray, float], signal: float) → numpy.ndarray¶ It computes squared exponential kernel over X and Xp, where lengthscales and signal are given.
Parameters: - X (numpy.ndarray) – inputs. Shape: (n, d).
- Xp (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 Xp. Shape: (n, m).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
cov_set
(str_cov: str, X: numpy.ndarray, Xp: numpy.ndarray, lengthscales: Union[numpy.ndarray, float], signal: float) → numpy.ndarray¶ It computes set kernel matrix over X and Xp, where lengthscales and signal are given.
Parameters: - str_cov (str.) – the name of covariance function.
- X (numpy.ndarray) – one inputs. Shape: (n, m, d).
- Xp (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 Xp. Shape: (n, l).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
get_kernel_cholesky
(X_train: numpy.ndarray, hyps: dict, str_cov: str, fix_noise: bool = True, use_gradient: bool = False, debug: bool = False) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]¶ This function computes a kernel inverse with Cholesky decomposition.
Parameters: - X_train (numpy.ndarray) – inputs. Shape: (n, d) or (n, m, d).
- hyps (dict.) – dictionary of hyperparameters for Gaussian process.
- str_cov (str.) – the name of covariance function.
- fix_noise (bool., optional) – flag for fixing a noise.
- use_gradient (bool., optional) – flag for computing and returning gradients of negative log marginal likelihood.
- debug (bool., optional) – flag for printing log messages.
Returns: a tuple of kernel matrix over X_train, lower matrix computed by Cholesky decomposition, and gradients of kernel matrix. If use_gradient is False, gradients of kernel matrix would be None.
Return type: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray)
Raises: AssertionError
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bayeso.covariance.
get_kernel_inverse
(X_train: numpy.ndarray, hyps: dict, str_cov: str, fix_noise: bool = True, use_gradient: bool = False, debug: bool = False) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]¶ This function computes a kernel inverse without any matrix decomposition techniques.
Parameters: - X_train (numpy.ndarray) – inputs. Shape: (n, d) or (n, m, d).
- hyps (dict.) – dictionary of hyperparameters for Gaussian process.
- str_cov (str.) – the name of covariance function.
- fix_noise (bool., optional) – flag for fixing a noise.
- use_gradient (bool., optional) – flag for computing and returning gradients of negative log marginal likelihood.
- debug (bool., optional) – flag for printing log messages.
Returns: a tuple of kernel matrix over X_train, kernel matrix inverse, and gradients of kernel matrix. If use_gradient is False, gradients of kernel matrix would be None.
Return type: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray)
Raises: AssertionError
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bayeso.covariance.
grad_cov_main
(str_cov: str, X: numpy.ndarray, Xp: numpy.ndarray, hyps: dict, fix_noise: bool, same_X_Xp: bool = True, jitter: float = 1e-05) → numpy.ndarray¶ 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).
- Xp (numpy.ndarray) – another inputs. Shape: (m, d).
- hyps (dict.) – dictionary of hyperparameters for covariance function.
- fix_noise (bool.) – flag for fixing a noise.
- same_X_Xp (bool., optional) – flag for checking X and Xp 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
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bayeso.covariance.
grad_cov_matern32
(cov_X_Xp: numpy.ndarray, X: numpy.ndarray, Xp: numpy.ndarray, hyps: dict, num_hyps: int, fix_noise: bool) → numpy.ndarray¶ It computes gradients of Matern 3/2 kernel over X and Xp, where hyps is given.
Parameters: - cov_X_Xp (numpy.ndarray) – covariance matrix. Shape: (n, m).
- X (numpy.ndarray) – one inputs. Shape: (n, d).
- Xp (numpy.ndarray) – another inputs. Shape: (m, d).
- hyps (dict.) – dictionary of hyperparameters for covariance function.
- num_hyps (int.) – the number of hyperparameters == l.
- fix_noise (bool.) – flag for fixing a noise.
Returns: gradient matrix over hyperparameters. Shape: (n, m, l).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
grad_cov_matern52
(cov_X_Xp: numpy.ndarray, X: numpy.ndarray, Xp: numpy.ndarray, hyps: dict, num_hyps: int, fix_noise: bool) → numpy.ndarray¶ It computes gradients of Matern 5/2 kernel over X and Xp, where hyps is given.
Parameters: - cov_X_Xp (numpy.ndarray) – covariance matrix. Shape: (n, m).
- X (numpy.ndarray) – one inputs. Shape: (n, d).
- Xp (numpy.ndarray) – another inputs. Shape: (m, d).
- hyps (dict.) – dictionary of hyperparameters for covariance function.
- num_hyps (int.) – the number of hyperparameters == l.
- fix_noise (bool.) – flag for fixing a noise.
Returns: gradient matrix over hyperparameters. Shape: (n, m, l).
Return type: numpy.ndarray
Raises: AssertionError
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bayeso.covariance.
grad_cov_se
(cov_X_Xp: numpy.ndarray, X: numpy.ndarray, Xp: numpy.ndarray, hyps: dict, num_hyps: int, fix_noise: bool) → numpy.ndarray¶ It computes gradients of squared exponential kernel over X and Xp, where hyps is given.
Parameters: - cov_X_Xp (numpy.ndarray) – covariance matrix. Shape: (n, m).
- X (numpy.ndarray) – one inputs. Shape: (n, d).
- Xp (numpy.ndarray) – another inputs. Shape: (m, d).
- hyps (dict.) – dictionary of hyperparameters for covariance function.
- num_hyps (int.) – the number of hyperparameters == l.
- fix_noise (bool.) – flag for fixing a noise.
Returns: gradient matrix over hyperparameters. Shape: (n, m, l).
Return type: numpy.ndarray
Raises: AssertionError