# Adjustment Identification Distance: A ππππππ for Causal Structure Learning
This is an early release of ππππππ π₯ and feedback is very welcome!
Just [open an issue](https://github.com/CausalDisco/gadjid/issues/new/choose) on our github repository.
If you publish research using ππππππ, please cite
[our article](https://doi.org/10.48550/arXiv.2402.08616)
```bibtex
@article{henckel2024adjustment,
title = {{Adjustment Identification Distance: A gadjid for Causal Structure Learning}},
author = {Leonard Henckel and Theo WΓΌrtzen and Sebastian Weichwald},
journal = {{arXiv preprint arXiv:2402.08616}},
year = {2024},
doi = {10.48550/arXiv.2402.08616},
}
```
## Get Started Real Quick π β Introductory Example
Just `pip install gadjid` to install the latest release of ππππππ \
and run `python -c "import gadjid; help(gadjid)"` to get started
(or see [install alternatives](https://github.com/CausalDisco/gadjid#installation--python)).
```python
import gadjid
from gadjid import example, ancestor_aid, oset_aid, parent_aid, shd
import numpy as np
help(gadjid)
example.run_parent_aid()
Gtrue = np.array([
[0, 1, 1, 1, 1],
[0, 0, 1, 1, 1],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]
], dtype=np.int8)
Gguess = np.array([
[0, 0, 1, 1, 1],
[1, 0, 1, 1, 1],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]
], dtype=np.int8)
print(ancestor_aid(Gtrue, Gguess))
print(shd(Gtrue, Gguess))
```
---
ππππππ is implemented in Rust
and can conveniently be called from Python via our Python wrapper
(implemented using [maturin](https://www.maturin.rs/) and [PyO3](https://pyo3.rs/)).
> Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We introduce a framework for developing causal distances between graphs which includes the
structural intervention distance for directed acyclic graphs as a special case. We use this framework to develop improved adjustment-based distances as well as extensions to completed partially directed acyclic graphs and causal orders. We develop polynomial-time reachability algorithms to compute the distances efficiently. In our package ππππππ, we provide implementations of our distances; they are orders of magnitude faster than the structural intervention distance and thereby provide a success metric for causal discovery that scales to graph sizes that were previously prohibitive.
## Implemented Distances
* `ancestor_aid(Gtrue, Gguess)`
* `oset_aid(Gtrue, Gguess)`
* `parent_aid(Gtrue, Gguess)`
* for convenience, the following distances are implemented, too
* `shd(Gtrue, Gguess)`
* `sid(Gtrue, Gguess)` β only for DAGs!
where Gtrue and Gguess are adjacency matrices of a DAG or CPDAG.
The functions are not symmetric in their input:
To calculate a distance,
identifying formulas for causal effects are inferred in the graph `Gguess`
and verified against the graph `Gtrue`.
Distances return a tuple `(normalised_distance, mistake_count)`
of the fraction of causal effects inferred in Gguess that are wrong relative to Gtrue, `normalised_distance`,
and the number of wrongly inferred causal effects, `mistake_count`.
There are $p(p-1)$ pairwise causal effects to infer in graphs with $p$ nodes
and we define normalisation as `normalised_distance = mistake_count / p(p-1)`.
All graphs are assumed simple, that is, at most one edge is allowed between any two nodes.
An adjacency matrix for a DAG may only contain 0s and 1s;
a `1` in row `s` and column `t` codes a directed edge `Xβ β Xβ`;
DAG inputs are validated for acyclicity.
An adjacency matrix for a CPDAG may only contain 0s, 1s and 2s;
a `2` in row `s` and column `t` codes a undirected edge `Xβ β Xβ`
(an additional `2` in row `t` and column `s` is ignored; only one of the two entries is required to code an undirected edge);
CPDAG inputs are not validated and __the user needs to ensure the adjacency matrix indeed codes a valid CPDAG (instead of just a PDAG)__.
