{
  "article_slug": "curriculum-sampling-objectives",
  "figures": [
    {
      "id": "curriculum-sampling-objectives-1",
      "kind": "line_chart",
      "title": "Nonuniform sampling changes the expected optimum",
      "x_label": "Probability q of zero-target example",
      "y_label": "Coefficient / half squared-loss units",
      "series": [
        {
          "name": "Uncorrected optimum",
          "x": [
            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,
            0.95
          ],
          "y": [
            1.9,
            1.8,
            1.7,
            1.6,
            1.5,
            1.4,
            1.3,
            1.2,
            1.1,
            1.0,
            0.8999999999999999,
            0.8,
            0.7,
            0.6000000000000001,
            0.5,
            0.3999999999999999,
            0.30000000000000004,
            0.19999999999999996,
            0.10000000000000009
          ]
        },
        {
          "name": "Uniform target optimum",
          "x": [
            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,
            0.95
          ],
          "y": [
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
          ]
        },
        {
          "name": "Excess uniform risk",
          "x": [
            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,
            0.95
          ],
          "y": [
            0.4049999999999999,
            0.32000000000000006,
            0.24499999999999997,
            0.18000000000000005,
            0.125,
            0.07999999999999996,
            0.04500000000000001,
            0.01999999999999999,
            0.005000000000000009,
            0.0,
            0.005000000000000009,
            0.01999999999999999,
            0.04500000000000001,
            0.07999999999999996,
            0.125,
            0.18000000000000005,
            0.24499999999999997,
            0.32000000000000006,
            0.4049999999999999
          ]
        }
      ],
      "caption": "Constructed half squared losses with targets 0 and 2. Uncorrected optimum 2*(1-q); risk uses a fixed uniform target. No neural training measurement."
    },
    {
      "id": "curriculum-sampling-objectives-2",
      "kind": "line_chart",
      "title": "Correcting the mean can increase variance",
      "x_label": "Probability q of zero-target example",
      "y_label": "Squared gradient units",
      "series": [
        {
          "name": "Corrected estimator variance",
          "x": [
            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,
            0.95
          ],
          "y": [
            0.05263157894736842,
            0.11111111111111113,
            0.17647058823529413,
            0.25,
            0.3333333333333333,
            0.4285714285714286,
            0.5384615384615383,
            0.6666666666666667,
            0.8181818181818181,
            1.0,
            1.2222222222222223,
            1.5,
            1.8571428571428572,
            2.333333333333333,
            3.0,
            4.000000000000001,
            5.666666666666666,
            9.000000000000002,
            18.999999999999982
          ]
        },
        {
          "name": "Uncorrected squared bias",
          "x": [
            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,
            0.95
          ],
          "y": [
            0.81,
            0.6400000000000001,
            0.48999999999999994,
            0.36,
            0.25,
            0.16000000000000003,
            0.09000000000000002,
            0.03999999999999998,
            0.009999999999999995,
            0.0,
            0.010000000000000018,
            0.03999999999999998,
            0.09000000000000002,
            0.15999999999999992,
            0.25,
            0.3600000000000001,
            0.48999999999999994,
            0.6400000000000001,
            0.8099999999999998
          ]
        }
      ],
      "caption": "At theta=0, corrected estimator takes 0 or -1/(1-q), mean -1, variance q/(1-q). Comparing one-step mechanisms, not final model quality."
    }
  ]
}