temporal_priors¶

Bases: tikreg.temporal_priors.TemporalPrior

Specify a custom temporal MVN prior.

__init__(self, *args, **kwargs)¶

Parameters:	covmat : 2D np.ndarray (d d) Covariance matrix of MVN delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to size of prior np.arange(d). hhparams : list_like, optional MVN hyper-prior parameters to evaluate. Only used if the prior is constructed from a hyper-prior. Defaults to [0].

Examples

>>> mat = np.random.randn(5, 5)
>>> cov = np.dot(mat.T, mat)
>>> custom_prior = CustomPrior(cov)
>>> prior_covar = custom_prior.get_prior()
>>> print(prior_covar.shape)
(5, 5)
>>> print(np.round(prior_covar, 2)) # doctest: +SKIP
[[ 4.98  0.   -0.66 -2.72 -3.89]
 [ 0.   12.28 -5.91  0.49 -4.39]
 [-0.66 -5.91  9.88 -2.15  7.56]
 [-2.72  0.49 -2.15  5.49  3.13]
 [-3.89 -4.39  7.56  3.13 12.95]]

Bases: tikreg.temporal_priors.TemporalPrior

Gaussian kernel temporal prior (a.k.a RBF kernel).

__init__(self, delays=None, sigma=1.0, **kwargs)¶

Construct a temporal MVN prior from a Gaussian (RBF) kernel

Parameters:

delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to: [0,1,2,3,4]. sigma : scalar, optional The width of the Gaussian. Defaults to 1. hhparams : list_like, optional Parameters used to regularize the computation of the prior from the penalty. Defaults to sigma value used on instantiation: [sigma]. dodetnorm : bool, optional Set the determinat of the initial prior to 1.

References

For a great description of Gaussian Processes and their relationship to RBF Kernels: https://distill.pub/2019/visual-exploration-gaussian-processes/

Examples

>>> gaussian_prior = GaussianKernelPrior(delays=np.arange(5))
>>> prior_covar = gaussian_prior.get_prior()
>>> print(prior_covar.shape)
(5, 5)
>>> print(np.round(prior_covar, 2))
[[1.   0.61 0.14 0.01 0.  ]
 [0.61 1.   0.61 0.14 0.01]
 [0.14 0.61 1.   0.61 0.14]
 [0.01 0.14 0.61 1.   0.61]
 [0.   0.01 0.14 0.61 1.  ]]

get_prior(self, alpha=1.0, hhparam=1.0, dodetnorm=False)¶

Gaussian/RBF kernel as a temporal prior covariance matrix.

Parameters:	alpha : scalar, optional The regularization scale (i.e. lambda). hhparam : scalar, optional The width of the Gaussian Defaults to 1. dodetnorm : bool, optional Set the determinat of the prior covariance matrix to 1.

Bases: tikreg.temporal_priors.TemporalPrior

Haemodynamic response function prior

__init__(self, delays=None, dt=2.0, duration=20, **kwargs)¶

Generates a discrete sampling of the HRF.

The time samples are generated as: time_samples = np.arange(0, duration, dt)

And the corresponding delays: delays = np.arange(len(time_samples))

Parameters:	dt : float Sampling rate of the BOLD signal (TR). duration : int Duration in seconds over which to sample the HRF. delays : list_like, optional Defaults to all delays spanning the requested duration.

Examples

>>> hrf_prior = HRFPrior(delays=range(5), dt=2.0, duration=20)
>>> print(hrf_prior.delays)
[0 1 2 3 4]
>>> prior_covar = hrf_prior.get_prior()
>>> print(prior_covar.shape)
(5, 5)
>>> print(np.round(prior_covar, 2))
[[0.   0.   0.   0.   0.  ]
 [0.   0.44 0.55 0.22 0.18]
 [0.   0.55 1.28 0.97 0.54]
 [0.   0.22 0.97 1.   0.56]
 [0.   0.18 0.54 0.56 0.36]]

Bases: tikreg.temporal_priors.TemporalPrior

Build a prior from a Tikhnov temporal penalty covariance.

__init__(self, penalty, delays=None, wishart=True, **kwargs)¶

Parameters:

penalty : 2D np.ndarray (d, d) Temporal penalty covariance. If the Tikhhov temporal penalty is C, then the temporal penalty covariance is: np.dot(C.T, C) delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to np.arange(d) wishart : bool, optional Regularize the temporal 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, hhparam=0.0, dodetnorm=False)¶

Convert the penalty to a prior.

Parameters:	alpha : scalar The regularization scale on the prior (i.e. lambda) hhparam : 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 (d, d) Regularized prior from penalty. By default, no regularization is applied.

Notes

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

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

set_wishart(self, wishart)¶

Set the covariance of the hyper-prior regularization.

wishart : 2D np.ndarray (d,d)

Defaults to an identity.

Bases: tikreg.temporal_priors.PriorFromPenalty

Smoothness temporal MVN prior.

__init__(self, delays=[0, 1, 2, 3, 4], order=2, wishart=True, **kwargs)¶

Parameters:

delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to: [0,1,2,3,4]. order : even integer, optional The order of the difference operator that defines the smoothness prior. Defaults to 2 for a second-order difference operator. wishart : bool, optional Regularize the temporal 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.

Examples

>>> smoothness_prior = SmoothnessPrior(delays=np.arange(5))
>>> print(smoothness_prior.penalty)
[[ 5. -4.  1.  0.  0.]
 [-4.  6. -4.  1.  0.]
 [ 1. -4.  6. -4.  1.]
 [ 0.  1. -4.  6. -4.]
 [ 0.  0.  1. -4.  5.]]
>>> prior_covar = smoothness_prior.get_prior()
>>> print(prior_covar.shape)
(5, 5)
>>> print(np.round(prior_covar, 2))
[[1.53 2.22 2.25 1.78 0.97]
 [2.22 3.78 4.   3.22 1.78]
 [2.25 4.   4.75 4.   2.25]
 [1.78 3.22 4.   3.78 2.22]
 [0.97 1.78 2.25 2.22 1.53]]

Bases: tikreg.temporal_priors.TemporalPrior

Equivalent to ridge regression.

__init__(self, delays=[0, 1, 2, 3, 4], **kwargs)¶

Parameters:	delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to: [0,1,2,3,4].

Examples

>>> spherical_prior = SphericalPrior(delays=np.arange(5))
>>> prior_covar = spherical_prior.get_prior()
>>> print(prior_covar.shape)
(5, 5)
>>> print(np.round(prior_covar, 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.]]

Bases: tikreg.BasePrior

Basic temporal MVN prior.

__init__(self, prior, delays=None, hhparams=[0.0], **kwargs)¶

Parameters:	prior : 2D np.ndarray (d d) Covariance matrix of MVN delays : list_like, optional Number of delays to use. Only positive delays supported. Defaults to size of prior np.arange(d). hhparams : list_like, optional MVN hyper-prior parameters to evaluate. Only used if the prior is constructed from a hyper-prior. Defaults to [0].

get_hhparams(self)¶

Return the active hyper-prior parameters.

set_hhparameters(self, hhparams)¶

Set the hyper-prior parameters