graphdot.model.gaussian_process.outlier_detector module

class graphdot.model.gaussian_process.outlier_detector.GPROutlierDetector(kernel, sigma_bounds=(0.0001, inf), beta=1e-08, optimizer=True, normalize_y=False, kernel_options={})[source]

Bases: graphdot.model.gaussian_process.base.GaussianProcessRegressorBase

Gaussian process regression (GPR) with noise/outlier detection via maximum likelihood estimation.

Parameters:
  • kernel (kernel instance) – The covariance function of the GP.
  • sigma_bounds (a tuple of two floats) – As Value added to the diagonal of the kernel matrix during fitting. The 2-tuple will be regarded as the lower and upper bounds of the values added to each diagonal element, which will be optimized individually by training. Larger values correspond to increased noise level in the observations. A practical usage of this parameter is to prevent potential numerical stability issues during fitting, and ensures that the kernel matrix is always positive definite in the precense of duplicate entries and/or round-off error.
  • beta (float > 0) – Cutoff value on the singular values for the spectral pseudoinverse computation, which serves as a backup mechanism to invert the kernel matrix in case if it is singular.
  • optimizer (one of (str, True, None, callable)) – A string or callable that represents one of the optimizers usable in the scipy.optimize.minimize method. If None, no hyperparameter optimization will be carried out in fitting. If True, the optimizer will default to L-BFGS-B.
  • normalize_y (boolean) – Whether to normalize the target values y so that the mean and variance become 0 and 1, respectively. Recommended for cases where zero-mean, unit-variance kernels are used. The normalization will be reversed when the GP predictions are returned.
  • kernel_options (dict, optional) – A dictionary of additional options to be passed along when applying the kernel to data.
fit(X, y, w, udist=None, tol=0.0001, repeat=1, theta_jitter=1.0, verbose=False)[source]

Train a GPR model. If the optimizer argument was set while initializing the GPR object, the hyperparameters of the kernel will be optimized using the specified loss function.

Parameters:
  • X (list of objects or feature vectors.) – Input values of the training data.
  • y (1D array) – Output/target values of the training data.
  • w (float) – The strength of L1 penalty on the noise terms.
  • udist (callable) – A random number generator for the initial guesses of the uncertainties. A lognormal distribution will be used by default if the argument is None.
  • tol (float) – Tolerance for termination.
  • repeat (int) – Repeat the hyperparameter optimization by the specified number of times and return the best result.
  • theta_jitter (float) – Standard deviation of the random noise added to the initial logscale hyperparameters across repeated optimization runs.
  • verbose (bool) – Whether or not to print out the optimization progress and outcome.
Returns:

self – returns an instance of self.
Return type:

GaussianProcessRegressor
log_marginal_likelihood(theta_ext, X=None, y=None, eval_gradient=False, clone_kernel=True, verbose=False)[source]

Returns the log-marginal likelihood of a given set of log-scale hyperparameters.

Parameters:
  • theta_ext (array-like) – Kernel hyperparameters and per-sample noise prior for which the log-marginal likelihood is to be evaluated. If None, the current hyperparameters will be used.
  • X (list of objects or feature vectors.) – Input values of the training data. If None, self.X will be used.
  • y (1D array) – Output/target values of the training data. If None, self.y will be used.
  • eval_gradient (boolean) – If True, the gradient of the log-marginal likelihood with respect to the kernel hyperparameters at position theta will be returned alongside.
  • clone_kernel (boolean) – If True, the kernel is copied so that probing with theta does not alter the trained kernel. If False, the kernel hyperparameters will be modified in-place.
  • verbose (boolean) – If True, the log-likelihood value and its components will be printed to the screen.
Returns:

  • log_likelihood (float) – Log-marginal likelihood of theta for training data.
  • log_likelihood_gradient (1D array) – Gradient of the log-marginal likelihood with respect to the kernel hyperparameters at position theta. Only returned when eval_gradient is True.
predict(Z, return_std=False, return_cov=False)[source]

Predict using the trained GPR model.

Parameters:
  • Z (list of objects or feature vectors.) – Input values of the unknown data.
  • return_std (boolean) – If True, the standard-deviations of the predictions at the query points are returned along with the mean.
  • return_cov (boolean) – If True, the covariance of the predictions at the query points are returned along with the mean.
Returns:

  • ymean (1D array) – Mean of the predictive distribution at query points.
  • std (1D array) – Standard deviation of the predictive distribution at query points.
  • cov (2D matrix) – Covariance of the predictive distribution at query points.
y_uncertainty

The learned uncertainty magnitude of each training sample.