FactorGraph

FactorGraph is a Julia package for constructing factor graphs and running belief propagation algorithms.

Gaussian models can use scalar or vector variables, linear Gaussian factors, belief propagation in moment, canonical, and min-sum form, and weighted least-squares validation utilities.

Discrete finite-state models are represented with variables over finite state spaces and factor tables, with iterative sum-product inference for marginals and min-sum inference for MAP estimates.

The Gaussian and discrete APIs share support for sequential, flooding, and residual schedules, damping, exact forward-backward inference on tree-structured graphs, dynamic graph updates, and inspection helpers for graphs, messages, marginals, and estimates.

Installation

FactorGraph is registered as FactorGraph.jl. Install it from the Julia package manager:

pkg> add FactorGraph

Then load it in Julia:

using FactorGraph

Quick Start

using FactorGraph

variables = [
    GaussianVariable(:x1, 1),
    GaussianVariable(:x2, 1),
]

factors = [
    GaussianFactor(:x1, 1.0, 1.0, 0.1; label = "prior_x1"),
    GaussianFactor(:x2, 2.0, 1.0, 0.1; label = "prior_x2"),
    GaussianFactor(:x1, :x2, -1.0, [1.0 -1.0], 0.2; label = "link"),
]

graph = factorGraph(variables, factors)
inference = moment(graph)

gbp!(graph, inference; iterations = 30)

marginalMean(graph, inference, :x1)
marginalCovariance(graph, inference, :x1)

Tree Inference

When the graph is tree-structured, pass a root variable to construct a TreeFactorGraph and run exact forward-backward belief propagation:

tree = treeFactorGraph(graph; root = :x1)
inference = moment(graph)

forwardBackward!(tree, inference)

Discrete Models

variables = [
    DiscreteVariable(:x1, 2; states = [:off, :on]),
    DiscreteVariable(:x2, 2; states = [:low, :high]),
]

factors = [
    DiscreteFactor(:x1, [0.8, 0.2]; label = "prior_x1"),
    DiscreteFactor(:x1, :x2, [1.0 0.2; 0.1 0.9]; label = "link"),
]

graph = factorGraph(variables, factors)
inference = sumproduct(graph)

gbp!(graph, inference; iterations = 10)

marginalProbability(graph, inference, :x1, :on)

Documentation

The full documentation is available at mcosovic.github.io/FactorGraph.jl/stable.

It includes:

• Gaussian and discrete factor graph construction
• Iterative sum-product and min-sum belief propagation
• Forward-backward inference on tree-structured graphs
• Dynamic graph updates and stale-inference checks
• API references for types, graphs, inference, validation, and printing helpers

License

FactorGraph is released under the MIT License.