bayeso.tp.tp

It defines Student-\(t\) process regression.

bayeso.tp.tp.predict_with_cov(X_train: ndarray, Y_train: ndarray, X_test: ndarray, cov_X_X: ndarray, inv_cov_X_X: ndarray, hyps: dict, str_cov: str = 'matern52', prior_mu: Callable | None = None, debug: bool = False) → Tuple[float, ndarray, ndarray, ndarray]

This function returns degree of freedom, posterior mean, posterior standard variance, and posterior covariance functions over X_test, computed by Student-$t$ process regression with X_train, Y_train, cov_X_X, inv_cov_X_X, and hyps.

Parameters:

  • X_train (numpy.ndarray) – inputs. Shape: (n, d) or (n, m, d).

  • Y_train (numpy.ndarray) – outputs. Shape: (n, 1).

  • X_test (numpy.ndarray) – inputs. Shape: (l, d) or (l, m, d).

  • cov_X_X (numpy.ndarray) – kernel matrix over X_train. Shape: (n, n).

  • inv_cov_X_X (numpy.ndarray) – kernel matrix inverse over X_train. Shape: (n, n).

  • hyps (dict.) – dictionary of hyperparameters for Student-$t$ process.

  • str_cov (str., optional) – the name of covariance function.

  • prior_mu (NoneType, or callable, optional) – None, or prior mean function.

  • debug (bool., optional) – flag for printing log messages.

Returns:

a tuple of degree of freedom, posterior mean function over X_test, posterior standrad variance function over X_test, and posterior covariance matrix over X_test. Shape: ((), (l, 1), (l, 1), (l, l)).

Return type:

tuple of (float, numpy.ndarray, numpy.ndarray, numpy.ndarray)

Raises:

AssertionError

bayeso.tp.tp.predict_with_hyps(X_train: ndarray, Y_train: ndarray, X_test: ndarray, hyps: dict, str_cov: str = 'matern52', prior_mu: Callable | None = None, debug: bool = False) → Tuple[float, ndarray, ndarray, ndarray]

This function returns degree of freedom, posterior mean, posterior standard variance, and posterior covariance functions over X_test, computed by Student-$t$ process regression with X_train, Y_train, and hyps.

Parameters:

  • X_train (numpy.ndarray) – inputs. Shape: (n, d) or (n, m, d).

  • Y_train (numpy.ndarray) – outputs. Shape: (n, 1).

  • X_test (numpy.ndarray) – inputs. Shape: (l, d) or (l, m, d).

  • hyps (dict.) – dictionary of hyperparameters for Student-$t$ process.

  • str_cov (str., optional) – the name of covariance function.

  • prior_mu (NoneType, or callable, optional) – None, or prior mean function.

  • debug (bool., optional) – flag for printing log messages.

Returns:

a tuple of degree of freedom, posterior mean function over X_test, posterior standrad variance function over X_test, and posterior covariance matrix over X_test. Shape: ((), (l, 1), (l, 1), (l, l)).

Return type:

tuple of (float, numpy.ndarray, numpy.ndarray, numpy.ndarray)

Raises:

AssertionError

bayeso.tp.tp.predict_with_optimized_hyps(X_train: ndarray, Y_train: ndarray, X_test: ndarray, str_cov: str = 'matern52', str_optimizer_method: str = 'SLSQP', prior_mu: Callable | None = None, fix_noise: float = True, debug: bool = False) → Tuple[float, ndarray, ndarray, ndarray]

This function returns degree of freedom, posterior mean, posterior standard variance, and posterior covariance functions over X_test, computed by the Student-$t$ process regression optimized with X_train and Y_train.

Parameters:

  • X_train (numpy.ndarray) – inputs. Shape: (n, d) or (n, m, d).

  • Y_train (numpy.ndarray) – outputs. Shape: (n, 1).

  • X_test (numpy.ndarray) – inputs. Shape: (l, d) or (l, m, d).

  • str_cov (str., optional) – the name of covariance function.

  • str_optimizer_method (str., optional) – the name of optimization method.

  • prior_mu (NoneType, or callable, optional) – None, or prior mean function.

  • fix_noise (bool., optional) – flag for fixing a noise.

  • debug (bool., optional) – flag for printing log messages.

Returns:

a tuple of degree of freedom, posterior mean function over X_test, posterior standrad variance function over X_test, and posterior covariance matrix over X_test. Shape: ((), (l, 1), (l, 1), (l, l)).

Return type:

tuple of (float, numpy.ndarray, numpy.ndarray, numpy.ndarray)

Raises:

AssertionError

bayeso.tp.tp.sample_functions(nu: float, mu: ndarray, Sigma: ndarray, num_samples: int = 1) → ndarray

It samples num_samples functions from multivariate Student-$t$ distribution (nu, mu, Sigma).

Parameters:

  • mu (numpy.ndarray) – mean vector. Shape: (n, ).

  • Sigma (numpy.ndarray) – covariance matrix. Shape: (n, n).

  • num_samples (int., optional) – the number of sampled functions

Returns:

sampled functions. Shape: (num_samples, n).

Return type:

numpy.ndarray

Raises:

AssertionError