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[ENH] Add the ability to check the validity of a PAG (#100)
* Added a _proper_pag function * Added some test for legal_pag * [pre-commit.ci] auto fixes from pre-commit.com hooks * Update examples/intro/checking_validity_of_a_pag.py --------- Signed-off-by: Aryan Roy <[email protected]> Co-authored-by: Adam Li <[email protected]> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,14 +1,29 @@ | ||
| name: CircleCI artifacts redirector | ||
| on: [status] | ||
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| # Restrict the permissions granted to the use of secrets.GITHUB_TOKEN in this | ||
| # github actions workflow: | ||
| # https://docs.github.com/en/actions/security-guides/automatic-token-authentication | ||
| permissions: read-all | ||
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| jobs: | ||
| circleci_artifacts_redirector_job: | ||
| if: "${{ startsWith(github.event.context, 'ci/circleci: build_doc') }}" | ||
| runs-on: ubuntu-20.04 | ||
| if: "github.repository == 'py-why/pywhy-graphs' && github.event.context == 'ci/circleci: build_doc'" | ||
| permissions: | ||
| statuses: write | ||
| name: Run CircleCI artifacts redirector | ||
| steps: | ||
| - name: GitHub Action step | ||
| uses: larsoner/circleci-artifacts-redirector-action@master | ||
| with: | ||
| repo-token: ${{ secrets.GITHUB_TOKEN }} | ||
| api-token: ${{ secrets.CIRCLECI_TOKEN }} | ||
| artifact-path: 0/dev/index.html | ||
| circleci-jobs: build_doc | ||
| job-title: Check the rendered docs here! | ||
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| - name: Check the URL | ||
| if: github.event.status != 'pending' | ||
| run: | | ||
| curl --fail ${{ steps.step1.outputs.url }} | grep $GITHUB_SHA |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,97 @@ | ||
| """ | ||
| =========================== | ||
| On PAGs and their validity | ||
| =========================== | ||
| A PAG or a Partial Ancestral Graph is a type of mixed edge | ||
| graph that can represent, in a single graph, the causal relationship | ||
| between several nodes as defined by an equivalence class of MAGs. | ||
| PAGs account for possible unobserved confounding and selection bias | ||
| in the underlying equivalence class of SCMs. | ||
| Another way to understand this is that PAGs encode conditional independence | ||
| constraints stemming from Causal Graphs. Since these constraints do not lead to a | ||
| unique graph, a PAG, in essence, represents a class of graphs that encode | ||
| the same conditional independence constraints. | ||
| PAGs model this relationship by displaying all common edge marks (tail and arrowhead) shared | ||
| by all members in the equivalence class and displaying circle endpoints for those marks | ||
| that are not common. That is, a circular endpoint (``*-o``) can represent both a directed | ||
| (``*->``) and tail (``*—``) endpoint in causal graphs within the equivalence class. | ||
| More details on PAGs can be found at :footcite:`Zhang2008`. | ||
| """ | ||
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| import pywhy_graphs | ||
| from pywhy_graphs.viz import draw | ||
| from pywhy_graphs import PAG | ||
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| try: | ||
| from dodiscover import FCI, make_context | ||
| from dodiscover.ci import Oracle | ||
| from dodiscover.constraint.utils import dummy_sample | ||
| except ImportError as e: | ||
| raise ImportError("The 'dodiscover' package is required to convert a MAG to a PAG.") | ||
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| # %% | ||
| # PAGs in pywhy-graphs | ||
| # --------------------------- | ||
| # Constructing a PAG in pywhy-graphs is an easy task since | ||
| # the library provides a separate class for this purpose. | ||
| # True to the definition of PAGs, the class can contain | ||
| # directed edges, bidirected edges, undirected edges and | ||
| # cicle edges. To illustrate this, we construct an example PAG | ||
| # as described in :footcite:`Zhang2008`, figure 4: | ||
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| pag = PAG() | ||
| pag.add_edge("I", "S", pag.directed_edge_name) | ||
| pag.add_edge("G", "S", pag.directed_edge_name) | ||
| pag.add_edge("G", "L", pag.directed_edge_name) | ||
| pag.add_edge("S", "L", pag.directed_edge_name) | ||
| pag.add_edge("PSH", "S", pag.directed_edge_name) | ||
| pag.add_edge("S", "PSH", pag.circle_edge_name) | ||
| pag.add_edge("S", "G", pag.circle_edge_name) | ||
| pag.add_edge("S", "I", pag.circle_edge_name) | ||
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| # Finally, the graph looks like this: | ||
| dot_graph = draw(pag) | ||
| dot_graph.render(outfile="valid_pag.png", view=True) | ||
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| # %% | ||
| # Validity of a PAG | ||
| # --------------------------- | ||
| # For a PAG to be valid, it must represent a valid | ||
| # equivalent class of MAGs. This can be verified by | ||
| # turning the PAG into an MAG and then checking the | ||
| # validity of the MAG. | ||
| # Theorem 2 in :footcite:`Zhang2008` provides a method for checking the validity of a PAG. | ||
| # To check if the constructed PAG is a valid one in pywhy-graphs, we can simply do: | ||
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| # returns True | ||
| print(pywhy_graphs.valid_pag(pag)) | ||
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| # %% | ||
| # If we want to test whether this algorithm is working correctly or not, we can change | ||
| # a single mark in the graph such that the PAG. By removing a circle edge, we are removing | ||
| # the representation of multiple marks as encoded by the different MAGs this PAG represents. | ||
| # In this specific case, by removing the circle endpoint ``S *-o I``, we are saying that ``S`` | ||
| # directly causes ``I``. However, there is no way of determining this using the FCI logical rules. | ||
| # One would not be able to determine that the adjacency is due to a direct | ||
| # causal relationship (directed edge), confounded relationship (bidirected edge), or an inducing path | ||
| # relationship. As such, the resulting graph is no longer a valid PAG. | ||
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| pag.remove_edge("S", "I", pag.circle_edge_name) | ||
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| # returns False | ||
| print(pywhy_graphs.valid_pag(pag)) | ||
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| # %% | ||
| # References | ||
| # ---------- | ||
| # .. footbibliography:: |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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@@ -52,6 +52,7 @@ doc = [ | |
| 'graphviz', | ||
| 'pygraphviz', | ||
| 'pgmpy', | ||
| 'dowhy', | ||
| ] | ||
| style = [ | ||
| "pre-commit", | ||
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