You may also calculate the SID between DAGs via `parent_aid(DAGtrue, DAGguess)`,
but we recommend `ancestor_aid` and `oset_aid` and for CPDAG inputs our `parent_aid` does not coincide with the SID
(see also our accompanying article).
## Empirical Runtime Analysis
Experiments run on a laptop with 8 GB RAM and 4-core i5-8365U processor.
Here, for a graph with $p$ nodes,
sparse graphs have $10p$ edges in expectation,
dense graphs have $0.3p(p-1)/2$ edges in expectation,
and
sparse graphs have $0.75p$ edges in expectation.
__Maximum graph size feasible within 1 minute__
| Method | sparse | dense |
|--------------|-------:|------:|
| Parent-AID | 13005 | 960 |
| Ancestor-AID | 8200 | 932 |
| Oset-AID | 546 | 250 |
| SID in R | 255 | 239 |
__Average runtime__
| Method | x-sparse ($p=1000$) | sparse ($p=256$) | dense ($p=239$) |
|--------------|--------------------:|-----------------:|----------------:|
| Parent-AID | 6.3 ms | 22.8 ms | 189 ms |
| Ancestor-AID | 2.7 ms | 38.7 ms | 226 ms |
| Oset-AID | 3.2 ms | 4.69 s | 47.3 s |
| SID in R | ~1β2 h | ~60 s | ~60 s |
## LICENSE
ππππππ is available in source code form at <https://github.com/CausalDisco/gadjid>.
This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
If a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
See also the [MPL-2.0 FAQ](https://mozilla.org/MPL/2.0/FAQ).
Raw data
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"description": "# Adjustment Identification Distance: A \ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d for Causal Structure Learning\n\nThis is an early release of \ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d \ud83d\udc25 and feedback is very welcome!\nJust [open an issue](https://github.com/CausalDisco/gadjid/issues/new/choose) on our github repository.\n\nIf you publish research using \ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d, please cite\n[our article](https://doi.org/10.48550/arXiv.2402.08616)\n```bibtex\n@article{henckel2024adjustment,\n title = {{Adjustment Identification Distance: A gadjid for Causal Structure Learning}},\n author = {Leonard Henckel and Theo W\u00fcrtzen and Sebastian Weichwald},\n journal = {{arXiv preprint arXiv:2402.08616}},\n year = {2024},\n doi = {10.48550/arXiv.2402.08616},\n}\n```\n\n\n## Get Started Real Quick \ud83d\ude80 \u2013 Introductory Example\n\nJust `pip install gadjid` to install the latest release of \ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d \\\nand run `python -c \"import gadjid; help(gadjid)\"` to get started\n(or see [install alternatives](https://github.com/CausalDisco/gadjid#installation--python)).\n\n```python\nimport gadjid\nfrom gadjid import example, ancestor_aid, oset_aid, parent_aid, shd\nimport numpy as np\n\nhelp(gadjid)\n\nexample.run_parent_aid()\n\nGtrue = np.array([\n [0, 1, 1, 1, 1],\n [0, 0, 1, 1, 1],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]\n], dtype=np.int8)\nGguess = np.array([\n [0, 0, 1, 1, 1],\n [1, 0, 1, 1, 1],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]\n], dtype=np.int8)\n\nprint(ancestor_aid(Gtrue, Gguess))\nprint(shd(Gtrue, Gguess))\n```\n\n\n---\n\n\n\ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d is implemented in Rust\nand can conveniently be called from Python via our Python wrapper\n(implemented using [maturin](https://www.maturin.rs/) and [PyO3](https://pyo3.rs/)).