{
 "release": "0.6.0",
 "generated": "2026-10-16",
 "theme": "mixed and discrete data",
 "build": "pre-release Andrey 0.6.0 builds, 13 to 16 October 2026",
 "builds": [
  {
   "build": "pre-release Andrey 0.6.0 build, 13 October 2026",
   "solutions": [
    "andrey.ges.cond_gauss",
    "andrey.ges.degen_gauss",
    "andrey.pc.cond_gauss",
    "andrey.pc.degen_gauss",
    "bnlearn.hc.cond_gauss",
    "bnlearn.pc-stable.cond_gauss",
    "tetrad.fges.cond_gauss",
    "tetrad.fges.degen_gauss",
    "tetrad.pc.cond_gauss",
    "tetrad.pc.degen_gauss"
   ]
  },
  {
   "build": "pre-release Andrey 0.6.0 build, 14 October 2026",
   "solutions": [
    "andrey.hc.cond_gauss",
    "andrey.hc.degen_gauss"
   ]
  },
  {
   "build": "pre-release Andrey 0.6.0 build, 16 October 2026",
   "solutions": [
    "andrey.ges.bdeu",
    "andrey.hc.BDeu",
    "andrey.hc.BIC_categorical",
    "andrey.pc.chisq",
    "andrey.pc.gsq",
    "bnlearn.hc.BDeu",
    "bnlearn.hc.BIC_categorical",
    "bnlearn.pc-stable.chisq",
    "bnlearn.pc-stable.gsq",
    "causal-learn.ges.bdeu",
    "causal-learn.pc.chisq",
    "causal-learn.pc.gsq",
    "pgmpy.hc.BDeu",
    "pgmpy.hc.BIC_categorical"
   ]
  }
 ],
 "andrey_source": "PC and GES on mixed data run the first build; hill climbing on mixed data was rerun on a later build, on the same datasets, and the earlier hill-climbing lane's records are not used; every method on discrete data runs the discrete campaign's build",
 "regime": {
  "PC on mixed data, degenerate Gaussian test": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "PC on mixed data, conditional Gaussian test": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "GES on mixed data, degenerate Gaussian score": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "GES on mixed data, conditional Gaussian score": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "Hill climbing on mixed data, degenerate Gaussian score": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "Hill climbing on mixed data, conditional Gaussian score": {
   "name": "mixed_er",
   "description": "a conditional linear Gaussian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_mixed): the first half of the variables in causal order are categorical, each with a count of categories drawn uniformly between the setting's two bounds and its table rows drawn from a symmetric Dirichlet with concentration 1; each continuous variable is the sum of its continuous parents times weights with |w| uniform on [0.5, 2] and a random sign, a shift per category of each categorical parent (evenly spaced from -m to m, m uniform on [0.5, 2]), and standard Gaussian noise, not standardized. A categorical variable has only categorical parents."
  },
  "PC on discrete data, chi-square test": {
   "name": "discrete_er",
   "description": "a discrete Bayesian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_discrete): every variable has 2 or 3 categories, drawn uniformly, and each row of its conditional probability table is drawn from a symmetric Dirichlet with concentration 1; the samples are category codes drawn forward in causal order."
  },
  "PC on discrete data, G-square test": {
   "name": "discrete_er",
   "description": "a discrete Bayesian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_discrete): every variable has 2 or 3 categories, drawn uniformly, and each row of its conditional probability table is drawn from a symmetric Dirichlet with concentration 1; the samples are category codes drawn forward in causal order."
  },
  "GES on discrete data, BDeu score": {
   "name": "discrete_er",
   "description": "a discrete Bayesian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_discrete): every variable has 2 or 3 categories, drawn uniformly, and each row of its conditional probability table is drawn from a symmetric Dirichlet with concentration 1; the samples are category codes drawn forward in causal order."
  },
  "Hill climbing on discrete data, BDeu score": {
   "name": "discrete_er",
   "description": "a discrete Bayesian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_discrete): every variable has 2 or 3 categories, drawn uniformly, and each row of its conditional probability table is drawn from a symmetric Dirichlet with concentration 1; the samples are category codes drawn forward in causal order."
  },
  "Hill climbing on discrete data, BIC score": {
   "name": "discrete_er",
   "description": "a discrete Bayesian network on an Erdos-Renyi DAG with mean degree 2 (andrey.data.sample_discrete): every variable has 2 or 3 categories, drawn uniformly, and each row of its conditional probability table is drawn from a symmetric Dirichlet with concentration 1; the samples are category codes drawn forward in causal order."
