GitHub

Built-in Functional Forms

This section describes built-in functional forms that can be used for posterior marginal and/or messages form constraints specification. Read more information about constraints specification syntax in the Constraints Specification section.

Custom functional forms

See the ReactiveMP.jl library documentation for more information about defining novel custom functional forms that are compatible with ReactiveMP inference backend.

UnspecifiedFormConstraint

Unspecified functional form constraint is used by default and uses only analytical update rules for computing posterior marginals. Throws an error if a product of two colliding messages cannot be computed analytically.

@constraints begin 
    q(x) :: Nothing # This is the default setting
end

PointMassFormConstraint

The most basic form of posterior marginal approximation is the PointMass function. In a few words PointMass represents delta function. In the context of functional form constraints PointMass approximation corresponds to the MAP estimate. For a given distribution d - PointMass functional form simply finds the argmax of the logpdf(d, x) by default. 

@constraints begin 
    q(x) :: PointMass # Materializes to the `PointMassFormConstraint` object
end
RxInfer.PointMassFormConstraint — Type
PointMassFormConstraint

One of the form constraint objects. Constraint a message to be in a form of dirac's delta point mass. By default uses Optim.jl package to find argmin of -logpdf(x). Accepts custom optimizer callback which might be used to customise optimisation procedure with different packages or different arguments for Optim.jl package.

Keyword arguments

  • optimizer: specifies a callback function for logpdf optimisation. See also: ReactiveMP.default_point_mass_form_constraint_optimizer
  • starting_point: specifies a callback function for initial optimisation point: See also: ReactiveMP.default_point_mass_form_constraint_starting_point
  • boundaries: specifies a callback function for determining optimisation boundaries: See also: ReactiveMP.default_point_mass_form_constraint_boundaries

Custom optimizer callback interface

# This is an example of the `custom_optimizer` interface
function custom_optimizer(::Type{ Univariate }, ::Type{ Continuous }, constraint::PointMassFormConstraint, distribution)
    # should return argmin of the -logpdf(distribution)
end

Custom starting point callback interface

# This is an example of the `custom_starting_point` interface
function custom_starting_point(::Type{ Univariate }, ::Type{ Continuous }, constraint::PointMassFormConstraint, distribution)
    # built-in optimizer expects an array, even for a univariate distribution
    return [ 0.0 ] 
end

Custom boundaries callback interface

# This is an example of the `custom_boundaries` interface
function custom_boundaries(::Type{ Univariate }, ::Type{ Continuous }, constraint::PointMassFormConstraint, distribution)
    # returns a tuple of `lower` and `upper` boundaries
    return (-Inf, Inf)
end

Traits

  • is_point_mass_form_constraint = true
  • default_form_check_strategy = FormConstraintCheckLast()
  • default_prod_constraint = GenericProd()
  • make_form_constraint = PointMass (for use in @constraints macro)
source

SampleListFormConstraint

SampleListFormConstraints approximates the resulting posterior marginal (product of two colliding messages) as a list of weighted samples. Hence, it requires one of the arguments to be a proper distribution (or at least be able to sample from it). This setting is controlled with LeftProposal(), RightProposal() or AutoProposal() objects. It also accepts an optional method object, but the only one available sampling method currently is the BootstrapImportanceSampling.

@constraints begin 
    q(x) :: SampleList(1000)
    # or 
    q(y) :: SampleList(1000, LeftProposal())
end
RxInfer.SampleListFormConstraint — Type
SampleListFormConstraint(rng, strategy, method)

One of the form constraint objects. Approximates DistProduct with a SampleList object.

Traits

  • is_point_mass_form_constraint = false
  • default_form_check_strategy = FormConstraintCheckLast()
  • default_prod_constraint = GenericProd()
  • make_form_constraint = SampleList (for use in @constraints macro)
source
RxInfer.LeftProposal — Type

Uses the left argument in the prod call as the proposal distribution in the SampleList approximation.

source
RxInfer.RightProposal — Type

Uses the right argument in the prod call as the proposal distribution in the SampleList approximation.

source

FixedMarginalFormConstraint

Fixed marginal form constraint replaces the resulting posterior marginal obtained during the inference procedure with the prespecified one. Worth to note that the inference backend still tries to compute real posterior marginal and may fail during this process. Might be useful for debugging purposes. If nothing is passed then the computed posterior marginal is returned.

@constraints function block_updates(x_posterior = nothing) 
    # `nothing` returns the computed posterior marginal
    q(x) :: Marginal(x_posterior)
end
RxInfer.FixedMarginalFormConstraint — Type
FixedMarginalFormConstraint

One of the form constraint objects. Provides a constraint on the marginal distribution such that it remains fixed during inference. Can be viewed as blocking of updates of a specific edge associated with the marginal. If nothing is passed then the computed posterior marginal is returned.

Traits

  • is_point_mass_form_constraint = false
  • default_form_check_strategy = FormConstraintCheckLast()
  • default_prod_constraint = GenericProd()
  • make_form_constraint = Marginal (for use in @constraints macro)
source

CompositeFormConstraint

It is possible to create a composite functional form constraint with either + operator or using @constraints macro, e.g:

form_constraint = SampleListFormConstraint(1000) + PointMassFormConstraint()
@constraints begin 
    q(x) :: SampleList(1000) :: PointMass()
end