spatial_priors¶

Bases: tikreg.BasePrior

Specify a custom feature prior

__init__(self, *args, **kwargs)¶

Parameters:	covmat : 2D np.ndarray (p, p) Covariance matrix of MVN.

Examples

>>> mat = np.random.randn(5, 5)
>>> cov = np.dot(mat.T, mat)
>>> custom_prior = CustomPrior(cov)
>>> print(custom_prior.asarray.shape)
(5, 5)
>>> prior_lambda_one = custom_prior.get_prior(1.0)
>>> print(np.round(prior_lambda_one, 2)) # doctest: +SKIP
[[ 3.27 -2.02  2.18  0.05 -5.37]
 [-2.02  6.59  0.47 -1.2   3.95]
 [ 2.18  0.47  3.75  0.35 -2.52]
 [ 0.05 -1.2   0.35  5.9   1.31]
 [-5.37  3.95 -2.52  1.31 10.86]]
>>> prior_lambda_two = custom_prior.get_prior(2.0)
>>> print(np.round(prior_lambda_two, 2)) # doctest: +SKIP
[[ 0.82 -0.51  0.54  0.01 -1.34]
 [-0.51  1.65  0.12 -0.3   0.99]
 [ 0.54  0.12  0.94  0.09 -0.63]
 [ 0.01 -0.3   0.09  1.48  0.33]
 [-1.34  0.99 -0.63  0.33  2.72]]

Bases: tikreg.BasePrior

Build a prior from a Tikhnov feature penalty covariance.

__init__(self, penalty, wishart=True, **kwargs)¶

Parameters:

penalty : 2D np.ndarray (p, p) Penalty covariance. If the Tikhhov penalty is C, then the penalty covariance is: np.dot(C.T, C) wishart : bool, optional Regularize the penalty covariance before taking the inverse to compute the prior. hhparams : list_like, optional Parameters used to regularize the computation of the prior from the penalty. dodetnorm : bool, optional Set the determinat of the initial prior to 1.

get_prior(self, alpha=1.0, wishart_lambda=0.0, dodetnorm=False)¶

Convert the penalty to a prior.

Parameters:	alpha : scalar The regularization scale on the prior (i.e. lambda) wishart_lambda : scalar The regularization parameter for the hyper-prior. Defaults to 0 for no regularization. dodetnorm : bool, optional Set the determinant of the MVN prior to 1.
Returns:	regularized_prior : 2D np.ndarray (p, p) Regularized prior from penalty. By default, no regularization is applied.

Notes

\[\Sigma = (P + \gamma I)^{-1}\]

where P is the penalty covariance, \(\gamma\) is the hyper-prior parameter (hhparam).

prior2penalty(self, regularizer=0.0, dodetnorm=True)¶

set_wishart(self, wishart_prior)¶

Bases: tikreg.BasePrior

Equivalent to ridge regression.

__init__(self, feature_space, **kwargs)¶

Create a spherical MVN prior for a feature space.

Parameters:	feature_space : 2D np.ndarray (n, p) or int Matrix containing features (one column per feature). Or a scalar corresponding to the number of features (i.e. p).

Examples

>>> spherical_prior = SphericalPrior(5)
>>> print(spherical_prior.asarray.shape)
(5, 5)
>>> print(np.round(spherical_prior.asarray, 2))
[[1. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0.]
 [0. 0. 1. 0. 0.]
 [0. 0. 0. 1. 0.]
 [0. 0. 0. 0. 1.]]

get_prior(self, alpha=1.0)¶

Apply regularization to prior

Parameters:	alpha : scalar Regularization parameter (lambda).
Returns:	ridge_matrix : 2D np.ndarray (p, p) Scaled ridge matrix (i.e. \(\lambda^{-2} I_p\))

Examples

>>> spherical_prior = SphericalPrior(5)
>>> prior_covar = spherical_prior.get_prior(2.0)
>>> print(np.round(prior_covar, 2))
[[0.25 0.   0.   0.   0.  ]
 [0.   0.25 0.   0.   0.  ]
 [0.   0.   0.25 0.   0.  ]
 [0.   0.   0.   0.25 0.  ]
 [0.   0.   0.   0.   0.25]]