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), list of tuples (callable proximal operator of f_i, linear operator L_i) or None) –

    If callable:

    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).

    If list of tuples (callable proximal operator of f_i, linear operator L_i):

    Each callable proximal operator of f_i accepts two arguments (x, p) and should return the minimizer of p/2||x-z||^2 + f(x) over z for some f. The corresponding regularization takes the form

    sum_i f_i(L_i x),

    where the sum ranges from 1 to an arbitrary n.

  • projector (callable 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.

  • constraint (string or None) –

    Preset constraints that generate the corresponding proximal parameter. 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

  • regularization (string or None) –

    Preset regularization that generate the corresponding proximal parameter. Can be set to “l1” or ‘tv’. Required for use in Gibbs in future update. For “l1” or “tv”, the following additional parameters can be passed:

    strengthscalar

    Regularization parameter, i.e., strength*||Lx||_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

strength

transformation