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CausalInference.jl

A Julia package for causal inference, graphical models and structure learning with the PC algorithm. This package contains for now the classical (unstable) PC algorithm pcalg, 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 and cpdag in this package).

See the Library for other implemented functionality.

The algorithms use the SimpleGraph and SimpleDiGraph graph representation of the Julia package LightGraphs. Both types of graphs are represented by sorted adjacency lists (vectors of vectors in the LightGraphs implementation).

CPDAGs are just modeled as SimpleDiGraphs, where unoriented edges are represented by a forward and a backward directed edge.

Example

Compute skeleton graph h with separating sets S and CPDAG g from the 47x1190 data set NCI-60 on expression profiles of miRNAs and mRNAs.

using Distributions
using CausalInference
using LightGraphs

using DelimitedFiles, LinearAlgebra, Statistics

p = 0.01

# Download data
run(`wget http://nugget.unisa.edu.au/ParallelPC/data/real/NCI-60.csv`)

# Read data and compute correlation matrix
X = readdlm("NCI-60.csv", ',')
d, n = size(X)
C = Symmetric(cor(X, dims=2))

# Compute skeleton `h` and separating sets `S`
h, S = skeleton(d, gausscitest, (C, n), quantile(Normal(), 1-p/2))

# Compute the CPDAG `g`
g = pcalg(d, gausscitest, (C, n), quantile(Normal(), 1-p/2))

(Using data from T. D. Le, L. Liu et al.: Inferring microRNA–mRNA causal regulatory relationships from expression data, Bioinformatics, vol. 29, no. 6, 765–771, 2013.)

Performance

The speed of the algorithm is comparable with the C++ code of the R package pcalg after some pending optimizations.

Contribution

See issue #1 (Roadmap/Contribution) for questions and coordination of the development.

References