RegularizedGaussian

class cuqi.implicitprior.RegularizedGaussian(mean=None, cov=None, prec=None, sqrtcov=None, sqrtprec=None, proximal=None, projector=None, constraint=None, regularization=None, **kwargs)

Implicit Regularized Gaussian.

Defines a so-called implicit prior based on a Gaussian distribution with implicit regularization. The regularization can be defined in the form of a proximal operator or a projector. Alternatively, preset constraints and regularization can be used.

Precisely one of proximal, projector, constraint or regularization needs to be provided. Otherwise, an error is raised.

Can be used as a prior in a posterior which can be sampled with the RegularizedLinearRTO sampler.

For more details on implicit regularized Gaussian see the following paper:

[1] Everink, Jasper M., Yiqiu Dong, and Martin S. Andersen. “Sparse Bayesian inference with regularized Gaussian distributions.” Inverse Problems 39.11 (2023): 115004.

Parameters:

• mean – See Gaussian for details.

• cov – See Gaussian for details.

• prec – See Gaussian for details.

• sqrtcov – See Gaussian for details.

• sqrtprec – See Gaussian for details.

• proximal (callable f(x, scale) or None) – Euclidean proximal operator f of the regularization function g, that is, a solver for the optimization problem min_z 0.5||x-z||_2^2+scale*g(x).

projectorcallable f(x) or None

Euclidean projection onto the constraint C, that is, a solver for the optimization problem min_(z in C) 0.5||x-z||_2^2.

constraintstring or None

Preset constraints. Can be set to “nonnegativity” and “box”. Required for use in Gibbs. For “box”, the following additional parameters can be passed:

lower_boundarray_like or None

Lower bound of box, defaults to zero

upper_boundarray_like

Upper bound of box, defaults to one

regularizationstring or None

Preset regularization. Can be set to “l1”. Required for use in Gibbs in future update. For “l1”, the following additional parameters can be passed:

strengthscalar

Regularization parameter, i.e., strength*||x||_1 , defaults to one

__init__(mean=None, cov=None, prec=None, sqrtcov=None, sqrtprec=None, proximal=None, projector=None, constraint=None, regularization=None, **kwargs)

Initialize the core properties of the distribution.

Parameters:

• name (str, default None) – Name of distribution.

• geometry (Geometry, default _DefaultGeometry (or None)) – Geometry of distribution.

• is_symmetric (bool, default None) – Indicator if distribution is symmetric.

Methods

__init__([mean, cov, prec, sqrtcov, ...])	Initialize the core properties of the distribution.
constraint_options()
disable_FD()	Disable finite difference approximation for logd gradient.
enable_FD([epsilon])	Enable finite difference approximation for logd gradient.
get_conditioning_variables()	Return the conditioning variables of this distribution (if any).
get_mutable_variables()	Return any public variable that is mutable (attribute or property) except those in the ignore_vars list
get_parameter_names()	Returns the names of the parameters that the density can be evaluated at or conditioned on.
gradient(*args, **kwargs)	Returns the gradient of the log density at x.
logd(*args, **kwargs)	Evaluate the un-normalized log density function of the distribution.
logpdf(x)	Evaluate the log probability density function of the distribution.
pdf(x)	Evaluate the log probability density function of the distribution.
regularization_options()
sample([N])	Sample from the distribution.
to_likelihood(data)	Convert conditional distribution to a likelihood function given observed data

Attributes

FD_enabled	Returns True if finite difference approximation of the logd gradient is enabled.
FD_epsilon	Spacing for the finite difference approximation of the logd gradient.
cov
dim	Return the dimension of the distribution based on the geometry.
gaussian
geometry	Return the geometry of the distribution.
is_cond	Returns True if instance (self) is a conditional distribution.
mean
name	Name of the random variable associated with the density.
prec
preset
proximal
sqrtcov
sqrtprec