squiggle/packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res

open Jest
open Expect
open TestHelpers

describe("kl divergence", () => {
  let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
  exception KlFailed
  test("of two uniforms is equal to the analytic expression", () => {
    let lowAnswer = 0.0
    let highAnswer = 1.0
    let lowPrediction = 0.0
    let highPrediction = 2.0
    let answer =
      uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let prediction =
      uniformMakeR(lowPrediction, highPrediction)->E.R2.errMap(s => DistributionTypes.ArgumentError(
        s,
      ))
    // integral along the support of the answer of answer.pdf(x) times log of prediction.pdf(x) divided by answer.pdf(x) dx
    let analyticalKl = Js.Math.log((highPrediction -. lowPrediction) /. (highAnswer -. lowAnswer))
    let kl = E.R.liftJoin2(klDivergence, prediction, answer)
    Js.Console.log2("Analytical: ", analyticalKl)
    Js.Console.log2("Computed: ", kl)
    switch kl {
    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
    | Error(err) => {
        Js.Console.log(DistributionTypes.Error.toString(err))
        raise(KlFailed)
      }
    }
  })
  test("of two normals is equal to the formula", () => {
    // This test case comes via Nuño https://github.com/quantified-uncertainty/squiggle/issues/433
    let mean1 = 4.0
    let mean2 = 1.0
    let stdev1 = 1.0
    let stdev2 = 4.0

    let prediction =
      normalMakeR(mean1, stdev1)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let answer = normalMakeR(mean2, stdev2)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
    let analyticalKl =
      Js.Math.log(stdev2 /. stdev1) +.
      stdev1 ** 2.0 /. 2.0 /. stdev2 ** 2.0 +.
      (mean1 -. mean2) ** 2.0 /. 2.0 /. stdev2 ** 2.0 -. 0.5
    let kl = E.R.liftJoin2(klDivergence, prediction, answer)

    Js.Console.log2("Analytical: ", analyticalKl)
    Js.Console.log2("Computed: ", kl)

    switch kl {
    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
    | Error(err) => {
        Js.Console.log(DistributionTypes.Error.toString(err))
        raise(KlFailed)
      }
    }
  })
})

describe("combine along support test", () => {
  let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument
  let lowAnswer = 0.0
  let highAnswer = 1.0
  let lowPrediction = -1.0
  let highPrediction = 2.0

  let answer =
    uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
  let prediction =
    uniformMakeR(lowPrediction, highPrediction)->E.R2.errMap(s => DistributionTypes.ArgumentError(
      s,
    ))
  let answerWrapped = E.R.fmap(a => run(FromDist(ToDist(ToPointSet), a)), answer)
  let predictionWrapped = E.R.fmap(a => run(FromDist(ToDist(ToPointSet), a)), prediction)

  let interpolator = XYShape.XtoY.continuousInterpolator(#Stepwise, #UseZero)
  let integrand = PointSetDist_Scoring.KLDivergence.integrand

  let result = switch (answerWrapped, predictionWrapped) {
  | (Ok(Dist(PointSet(Continuous(a)))), Ok(Dist(PointSet(Continuous(b))))) =>
    Some(combineAlongSupportOfSecondArgument(integrand, interpolator, a.xyShape, b.xyShape))
  | _ => None
  }
  test("combine along support test", _ => {
    Js.Console.log2("combineAlongSupportOfSecondArgument", result)
    false->expect->toBe(true)
  })
})