{
  "article_slug": "label-noise-identifiability",
  "figures": [
    {
      "id": "label-noise-identifiability-1",
      "kind": "line_chart",
      "title": "Several clean probabilities explain the same observed labels",
      "x_label": "False-negative probability b",
      "y_label": "Clean positive probability p",
      "series": [
        {
          "name": "p=(0.3-0.02)/(1-0.02-b)",
          "x": [
            0.0,
            0.05,
            0.1,
            0.15,
            0.2,
            0.25,
            0.3,
            0.35,
            0.4,
            0.45,
            0.5,
            0.55,
            0.6,
            0.65,
            0.7
          ],
          "y": [
            0.2857142857142857,
            0.3010752688172043,
            0.3181818181818181,
            0.3373493975903614,
            0.3589743589743589,
            0.3835616438356164,
            0.4117647058823529,
            0.4444444444444444,
            0.48275862068965514,
            0.5283018867924527,
            0.5833333333333333,
            0.6511627906976745,
            0.7368421052631579,
            0.8484848484848485,
            0.9999999999999998
          ]
        }
      ],
      "caption": "Fixed observed q=0.3 and false-positive rate a=0.02. Every displayed pair is probability-valid; the curve is not an estimated noise rate."
    },
    {
      "id": "label-noise-identifiability-2",
      "kind": "line_chart",
      "title": "Transition inversion becomes ill-conditioned",
      "x_label": "Total class-conditional noise a+b",
      "y_label": "Amplification of observed-probability error",
      "series": [
        {
          "name": "1/(1-a-b)",
          "x": [
            0.0,
            0.05,
            0.1,
            0.15,
            0.2,
            0.25,
            0.3,
            0.35,
            0.4,
            0.45,
            0.5,
            0.55,
            0.6,
            0.65,
            0.7,
            0.75,
            0.8,
            0.85,
            0.9
          ],
          "y": [
            1.0,
            1.0526315789473684,
            1.1111111111111112,
            1.1764705882352942,
            1.25,
            1.3333333333333333,
            1.4285714285714286,
            1.5384615384615383,
            1.6666666666666667,
            1.8181818181818181,
            2.0,
            2.2222222222222223,
            2.5,
            2.857142857142857,
            3.333333333333333,
            4.0,
            5.000000000000001,
            6.666666666666666,
            10.000000000000002
          ]
        }
      ],
      "caption": "Exact derivative for known noise parameters below the singular boundary; not an empirical learning curve."
    }
  ]
}