109 lines
3.7 KiB
Plaintext
109 lines
3.7 KiB
Plaintext
open Jest
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open Expect
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open TestHelpers
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describe("kl divergence", () => {
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let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
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exception KlFailed
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let testUniform = (lowAnswer, highAnswer, lowPrediction, highPrediction) => {
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test("of two uniforms is equal to the analytic expression", () => {
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let answer =
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uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
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let prediction =
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uniformMakeR(
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lowPrediction,
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highPrediction,
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)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
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// integral along the support of the answer of answer.pdf(x) times log of prediction.pdf(x) divided by answer.pdf(x) dx
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let analyticalKl = Js.Math.log((highPrediction -. lowPrediction) /. (highAnswer -. lowAnswer))
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let kl = E.R.liftJoin2(klDivergence, prediction, answer)
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switch kl {
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| Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
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| Error(err) => {
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Js.Console.log(DistributionTypes.Error.toString(err))
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raise(KlFailed)
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}
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}
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})
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}
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testUniform(0.0, 1.0, -1.0, 2.0)
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testUniform(0.0, 1.0, 0.0, 2.0)
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// testUniform(-1.0, 1.0, 0.0, 2.0)
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test("of two normals is equal to the formula", () => {
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// This test case comes via Nuño https://github.com/quantified-uncertainty/squiggle/issues/433
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let mean1 = 4.0
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let mean2 = 1.0
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let stdev1 = 4.0
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let stdev2 = 1.0
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let prediction =
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normalMakeR(mean1, stdev1)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
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let answer = normalMakeR(mean2, stdev2)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
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// https://stats.stackexchange.com/questions/7440/kl-divergence-between-two-univariate-gaussians
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let analyticalKl =
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Js.Math.log(stdev1 /. stdev2) +.
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(stdev2 ** 2.0 +. (mean2 -. mean1) ** 2.0) /. (2.0 *. stdev1 ** 2.0) -. 0.5
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let kl = E.R.liftJoin2(klDivergence, prediction, answer)
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switch kl {
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| Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
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| Error(err) => {
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Js.Console.log(DistributionTypes.Error.toString(err))
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raise(KlFailed)
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}
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}
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})
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})
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describe("combine along support test", () => {
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test("combine along support test", _ => {
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let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument0
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let lowAnswer = 0.0
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let highAnswer = 1.0
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let lowPrediction = 0.0
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let highPrediction = 2.0
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let answer =
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uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
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let prediction =
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uniformMakeR(lowPrediction, highPrediction)->E.R2.errMap(s => DistributionTypes.ArgumentError(
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s,
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))
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let answerWrapped = E.R.fmap(a => run(FromDist(ToDist(ToPointSet), a)), answer)
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let predictionWrapped = E.R.fmap(a => run(FromDist(ToDist(ToPointSet), a)), prediction)
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let interpolator = XYShape.XtoY.continuousInterpolator(#Stepwise, #UseZero)
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let integrand = PointSetDist_Scoring.KLDivergence.integrand
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let result = switch (answerWrapped, predictionWrapped) {
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| (Ok(Dist(PointSet(Continuous(a)))), Ok(Dist(PointSet(Continuous(b))))) =>
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Some(combineAlongSupportOfSecondArgument(integrand, interpolator, a.xyShape, b.xyShape))
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| _ => None
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}
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result
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->expect
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->toEqual(
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Some(
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Ok({
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xs: [
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0.0,
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MagicNumbers.Epsilon.ten,
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2.0 *. MagicNumbers.Epsilon.ten,
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1.0 -. MagicNumbers.Epsilon.ten,
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1.0,
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],
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ys: [
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-0.34657359027997264,
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-0.34657359027997264,
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-0.34657359027997264,
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-0.34657359027997264,
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-0.34657359027997264,
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],
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}),
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),
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)
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})
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})
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