Samples with mixed effects

match ← All linear growth benchmarks

512 raw simulated values per date for the same mixed model.

Input

benchmark/inputs/v1/linear-mixed-components.json: 96 history rows and 24 forecast rows.

Output

Largest difference: 1.8e-10 (< 0.0001% of the input's range).

Every forecast row from both libraries.

Date	Effect Prophet	Python Prophet	Difference
2020-04-02	56.8946	56.8946	1.8e-10
2020-04-03	58.9619	58.9619	1.7e-10
2020-04-04	49.8863	49.8863	1.4e-10
2020-04-05	42.5866	42.5866	1.4e-10
2020-04-06	26.0176	26.0176	1.2e-10
2020-04-08	44.1660	44.1660	1.7e-10
2020-04-10	42.9853	42.9853	1.5e-10
2020-04-12	35.6534	35.6534	1.2e-10
2020-04-14	31.1089	31.1089	1.6e-10
2020-04-16	57.0518	57.0518	1.7e-10
2020-04-18	51.1965	51.1965	1.5e-10
2020-04-20	45.1353	45.1353	1.7e-10

Timing

Median of all measured repetitions.

Step	Effect Prophet	Python Prophet	Effect Prophet is
Convert input rows	39 µs	540 µs	14× faster
Save model to JSON	25 µs	677 µs	27× faster
Load model from JSON	192 µs	3.62 ms	19× faster
Simulate uncertainty	798 µs	68.6 ms	Not compared: different work
First simulation in a new process	181 ms	1.54 s	Not compared: different work
Load and simulate in a new process	168 ms	1.53 s	Not compared: different work

Some steps aren't compared, because the two libraries' public calls produce different outputs. Their times show what each call costs, not which library is faster.

• Simulate uncertainty, First simulation in a new process, Load and simulate in a new process: Python's predictive_samples(vectorized=False) and Effect Prophet's predictUncertainty are different public calls: Python's timing includes resetting NumPy's random generator and returns NumPy matrices, and the two don't draw the same random numbers.

Settings

The case declaration both libraries ran.

{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "linear-output-first-v4"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "multiplicative",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "explicit",
      "timestamps": [
        "2020-02-10T00:00:00.000Z"
      ]
    },
    "changepointPriorScale": 0.2,
    "seasonalities": [
      {
        "name": "weekly-custom",
        "periodDays": 7,
        "fourierOrder": 2,
        "priorScale": 10,
        "conditionName": "active"
      }
    ],
    "events": [
      {
        "name": "campaign",
        "date": "2020-01-22",
        "lowerWindowDays": 0,
        "upperWindowDays": 0,
        "priorScale": 10
      }
    ],
    "regressors": [
      {
        "name": "promotion",
        "priorScale": 10,
        "standardization": "never"
      }
    ]
  },
  "effectOptimizer": {
    "algorithm": "auto",
    "maxIterations": 10000,
    "fallback": "newton",
    "lbfgs": {
      "historySize": 5,
      "initAlpha": 0.001,
      "tolObj": 1e-12,
      "tolRelObj": 10000,
      "tolGrad": 1e-8,
      "tolRelGrad": 10000000,
      "tolParam": 1e-8
    }
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  },
  "uncertainty": {
    "seed": 19,
    "samples": 512,
    "intervalWidth": 0.8,
    "output": "samples",
    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
  }
}