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Project.toml

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HDF5 = "0.15.6"
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PrettyTables = "1.1.0"
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XLSX = "0.7.6"
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julia = "1.6"
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julia = "1.6"

docs/make.jl

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"Output Data" => "man/discreteTreeOutput.md",
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],
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],
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"Theoretical Background" => "man/theoretical.md",
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"Theoretical Background" => [
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"Inference in Factor Graphs" => "man/theoreticalInference.md",
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"Continuous Variables" => "man/theoreticalBelief.md"
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],
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],
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)
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docs/src/index.md

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----
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#### Continuous framework
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In the case of continuous random variables described by Gaussian distributions, we are using the linear Gaussian belief propagation (GBP) algorithm to solve the inference problem. The linear GBP model requires the set of linear equations and provides the minimum mean squared error (MMSE) estimate of the state variables. To perform inference the FactorGraph package uses several algorithms based on the [synchronous message passing schedule] (@ref synchronous):
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In the case of continuous random variables described by Gaussian distributions, we are using the linear Gaussian belief propagation (GBP) algorithm to solve the inference problem. The linear GBP model requires the set of linear equations and provides the minimum mean squared error (MMSE) estimate of the state variables. To perform inference the FactorGraph package uses several algorithms based on the [synchronous message passing schedule] (@ref synchronousSchedule):
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- [vanilla GBP algorithm] (@ref vanillaGBP);
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- [broadcast GBP algorithm] (@ref broadcastGBP);
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- [broadcast GBP with Kahan–Babuška algorithm] (@ref kahanGBP).
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Within these algorithms, the packege provides several routines to allow dynamic GBP framework:
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- [dynamic GBP algorithm] (@ref dynamicGBP);
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- [ageing GBP algorithm] (@ref ageingGBP).
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Finally, the package also includes a message passing algorithm that allows inference in tree factor graph:
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- [forward–backward algorithm] (@ref treeGBP).
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- [forward–backward algorithm] (@ref treeSchedule).
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---
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#### Discrete framework
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In the case of discrete random variables the package currently provides only the BP algorithm that allows exact inference in the tree factor graph.
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In the case of discrete random variables the package currently provides only the BP algorithm that allows exact inference in the tree factor graph:
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- [forward–backward algorithm] (@ref treeSchedule).
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---
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docs/src/man/continuousInference.md

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# [Inference](@id inferenceContinuous)
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We advise the reader to read the [theoretical background] (@ref theoretical) which provides a detailed description of the inference algorithms. To exchange information over the factor graph, the FactorGraph provides three inference approaches:
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We advise the reader to read the Section [continuous Gaussian random variables] (@ref continuousVariables) which provides a detailed description of the inference algorithms. To exchange information over the factor graph, the FactorGraph provides three inference approaches:
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- [vanilla GBP algorithm] (@ref vanillaGBP);
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- [broadcast GBP algorithm] (@ref broadcastGBP);
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- [broadcast GBP with Kahan–Babuška algorithm] (@ref kahanGBP).
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Each of the inference functions accepts only the composite type `ContinuousModel`, i.e., an output variable of the function `gbp = continuousModel()` and applies the [synchronous message passing schedule] (@ref synchronous).
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Each of the inference functions accepts only the composite type `ContinuousModel`, i.e., an output variable of the function `gbp = continuousModel()` and applies the [synchronous message passing schedule] (@ref synchronousSchedule).
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docs/src/man/continuousModel.md

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# [Graphical Model](@id graphicalModelContinuous)
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The FactorGraph supports the composite type `ContinuousModel` related with the [synchronous message passing schedule] (@ref synchronous), with three fields:
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The FactorGraph supports the composite type `ContinuousModel` related with the [synchronous message passing schedule] (@ref synchronousSchedule), with three fields:
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- `ContinuousGraph`;
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- `ContinuousInference`;
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- `ContinuousSystem`.
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#### Virtual factor nodes
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The GBP function `continuousModel()` receives arguments by keyword to set the mean and variance of the virtual factor nodes. We advise the reader to read the section [message passing schedule] (@ref synchronous) which provides a detailed description of the virtual factor nodes.
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The GBP function `continuousModel()` receives arguments by keyword to set the mean and variance of the virtual factor nodes. We advise the reader to read the Section [initialisation procedure] (@ref initialisationProcedure) which provides a detailed description of the virtual factor nodes.
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```julia-repl
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gbp = continuousModel(DATA; mean = value, variance = value)

docs/src/man/continuousTreeInference.md

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# [Inference](@id inferenceTreeContinuous)
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To exchange information over the tree factor graph, the FactorGraph provides forward–backward algorithm. We advise the reader to read the [forward–backward algorithm] (@ref treeGBP) which provides a detailed description of the inference algorithm.
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To exchange information over the tree factor graph, the FactorGraph provides forward–backward algorithm. We advise the reader to read the Section [forward–backward schedule] (@ref treeSchedule) which provides a detailed description of the inference algorithm.
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Each of the inference functions accepts only the composite type `ContinuousTreeModel`, i.e., an output variable of the function `gbp = continuousTreeModel()`.
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docs/src/man/continuousTreeModel.md

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# [Tree Graphical Model](@id graphicalTreeModelContinuous)
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The FactorGraph supports the composite type `ContinuousTreeModel` related with the [forward–backward message passing] (@ref treeGBP), with three fields:
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The FactorGraph supports the composite type `ContinuousTreeModel` related with the [forward–backward schedule] (@ref synchronousSchedule), with three fields:
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- `ContinuousTreeGraph`;
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- `ContinuousInference`;
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- `ContinuousSystem`.

docs/src/man/discreteTreeInference.md

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# [Inference](@id inferenceTreeDiscrete)
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To exchange information over the tree factor graph, the FactorGraph provides forward–backward algorithm. We advise the reader to read the [forward–backward algorithm] (@ref treeGBP) which provides a detailed description of the inference algorithm.
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To exchange information over the tree factor graph, the FactorGraph provides forward–backward algorithm. We advise the reader to read the Section [forward–backward schedule] (@ref treeSchedule) which provides a detailed description of the inference algorithm.
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Each of the inference functions accepts only the composite type `DiscreteTreeModel`, i.e., an output variable of the function `bp = discreteTreeModel()`.
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docs/src/man/discreteTreeModel.md

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# [Tree Graphical Model](@id graphicalTreeModelDiscrete)
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The FactorGraph supports the composite type `DiscreteTreeModel` related with the [forward–backward message passing] (@ref treeGBP), with three fields:
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The FactorGraph supports the composite type `DiscreteTreeModel` related with the [forward–backward message passing] (@ref treeSchedule), with three fields:
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- `DiscreteTreeGraph`;
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- `DiscreteInference`;
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- `DiscreteSystem`.

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