{
  "handle": "AdaptiveSplineSeparator",
  "ref": "AdaptiveSplineSeparator#6cd0",
  "stub": "6cd0",
  "semaId": "sema:AdaptiveSplineSeparator#mh:SHA-256:6cd0be0ce642cfb16527c769bc946c7c7561d30e809bb9f5c0be55d20d42e5f0",
  "layer": "Mind",
  "category": "Inference",
  "gloss": "Fit a curve through a 2-D scatter that maximally separates two groups, to catch oblique separation",
  "mechanism": "Axis-wise tests ask whether groups differ in x or in y; groups can differ along a diagonal and pass both. In a 2-D space (for example the rescaled coordinates from an {{entropy_collapse}}), define a smooth spline C(l) through c control points (40) with x fixed, log-spaced over the data range, and y free. Initialise the y values on an existing curve such as the fitted scaling function. For each observation r_j, find the nearest point on the curve and take the signed perpendicular distance d_j (positive below, negative above). Optimise the log-y control values with L-BFGS-B, box-bounded to the observed y range, to maximise |mean d(group 1) - mean d(group 2)|, stopping on small gradient or function change (e.g. 1e-5, 1e-6, at most 200 iterations). Report the share of each group on each side, and judge significance with a permutation test that shuffles group labels between whole samples, as in {{clustered_testing}}. For fire ant trailing versus aggression, 67.8% of aggression windows fell below the curve and 70.6% of trail windows above (colony-level permutation p = 0.03), a split invisible to axis-wise GEE (p = 0.47, 0.97).",
  "invariants": [
    "The separator is optimised and tested under the same grouping of observations",
    "Control points stay inside the observed data range, so the curve does not extrapolate",
    "Significance comes from re-optimising under permuted labels, not from the optimised score itself"
  ],
  "failureModes": [
    "Overfitting: 40 free control points can separate noise; without re-fitting on permuted labels the score is optimistic",
    "Permuting windows instead of samples inflates significance",
    "Defining 'below' and 'above' only for a single-valued curve; it cannot represent groups that interleave"
  ],
  "ring": 2,
  "tier": 2,
  "aliases": {
    "entropy_collapse": "EntropyDensityCollapse",
    "clustered_testing": "ClusteredObservationTesting"
  },
  "buildsOn": [
    {
      "handle": "EntropyDensityCollapse",
      "type": "references",
      "alias": "entropy_collapse",
      "url": "/knowledge-graph/EntropyDensityCollapse/",
      "json": "/knowledge-graph/EntropyDensityCollapse.json"
    },
    {
      "handle": "ClusteredObservationTesting",
      "type": "composes_with",
      "alias": "clustered_testing",
      "url": "/knowledge-graph/ClusteredObservationTesting/",
      "json": "/knowledge-graph/ClusteredObservationTesting.json"
    }
  ],
  "usedBy": [],
  "sources": {
    "research": [],
    "works": [
      {
        "kind": "thesis",
        "label": "Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026)",
        "note": "Ch. 3.3, Eqs. 3.29-3.32; Ch. 4.2.3, Fig. 4.4",
        "url": ""
      }
    ],
    "homePage": false
  },
  "url": "/knowledge-graph/AdaptiveSplineSeparator/",
  "graphUrl": "/knowledge-graph#AdaptiveSplineSeparator",
  "directory": "/knowledge-graph/patterns.json"
}