\n\n> Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We introduce a framework for developing causal distances between graphs which includes the\nstructural intervention distance for directed acyclic graphs as a special case. We use this framework to develop improved adjustment-based distances as well as extensions to completed partially directed acyclic graphs and causal orders. We develop polynomial-time reachability algorithms to compute the distances efficiently. In our package \ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d, we provide implementations of our distances; they are orders of magnitude faster than the structural intervention distance and thereby provide a success metric for causal discovery that scales to graph sizes that were previously prohibitive.\n\n\n## Implemented Distances\n\n* `ancestor_aid(Gtrue, Gguess)`\n* `oset_aid(Gtrue, Gguess)`\n* `parent_aid(Gtrue, Gguess)`\n* for convenience, the following distances are implemented, too\n * `shd(Gtrue, Gguess)`\n * `sid(Gtrue, Gguess)` \u2013 only for DAGs!\n\nwhere Gtrue and Gguess are adjacency matrices of a DAG or CPDAG.\nThe functions are not symmetric in their input:\nTo calculate a distance,\nidentifying formulas for causal effects are inferred in the graph `Gguess`\nand verified against the graph `Gtrue`.\nDistances return a tuple `(normalised_distance, mistake_count)`\nof the fraction of causal effects inferred in Gguess that are wrong relative to Gtrue, `normalised_distance`,\nand the number of wrongly inferred causal effects, `mistake_count`.\nThere are $p(p-1)$ pairwise causal effects to infer in graphs with $p$ nodes\nand we define normalisation as `normalised_distance = mistake_count / p(p-1)`.\n\nAll graphs are assumed simple, that is, at most one edge is allowed between any two nodes.\nAn adjacency matrix for a DAG may only contain 0s and 1s;\na `1` in row `s` and column `t` codes a directed edge `X\u209b \u2192 X\u209c`;\nDAG inputs are validated for acyclicity.\nAn adjacency matrix for a CPDAG may only contain 0s, 1s and 2s;\na `2` in row `s` and column `t` codes a undirected edge `X\u209b \u2014 X\u209c`\n(an additional `2` in row `t` and column `s` is ignored; only one of the two entries is required to code an undirected edge);\nCPDAG inputs are not validated and __the user needs to ensure the adjacency matrix indeed codes a valid CPDAG (instead of just a PDAG)__.\nYou may also calculate the SID between DAGs via `parent_aid(DAGtrue, DAGguess)`,\nbut we recommend `ancestor_aid` and `oset_aid` and for CPDAG inputs our `parent_aid` does not coincide with the SID\n(see also our accompanying article).\n\n\n## Empirical Runtime Analysis\n\nExperiments run on a laptop with 8 GB RAM and 4-core i5-8365U processor.\nHere, for a graph with $p$ nodes,\nsparse graphs have $10p$ edges in expectation,\ndense graphs have $0.3p(p-1)/2$ edges in expectation,\nand\nsparse graphs have $0.75p$ edges in expectation.\n\n__Maximum graph size feasible within 1 minute__\n\n| Method | sparse | dense |\n|--------------|-------:|------:|\n| Parent-AID | 13005 | 960 |\n| Ancestor-AID | 8200 | 932 |\n| Oset-AID | 546 | 250 |\n| SID in R | 255 | 239 |\n\n__Average runtime__\n| Method | x-sparse ($p=1000$) | sparse ($p=256$) | dense ($p=239$) |\n|--------------|--------------------:|-----------------:|----------------:|\n| Parent-AID | 6.3 ms | 22.8 ms | 189 ms |\n| Ancestor-AID | 2.7 ms | 38.7 ms | 226 ms |\n| Oset-AID | 3.2 ms | 4.69 s | 47.3 s |\n| SID in R | ~1\u20132 h | ~60 s | ~60 s |\n\n\n## LICENSE\n\n\ud835\ude90\ud835\ude8a\ud835\ude8d\ud835\ude93\ud835\ude92\ud835\ude8d is available in source code form at <https://github.com/CausalDisco/gadjid>.\n\nThis Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.\nIf a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.\n\nSee also the [MPL-2.0 FAQ](https://mozilla.org/MPL/2.0/FAQ).\n\n",
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