  }
 },
 "seeds_per_setting": 5,
 "speed_floor_s": 0.1,
 "error_metric": "SHD between the estimate's CPDAG and the true DAG's CPDAG: one per variable pair whose edge differs (missing, extra, or oriented differently); a DAG estimate is compared through its CPDAG. The empty graph's SHD is the number of true edges.",
 "same_graph_test": "the same CPDAG: SHD 0 between the two packages' CPDAGs",
 "hardware": {
  "PC on mixed data, degenerate Gaussian test": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "PC on mixed data, conditional Gaussian test": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "GES on mixed data, degenerate Gaussian score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "GES on mixed data, conditional Gaussian score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "Hill climbing on mixed data, degenerate Gaussian score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "Hill climbing on mixed data, conditional Gaussian score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "PC on discrete data, chi-square test": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "PC on discrete data, G-square test": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "GES on discrete data, BDeu score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "Hill climbing on discrete data, BDeu score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  },
  "Hill climbing on discrete data, BIC score": {
   "cpu": "Intel Core i7-7820X",
   "cores_per_fit": 4
  }
 },
 "threads": "every fit runs with 4 BLAS and OpenMP threads; Tetrad's JVM sees 4 processors; bnlearn's searches run in one R thread, and pgmpy's in Python",
 "packages": {
  "tetrad": "causal-cmd 1.12.0 (tetrad-lib 7.6.3), jar SHA-1 b0e3c3fb3b0277e0a44c54dbb82f0023c4fd9e54",
  "java": "OpenJDK 21.0.6",
  "bnlearn": "5.2.1",
  "R": "4.6.1",
  "rpy2": "3.6.9",
  "causal-learn": "0.1.4.8",
  "pgmpy": "1.1.2",
  "python": "3.13.16",
  "numpy": "2.5.4",
  "scipy": "1.18.1",
  "pandas": "3.0.6"
 },
 "complete": false,
 "pending_fits": 0,
 "incomplete": [
  {
   "method": "PC on mixed data, degenerate Gaussian test",
   "comparator": "Tetrad",
   "d": 40,
   "categories": "3-5"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 10,
   "categories": "2-3"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 10,
   "categories": "3-5"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 20,
   "categories": "2-3"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 20,
   "categories": "3-5"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 40,
   "categories": "2-3"
  },
  {
   "method": "PC on mixed data, conditional Gaussian test",
   "comparator": "Tetrad",
   "d": 40,
   "categories": "3-5"
  }
 ],
 "methods": [
  {
   "method": "PC on mixed data, degenerate Gaussian test",
   "setting": "indep_test='degen_gauss', alpha=0.05",
   "solution": "andrey.pc.degen_gauss",
   "comparator": "Tetrad",
   "comparator_method": "PC",
   "comparator_setting": "--test dg-lr-test --alpha 0.05 --stableFAS --conflictRule 1 --depth -1",
   "comparator_solution": "tetrad.pc.degen_gauss",
   "regime": "mixed_er",
   "note": "Tetrad is the causal-cmd 1.12.0 jar (tetrad-lib 7.6.3), run with causal-cmd's own argument parser, parameters, and algorithm factory through a small driver that declares the categorical columns (causal-cmd's command line accepts --numCategories but never stores it, so it reads every column as continuous). Tetrad's time is its search call, timed inside the JVM; the whole process, with the JVM start and the CSV read, is recorded apart and not used. Tetrad 7.6.3's PC with the conditional Gaussian test stops with an error on some datasets (a likelihood it cannot evaluate); those fits count as failed and are not scored",
   "hardware": "Intel Core i7-7820X, 4 cores",
   "cores": 4,
   "build": "pre-release Andrey 0.6.0 build, 13 October 2026",
   "category_settings": [
    "2-3",
    "3-5"
   ],
   "fit_protocol": "one fit at a time, 4 cores per fit, 1 timed repeat and 0 warm-up fits per dataset, a 2400 s wall cap and a 30000 MB memory cap per fit",
   "same_graph_test": "the same CPDAG: SHD 0 between the two packages' CPDAGs",
   "complete": false,
   "column_rule": "every package reads a column as categorical when it holds at most 10 distinct whole numbers (Andrey: max_categories=10 with categorical inferred; Tetrad: --numCategories 10; bnlearn: such columns become factors)",
   "rows": [
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     "andrey_failed": 0,
     "comparator_ok": 10,
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     "paired": 10,
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     "between_shd": 9.0,
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     "empty_shd": 10.0,
     "andrey_worse_than_empty": 0,
     "comparator_worse_than_empty": 2,
     "andrey_fewer_errors": 5,
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     "empty_shd": 40.0,
     "andrey_worse_than_empty": 0,
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     "andrey_fewer_errors": 0,
     "comparator_fewer_errors": 0,
     "andrey_skeleton_f1": 0.9,
     "comparator_skeleton_f1": 0.9,
     "andrey_arrowhead_f1": 0.6666666666666666,
     "comparator_arrowhead_f1": 0.6666666666666666,
     "complete": true,
     "different_graph": []
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  {
   "method": "Hill climbing on discrete data, BIC score",
   "setting": "score_func='local_score_BIC_categorical', lambda_value=1, max_iter=100000, from the empty graph",
   "solution": "andrey.hc.BIC_categorical",
   "comparator": "pgmpy",
   "comparator_method": "HillClimbSearch",
   "comparator_setting": "BIC, tabu_length=0, max_indegree=None, max_iter=100000",
   "comparator_solution": "pgmpy.hc.BIC_categorical",
   "regime": "discrete_er",
   "note": "pgmpy reads the category codes as integer columns, named by position so that its order among equal moves is fixed. HillClimbSearch with tabu_length=0 is plain hill climbing: the best add, remove, or reverse move from the empty graph until none improves the score by its epsilon, 1e-4 log-likelihood units, with no parent cap. pgmpy has no structure prior for BDeu, so the harness adds Andrey's through pgmpy's structure_prior_ratio hook. It returns a DAG, compared through its CPDAG. The two scores agree on every move (Andrey's is -2 times pgmpy's), but adding x -> y and adding y -> x always tie, and the two searches break that tie differently: Andrey takes the lower column pair, pgmpy the first in its own move order. From the first such tie on, the searches follow different paths to different local optima of the same score",
   "hardware": "Intel Core i7-7820X, 4 cores",
   "cores": 4,
   "build": "pre-release Andrey 0.6.0 build, 16 October 2026",
   "category_settings": [
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   "fit_protocol": "one fit at a time, 4 cores per fit, 1 timed repeat and 1 warm-up fits per dataset, a 1800 s wall cap and a 30000 MB memory cap per fit",
   "same_graph_test": "the same CPDAG: SHD 0 between the two packages' CPDAGs",
   "complete": true,
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  }
 ]
}