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https://github.com/mcosovic/FactorGraph.jl

The FactorGraph package provides the set of different functions to perform inference over the factor graph with continuous or discrete random variables using the belief propagation algorithm.
https://github.com/mcosovic/FactorGraph.jl

aging-model belief-propagation dynamical-systems factor-graph fast-algorithm forward-backward-algorithm gaussian-distribution ill-conditioned inference-algorithms julia kahan-summation linear-systems loopy-belief-propagation message-passing noisy-data random-variables state-estimation sum-product tree-graph

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The FactorGraph package provides the set of different functions to perform inference over the factor graph with continuous or discrete random variables using the belief propagation algorithm.

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README 

        
# FactorGraph



[![Documentation][documentation-badge]][documentation] ![Build][build-badge]






FactorGraph is an open-source, easy-to-use simulation tool/solver for researchers and educators provided as a Julia package, with source code released under MIT License. The FactorGraph package provides the set of different functions to perform inference over the factor graph with continuous or discrete random variables using the belief propagation (BP) algorithm, also known as the sum-product algorithm.



We have tested and verified simulation tool using different scenarios to the best of our ability. As a user of this simulation tool, you can help us to improve future versions, we highly appreciate your feedback about any errors, inaccuracies, and bugs. For more information, please visit [documentation][documentation] site.



---



#### Requirement

FactorGraph requires Julia 1.6 and higher.



---



#### Installation

To install the FactorGraph package, run the following command:

```julia-repl

pkg> add FactorGraph

```



To use FactorGraph package, add the following code to your script, or alternatively run the same command in Julia REPL:

```julia-repl

using FactorGraph

```



---



#### Quick start whitin continuous framework

The following examples are intended for a quick introduction to FactorGraph package within the continuous framework.



- The broadcast GBP algorithm:

```julia-repl

using FactorGraph



H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix

z = [0.5; 0.8; 4.1]                         # observation vector

v = [0.1; 1.0; 1.0]                         # variance vector



gbp = continuousModel(H, z, v)              # initialize the graphical model

for iteration = 1:50                        # the GBP inference

    messageFactorVariableBroadcast(gbp)     # compute messages using the broadcast GBP

    messageVariableFactorBroadcast(gbp)     # compute messages using the broadcast GBP

end

marginal(gbp)                               # compute marginals

```



- The vanilla GBP algorithm in the dynamic framework:

```julia-repl

using FactorGraph



H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix

z = [0.5; 0.8; 4.1]                         # observation vector

v = [0.1; 1.0; 1.0]                         # variance vector



gbp = continuousModel(H, z, v)              # initialize the graphical model

for iteration = 1:200                       # the GBP inference

    messageFactorVariable(gbp)              # compute messages using the vanilla GBP

    messageVariableFactor(gbp)              # compute messages using the vanilla GBP

end



dynamicFactor!(gbp;                         # integrate changes in the running GBP

    factor = 1,

    observation = 0.85,

    variance = 1e-10)

for iteration = 201:400                     # continues the GBP inference

    messageFactorVariable(gbp)              # compute messages using the vanilla GBP

    messageVariableFactor(gbp)              # compute messages using the vanilla GBP

end

marginal(gbp)                               # compute marginals

```



- The vanilla GBP algorithm in the ageing framework:

```julia-repl

using FactorGraph



H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix

z = [0.5; 0.8; 4.1]                         # observation vector

v = [0.1; 1.0; 1.0]                         # variance vector



gbp = continuousModel(H, z, v)              # initialize the graphical model

for iteration = 1:200                       # the GBP inference

    messageFactorVariable(gbp)              # compute messages using the vanilla GBP

    messageVariableFactor(gbp)              # compute messages using the vanilla GBP

end



for iteration = 1:400                       # continues the GBP inference

    ageingVariance!(gbp;                    # integrate changes in the running GBP

        factor = 3,

        initial = 1,

        limit = 50,

        model = 1,

        a = 0.05,

        tau = iteration)

    messageFactorVariable(gbp)              # compute messages using the vanilla GBP

    messageVariableFactor(gbp)              # compute messages using the vanilla GBP

end

marginal(gbp)                               # compute marginals

```



 - The forward–backward GBP algorithm over the tree factor graph:

```julia-repl

using FactorGraph



H = [1 0 0 0 0; 6 8 2 0 0; 0 5 0 0 0;       # coefficient matrix

     0 0 2 0 0; 0 0 3 8 2]

z = [1; 2; 3; 4; 5]                         # observation vector

v = [3; 4; 2; 5; 1]                         # variance vector



gbp = continuousTreeModel(H, z, v)          # initialize the tree graphical model

while gbp.graph.forward                     # inference from leaves to the root

     forwardVariableFactor(gbp)             # compute forward messages

     forwardFactorVariable(gbp)             # compute forward messages

end

while gbp.graph.backward                    # inference from the root to leaves

     backwardVariableFactor(gbp)            # compute backward messages

     backwardFactorVariable(gbp)            # compute backward messages

end

marginal(gbp)                               # compute marginals

```



---



#### Quick start whitin discrete framework

Following example is intended for a quick introduction to FactorGraph package within the discrete framework.



 - The forward–backward BP algorithm over the tree factor graph:

```julia-repl

using FactorGraph



probability1 = [1]

table1 = [0.2; 0.3; 0.4; 0.1]



probability2 = [1; 2; 3]

table2 = zeros(4, 3, 1)

table2[1, 1, 1] = 0.2; table2[2, 1, 1] = 0.5; table2[3, 1, 1] = 0.3; table2[4, 1, 1] = 0.0

table2[1, 2, 1] = 0.1; table2[2, 2, 1] = 0.1; table2[3, 2, 1] = 0.7; table2[4, 2, 1] = 0.1

table2[1, 3, 1] = 0.5; table2[2, 3, 1] = 0.2; table2[3, 3, 1] = 0.1; table2[4, 3, 1] = 0.1



probability = [probability1, probability2]

table = [table1, table2]



bp = discreteTreeModel(probability, table)  # initialize the tree graphical model

while bp.graph.forward                      # inference from leaves to the root

    forwardVariableFactor(bp)               # compute forward messages

    forwardFactorVariable(bp)               # compute forward messages

end

while bp.graph.backward                     # inference from the root to leaves

    backwardVariableFactor(bp)              # compute backward messages

    backwardFactorVariable(bp)              # compute backward messages

end

marginal(bp)                                # compute normalized marginals

```



[documentation-badge]: https://github.com/mcosovic/FactorGraph.jl/workflows/Documentation/badge.svg

[build-badge]: https://github.com/mcosovic/FactorGraph.jl/workflows/Build/badge.svg

[documentation]: https://mcosovic.github.io/FactorGraph.jl/stable/