Pith Number

pith:L4HUQNFG

pith:2026:L4HUQNFGGX2RMSHGL2ENUSDROA

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Towards a holistic understanding of Selection Bias for Causal Effect Identification

Filip Kovacevic, Francesco Locatello, Peter Spirtes, Shimeng Huang, Yiwen Qiu

Necessary and sufficient conditions identify the average treatment effect under selection bias via weak assumptions on probability classes.

arxiv:2605.13430 v1 · 2026-05-13 · stat.ME · cs.AI · cs.LG

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Claims

C1strongest claim

We provide necessary and sufficient conditions for ATE identifiability, leveraging weak assumptions on probability classes to characterize propensity score and selection probability. Compared to previous works, our results extend existing graphical identifiability criteria and offer a more comprehensive understanding of causal effect identification with strictly weaker conditions in the presence of selection bias.

C2weakest assumption

The weak assumptions on probability classes that allow characterization of the propensity score and selection probability (stated in the abstract as the basis for the necessary and sufficient conditions).

C3one line summary

Necessary and sufficient conditions for ATE identifiability under selection bias using weaker assumptions on probability classes than prior graphical criteria.

References

85 extracted · 85 resolved · 4 Pith anchors

[1] Causal inference in statistics, social, and biomedical sciences , author=. 2015 , publisher= 2015

[2] Abouei, Amir Mohammad and Mokhtarian, Ehsan and Kiyavash, Negar and Grossglauser, Matthias , langid =. Causal

[3] Abouei, Amir Mohammad and Mokhtarian, Ehsan and Kiyavash, Negar , year = 2024, month = jan, number =. S-. doi:10.48550/arXiv.2309.02281 , urldate =. 2309.02281 , primaryclass = 2024 · doi:10.48550/arxiv.2309.02281

[4] Bareinboim, Elias and Pearl, Judea , year = 2011, month = aug, journal =. Controlling. doi:10.1609/aaai.v25i1.8056 , urldate = 2011 · doi:10.1609/aaai.v25i1.8056

[5] Bellot, Alexis , langid =. Towards

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.192685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f0f4834a635f51648e65e88da4871703225702fa72d814a6793991b676aa5c1

Aliases

arxiv: 2605.13430 · arxiv_version: 2605.13430v1 · doi: 10.48550/arxiv.2605.13430 · pith_short_12: L4HUQNFGGX2R · pith_short_16: L4HUQNFGGX2RMSHG · pith_short_8: L4HUQNFG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L4HUQNFGGX2RMSHGL2ENUSDROA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5f0f4834a635f51648e65e88da4871703225702fa72d814a6793991b676aa5c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4538e55dd25b1612bb612f24952653ec437f34d73916b11213ef0304cf8be11e",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T12:24:34Z",
    "title_canon_sha256": "d817ef54ccd0653c1fcbe50a34e3768273a314dca05a052eb52a003dd0432c45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13430",
    "kind": "arxiv",
    "version": 1
  }
}