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Update index.md #169

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15 changes: 9 additions & 6 deletions docs/src/index.md
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Expand Up @@ -14,11 +14,17 @@ Causal inference is by no means an easy subject. Readers without any prior expos

There are also tutorials and examples linked in the navigation bar of this package.

## Implementation Details
See the [Library](https://mschauer.github.io/CausalInference.jl/latest/library/) for implemented functionality.

The PC algorithm was tested on random DAGs by comparing the result of the PC algorithm using the *d*-separation oracle with the CPDAG computed with Chickering's DAG->CPDAG conversion algorithm (implemented as [`dsep`](@ref) and [`cpdag`](@ref) in this package).

See the [Library](https://mschauer.github.io/CausalInference.jl/latest/library/) for other implemented functionality.
## Performance and Implementation Details

The package uses the very efficient [Graphs.jl](https://github.com/JuliaGraphs/Graphs.jl) package internally.
The speed of the PC and GES algorithm is comparable with the C++ code of the R package `pcalg`. The exact score-based algorithm scales to 20-25 variables on consumer hardware, which comes close to the theoretical limits of these approaches.
A couple of packages provide high-performance implementatiosn of algorithms or provide performance relevant infrastructure:
[CliqueTrees.jl](https://github.com/AlgebraicJulia/CliqueTrees.jl), [NearestNeighbors.jl](https://github.com/KristofferC/NearestNeighbors.jl) [Memoization.jl](https://github.com/marius311/Memoization.jl), [PrecompileTools.jl](https://github.com/JuliaLang/PrecompileTools.jl), [ThreadsX.jl](https://github.com/tkf/ThreadsX.jl).

The PC algorithm was tested on random DAGs by comparing the result of the PC algorithm using the *d*-separation oracle with the CPDAG computed with Chickering's DAG->CPDAG conversion algorithm (implemented as [`dsep`](@ref) and [`cpdag`](@ref) in this package).

The algorithms use the `SimpleGraph` and `SimpleDiGraph` graph representation of the Julia package [Graphs](https://github.com/JuliaGraphs/Graphs.jl).
Both types of graphs are represented by sorted adjacency lists (vectors of vectors in the Graphs implementation).
Expand All @@ -27,9 +33,6 @@ CPDAGs are just modeled as `SimpleDiGraph`s, where unoriented edges are represen

The listing algorithms for adjustment sets are implemented from scratch using an memority efficient iterator protocol to handle large problems.

## Performance
The speed of the PC and GES algorithm is comparable with the C++ code of the R package `pcalg`. The exact score-based algorithm scales to 20-25 variables on consumer hardware, which comes close to the theoretical limits of these approaches.

## Plotting
Main package provides a text-based output describing all identified edges for PC and FCI algorithm ([`plot_pc_graph_text`](@ref) and [`plot_fci_graph_text`](@ref), respectively).

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