StandardMessagePassingRules

StandardMessagePassingRules holds the rules of the standard factor nodes: the distributions a model uses most, the arithmetic functions, Boolean logic, the mixtures and the probit link, an expectation propagation node. Load it next to an engine, such as ReactiveMP, and every rule is available. A model written with RxInfer uses the nodes by their usual names, x ~ NormalMeanVariance(μ, v) or y ~ x + z. Nodes outside this set, such as Delta or AR, have packages of their own, which build on this one.

StandardMessagePassingRules

julia> result = @call_message_update_rule(
           node = NormalMeanVariance, target = :out,
           m = (μ = NormalMeanVariance(0.0, 1.0), v = PointMass(2.0)),
       );

julia> message = getresult(result);

julia> message isa NormalMeanVariance && mean(message) ≈ 0.0 && var(message) ≈ 3.0
true

A first rule call

A rule is an ordinary Julia method. @call_message_update_rule runs one by hand, as an engine would. Here it computes the message towards out of a NormalMeanVariance node, from a normal message on the mean and a known variance, a point mass:

using StandardMessagePassingRules, MessagePassingRulesBase, ExponentialFamily, BayesBase

@call_message_update_rule(
    node = NormalMeanVariance, target = :out,
    m = (μ = NormalMeanVariance(1.0, 1.0), v = PointMass(2.0)),
)

args->begin
        (μ_mean, μ_var) = mean_var(args.m[:μ])
        NormalMeanVariance(μ_mean, μ_var + mean(args.m[:v]))
    end

The call returns a RuleResult, drawn as a card: the node, the inputs it read as arrows in, and the target as the arrow out. The variances add, so the message is NormalMeanVariance(1.0, 3.0). getresult returns the message itself:

julia> using StandardMessagePassingRules, MessagePassingRulesBase, ExponentialFamily, BayesBase

julia> result = @call_message_update_rule(
           node = NormalMeanVariance, target = :out,
           m = (μ = NormalMeanVariance(1.0, 1.0), v = PointMass(2.0)),
       );

julia> message = getresult(result);

julia> message isa NormalMeanVariance && mean(message) ≈ 1.0 && var(message) ≈ 3.0
true

With marginals instead of messages, the same call selects the variational rule. That rule replaces the variance with 1/E[1/v] under the variance's marginal:

julia> message = getresult(@call_message_update_rule(
           node = NormalMeanVariance, target = :out,
           q = (μ = PointMass(1.0), v = GammaShapeRate(3.0, 4.0)),
       ));

julia> mean(message) ≈ 1.0 && var(message) ≈ inv(mean(inv, GammaShapeRate(3.0, 4.0)))
true

Which rules a node has

The engine selects a rule by the node, the target interface and the types of the inputs. An input is a message m or a marginal q. The factorisation of the approximate posterior decides which one a rule receives. It splits a node's interfaces into clusters, and under the default scheme a rule takes messages from its target's own cluster and marginals from the other clusters. One set of rules therefore serves three kinds of inference:

All of them run under the one DefaultAlgorithm. rule_coverage tabulates a node's rules:

MessagePassingRulesBase.rule_coverage(NormalMeanVariance)

The table has a row per message target (→ μ), per joint marginal (q(out, μ)) and one for the average energy. It has a column per algorithm, and each cell counts the rules. An empty row is a target that no rule reaches. Every node section on this site shows this table, generated from the loaded rules.

@which_message_update_rule shows the rule a call would run, with its source. list_rules lists all the rules of a node.

Conventions

• Variational expectations. A variational rule uses the expectations that naive variational message passing gives. A variance contributes 1/E[1/v] and a covariance E[Σ⁻¹]⁻¹, as in the nodes' average energies.
• Matrix corrections. *, dot and the rule towards MvNormalMeanPrecision's Λ read the service matrix_correction. The precision matrices that * and dot build may be singular. These rules correct them with MatrixCorrectionTools' ReplaceZeroDiagonalEntries(tiny) unless the context sets another correction, and NoCorrection() applies none. MvNormalMeanPrecision corrects nothing unless the context sets a correction.
• Sampling. The * rules between two general univariate distributions draw samples from the context's rng. MultiplicationSampling sets how many.
• Log scales. Most belief propagation rules declare the log scale of their message. Most variational rules declare none, since the free energy does not need it. A rule's card shows the log scale as undefined when the rule declares none.

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