qumphy.uq module

File: qumphy/uq.py Project: 22HLT01 QUMPHY Contact: oskar.pfeffer@ptb.de Gitlab: https://gitlab.com/qumphy Description: Uncertainty quantification utilities.

qumphy.uq.deep_ensemble(models, data, weights=None)[source]

Compute deep ensemble of the data using the given models.

Return type:

np.ndarray

Parameters:

  • models (list) – List of callable models. Expected to return type np.ndarray.

  • data (np.ndarray) – Input data.

  • weights (np.ndarray, optional) – Weights for each model.

Returns:

Weighted model output predictions.

Return type:

np.ndarray

Examples

Compute unweighted deep ensemble prediction of two models on given data.

>>> model0 = lambda x : np.dot(np.zeros((1, 2)), x.T).reshape(-1, 1)
>>> model1 = lambda x : np.dot(np.ones((1, 2)), x.T).reshape(-1, 1)
>>> data = np.array([[0.0, 0.0], [0.0, 1.0], [1.0, 0.0], [1.0, 1.0]])
>>> deep_ensemble([model0, model1], data)
[[0. ]
 [0.5]
 [0.5]
 [1. ]]

Compute weighted deep ensemble prediction of two models on given data.

>>> model0 = lambda x : np.dot(np.zeros((1, 2)), x.T).reshape(-1, 1)
>>> model1 = lambda x : np.dot(np.ones((1, 2)), x.T).reshape(-1, 1)
>>> data = np.array([[0.0, 0.0], [0.0, 1.0], [1.0, 0.0], [1.0, 1.0]])
>>> weights=np.array([0.0, 1.0])
>>> deep_ensemble([model0, model1], data)
[[0.]
 [1.]
 [1.]
 [2.]]
qumphy.uq.deep_ensemble_gaussian(prediction_mean, prediction_var, weights=None)[source]

Compute deep ensemble using the given predictions.

Return type:

typing.Tuple[np.ndarray, np.ndarray]

Parameters:

  • prediction_mean (np.ndarray) – Mean of the predicted gaussian distribution.

  • prediction_std (np.ndarray) – Variance of the predicted gaussian distribution.

  • weights (np.ndarray, optional) – Weights for each model.

Returns:

Weighted ensemble prediction mean and variance.

Return type:

Tuple[np.ndarray, np.ndarray]

Examples

Compute deep ensemble using the given predictions. Shape of prediction_mean and prediction_var should be:

[#models, #samples, #outputs]

>>> prediction_mean_1 = np.array([[[0.0], [0.5]], [[0.5], [1.0]]])
>>> prediction_mean_2 = np.array([[[1.0], [0.5]], [[0.5], [1.0]]])
>>> prediction_var_1 = np.array([[[0.0], [1.0]], [[0.5], [1.0]]])
>>> prediction_var_2 = np.array([[[0.0], [0.0]], [[0.5], [1.0]]])
>>> prediction_mean = np.array([prediction_mean_1, prediction_mean_2])
>>> prediction_var = np.array([prediction_var_1, prediction_var_2])
>>> weights = np.array([0.25, 0.75])
>>> deep_ensemble_gaussian(prediction_mean, prediction_var, weights)