Dragon

Degenerate Gaussian (DG) score-based causal discovery

Installation

1. Download the latest Dragon.mltbx file from the release/ folder.
2. Double-click Dragon.mltbx.
3. MATLAB will automatically install the toolbox and add the required paths.

Function and Parameters

DG_M3HC(data, discreteVars, predefined, forbidden, maxCondSet, threshold, tol, verbose, cor, skeleton)

Run Dragon_M3HC.

Parameters

Parameter	Type	Description
data	matrix	Input data matrix of shape (n_samples, n_variables).
discreteVars	vector	Indices of discrete variables. Default: [].
predefined	cell array	Predefined directed edges {[i,j]} representing i -> j. Default: {}.
forbidden	cell array	Forbidden directed edges {[i,j]} representing i -> j. Default: {}.
maxCondSet	integer	Maximum conditioning set size used by MMPC. Default: 10.
threshold	double	Significance level used by MMPC. Default: 0.05.
tol	double	Numerical tolerance used in score computation. Default: 1e-6.
verbose	logical	Whether to print debugging information. Default: false.
cor	logical	If true, use the correlation matrix; otherwise use the covariance matrix. Default: false.
skeleton	string	Method used to construct the initial skeleton. Default: "MMPC".

Returns

Return	Type	Description
mag	matrix	Estimated ancestral graph.
curScore	double	Final overall DG-BIC score.
iter	integer	Number of greedy search iterations used.
gs	struct	Records of selected iterations during greedy search.
skeleton_final	cell array	Final skeleton obtained before greedy search.

---

mag = ag2mag(ag)

Convert an ancestral graph into a maximal ancestral graph (MAG) over the same variables.

Parameters

Parameter	Type	Description
ag	matrix	Input ancestral graph represented using the same matrix encoding as MAG.

Returns

Return	Type	Description
mag	matrix	Converted maximal ancestral graph (MAG). Additional bidirected edges may be added when inducing paths are detected between non-adjacent variables.

MAG Encoding

The returned MAG is represented as an adjacency matrix:

Pattern	Interpretation
mag(i,j)=2, mag(j,i)=3	i → j
mag(i,j)=3, mag(j,i)=2	j → i
mag(i,j)=2, mag(j,i)=2	i ↔ j
mag(i,j)=0, mag(j,i)=0	No edge

Usage

kingdom = "BacteriaClay";
% kingdom = "BacteriaSand";
% kingdom = "combi";

toolboxRoot = fileparts(which("DG_M3HC"));
dataFile = fullfile(toolboxRoot, "data", kingdom, "variables_all.csv");

dataOri = readtable(dataFile, ...
    "Delimiter", ",", ...
    "ReadVariableNames", true, ...
    "ReadRowNames", true);

data = table2array(dataOri);
nVars = size(data, 2);

numBoot = 100;
n = size(data, 1);

rng(123)

for id = 0:numBoot
    fprintf("\n==========================================================\n");
    fprintf("Bootstrap: %d\n", id);

    if id == 0
        sample = data;
    else
        idx = randi(n, n, 1);
        sample = data(idx, :);
    end

    if kingdom == "combi"
        discreteVars = [11, 20, 21, 25];
        managementVars = [20, 21, 22, 23, 24, 25];
    else
        discreteVars = [19, 20, 24];
        managementVars = [19, 20, 21, 22, 23, 24];
    end

    isDiscrete = false(1, nVars);
    isDiscrete(discreteVars) = true;
    sample(:, ~isDiscrete) = zscore(sample(:, ~isDiscrete));

    forbiddenEdges = {};
    for i = 1:nVars
        for j = managementVars
            if i ~= j
                forbiddenEdges = [forbiddenEdges, [i, j]];
            end
        end
    end

    fprintf("Running DG_M3HC...\n")
    [m3hcMag, m3hc_bs, m3hcIters, m3hc, mmpc_final] = ...
        DG_M3HC(sample, discreteVars, {}, forbiddenEdges);

    m3hcMag = ag2mag(m3hcMag);
end