{
  "id": "1403.0408",
  "version": "v2",
  "published": "2014-03-03T12:31:05.000Z",
  "updated": "2014-03-04T10:25:06.000Z",
  "title": "On the Intersection Property of Conditional Independence and its Application to Causal Discovery",
  "authors": [
    "Jonas Peters"
  ],
  "categories": [
    "math.PR",
    "stat.ML"
  ],
  "abstract": "This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent of $(A,B)$ given $C$. Under the assumption that the joint distribution has a continuous density, we provide necessary and sufficient conditions under which the intersection property holds. The result has direct applications to causal inference: it leads to strictly weaker conditions under which the graphical structure becomes identifiable from the joint distribution of an additive noise model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-04T10:25:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conditional independence",
      "causal discovery",
      "joint distribution",
      "intersection property holds",
      "independent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.0408P"
    }
  }
}