verse.utils.utils.confidence_ellipsoid

verse.utils.utils.confidence_ellipsoid(data: Dict[str, ndarray], lambda_: float = 1e-05, delta: float = 0.1, sigma: float = 0.1, param_bound: float = 1.0) → Tuple[ndarray, ndarray, float]

Compute a confidence ellipsoid over the parameter theta, where y = theta^T phi

Parameters:

• data – a dictionary {“features”: [phi_0,…,phi_N], “outputs”: [y_0,…,y_N]}

• lambda – l2 regularization parameter

• delta – confidence level

• sigma – noise covariance

• param_bound – an upper-bound on the parameter norm

Returns:

estimated theta, Gramian matrix G_N_lambda, radius beta_N