{
  "orid": "xILwgiWAUk",
  "arxiv_id": "2602.01399",
  "claims": [
    {
      "index": 1,
      "text": "Observation 3.1 proves that Shapley values depend exclusively on the odd component of the coalition set function, so the even component can be discarded without loss (Section 3)."
    },
    {
      "index": 2,
      "text": "Theorem 3.2 proves that paired sampling orthogonalizes the regression, provably separating the odd and even objectives and giving the first general theoretical justification for this widely used sampling heuristic (Section 3.1)."
    },
    {
      "index": 3,
      "text": "Theorem 3.5 shows that Fourier basis regression exactly recovers Shapley values, which forms the theoretical basis of the OddSHAP algorithm (Section 3.2)."
    },
    {
      "index": 4,
      "text": "In Table 1, across eight estimators and eight benchmarks (with sample budget m\u2248100d), OddSHAP attains the lowest average rank (1.50), beating the prior best method RegressionMSR (rank 2.25) (Section 5, Table 1)."
    },
    {
      "index": 5,
      "text": "OddSHAP reduces estimation error by 6\u201362x relative to LeverageSHAP on tabular data benchmarks (Section 5, Table 1)."
    },
    {
      "index": 6,
      "text": "Figure 2 shows OddSHAP's advantage over baselines is largest for moderate-to-high dimensional problems (d\u226530) when given sufficient sampling budget (Figure 2)."
    }
  ]
}