Pith Number

pith:D5UPXKKZ

pith:2026:D5UPXKKZ64HMJUYREGZQT2I2RK

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Prediction-Intervention Games and Invariant Sets

Felix Schur, Jonas Peters, Linus K\"uhne

In prediction-intervention games, stable-blanket predictors are always at least as good as causal-parent predictors for two common follower objective classes.

arxiv:2605.16828 v1 · 2026-05-16 · stat.ML · cs.AI · cs.LG · stat.ME

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Claims

C1strongest claim

We prove, for two common classes of follower objectives, that predictors based on the stable blanket, a specific invariant subset, are always better or as good as those based on the causal parents.

C2weakest assumption

The leader knows the intervention targets but may have limited knowledge of the follower's objective; the proof relies on the follower objectives belonging to two specific common classes whose exact definitions are not given in the abstract.

C3one line summary

In prediction-intervention games, stable-blanket predictors are at least as good as causal-parent predictors for two classes of follower objectives and can be worst-case optimal under additional conditions.

References

63 extracted · 63 resolved · 3 Pith anchors

[1] Invariant Risk Minimization 1907 · arXiv:1907.02893

[2] Geometric and Computational Hardness of Bilevel Programming.Mathematical Pro- gramming, 215(1):539–574, 2026 2026

[3] Stephan Bongers, Patrick Forré, Jonas Peters, and Joris M. Mooij. Foundations of Structural Causal Models with Cycles and Latent Variables.The Annals of Statistics, 49(5):2885–2915, 2021 2021

[4] Stackelberg Games for Adversarial Prediction Prob- lems 2011

[5] Invariance, Causality and Robustness.Statistical Science, 35(3):404–426, 2020 2020

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:24.792170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f68fba959f70ec4d31121b309e91a8a932f284a6e896089e7bf2a05e9c6ead6

Aliases

arxiv: 2605.16828 · arxiv_version: 2605.16828v1 · doi: 10.48550/arxiv.2605.16828 · pith_short_12: D5UPXKKZ64HM · pith_short_16: D5UPXKKZ64HMJUYR · pith_short_8: D5UPXKKZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D5UPXKKZ64HMJUYREGZQT2I2RK \
  | 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: 1f68fba959f70ec4d31121b309e91a8a932f284a6e896089e7bf2a05e9c6ead6

Canonical record JSON

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    "cross_cats_sorted": [
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      "stat.ME"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-16T06:15:41Z",
    "title_canon_sha256": "33b69664fc71426d6bdaf25ea21999d4db44729cf40f913b92cd1d34d03d6662"
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    "kind": "arxiv",
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