229 lines
8.3 KiB
Plaintext
229 lines
8.3 KiB
Plaintext
open Jest
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open Expect
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open TestHelpers
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open GenericDist_Fixtures
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// integral from low to high of 1 / (high - low) log(normal(mean, stdev)(x) / (1 / (high - low))) dx
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let klNormalUniform = (mean, stdev, low, high): float =>
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-.Js.Math.log((high -. low) /. Js.Math.sqrt(2.0 *. MagicNumbers.Math.pi *. stdev ** 2.0)) +.
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1.0 /.
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stdev ** 2.0 *.
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(mean ** 2.0 -. (high +. low) *. mean +. (low ** 2.0 +. high *. low +. high ** 2.0) /. 3.0)
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describe("klDivergence: continuous -> continuous -> float", () => {
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let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
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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->toBeSoCloseTo(analyticalKl, ~digits=7)
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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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// The pair on the right (the answer) can be wider than the pair on the left (the prediction), but not the other way around.
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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) // equal left endpoints
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testUniform(0.0, 1.0, -1.0, 1.0) // equal rightendpoints
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testUniform(0.0, 1e1, 0.0, 1e1) // equal (klDivergence = 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->toBeSoCloseTo(analyticalKl, ~digits=3)
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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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test("of a normal and a uniform is equal to the formula", () => {
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let prediction = normalDist10
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let answer = uniformDist
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let kl = klDivergence(prediction, answer)
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let analyticalKl = klNormalUniform(10.0, 2.0, 9.0, 10.0)
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switch kl {
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| Ok(kl') => kl'->expect->toBeSoCloseTo(analyticalKl, ~digits=1)
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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("klDivergence: discrete -> discrete -> float", () => {
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let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
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let mixture = a => DistributionTypes.DistributionOperation.Mixture(a)
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let a' = [(point1, 1e0), (point2, 1e0)]->mixture->run
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let b' = [(point1, 1e0), (point2, 1e0), (point3, 1e0)]->mixture->run
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let (a, b) = switch (a', b') {
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| (Dist(a''), Dist(b'')) => (a'', b'')
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| _ => raise(MixtureFailed)
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}
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test("agrees with analytical answer when finite", () => {
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let prediction = b
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let answer = a
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let kl = klDivergence(prediction, answer)
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// Sigma_{i \in 1..2} 0.5 * log(0.5 / 0.33333)
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let analyticalKl = Js.Math.log(3.0 /. 2.0)
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switch kl {
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| Ok(kl') => kl'->expect->toBeSoCloseTo(analyticalKl, ~digits=7)
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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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test("returns infinity when infinite", () => {
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let prediction = a
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let answer = b
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let kl = klDivergence(prediction, answer)
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switch kl {
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| Ok(kl') => kl'->expect->toEqual(infinity)
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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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describe("klDivergence: mixed -> mixed -> float", () => {
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let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
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let mixture' = a => DistributionTypes.DistributionOperation.Mixture(a)
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let mixture = a => {
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let dist' = a->mixture'->run
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switch dist' {
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| Dist(dist) => dist
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| _ => raise(MixtureFailed)
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}
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}
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let a = [(point1, 1.0), (uniformDist, 1.0)]->mixture
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let b = [(point1, 1.0), (floatDist, 1.0), (normalDist10, 1.0)]->mixture
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let c = [(point1, 1.0), (point2, 1.0), (point3, 1.0), (uniformDist, 1.0)]->mixture
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let d =
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[(point1, 1.0), (point2, 1.0), (point3, 1.0), (floatDist, 1.0), (uniformDist2, 1.0)]->mixture
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test("finite klDivergence produces correct answer", () => {
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let prediction = b
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let answer = a
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let kl = klDivergence(prediction, answer)
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// high = 10; low = 9; mean = 10; stdev = 2
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let analyticalKlContinuousPart = klNormalUniform(10.0, 2.0, 9.0, 10.0) /. 2.0
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let analyticalKlDiscretePart = 1.0 /. 2.0 *. Js.Math.log(2.0 /. 1.0)
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switch kl {
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| Ok(kl') =>
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kl'->expect->toBeSoCloseTo(analyticalKlContinuousPart +. analyticalKlDiscretePart, ~digits=1)
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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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test("returns infinity when infinite", () => {
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let prediction = a
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let answer = b
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let kl = klDivergence(prediction, answer)
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switch kl {
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| Ok(kl') => kl'->expect->toEqual(infinity)
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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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test("finite klDivergence produces correct answer", () => {
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let prediction = d
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let answer = c
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let kl = klDivergence(prediction, answer)
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let analyticalKlContinuousPart = Js.Math.log((11.0 -. 8.0) /. (10.0 -. 9.0)) /. 4.0 // 4 = length of c' array
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let analyticalKlDiscretePart = 3.0 /. 4.0 *. Js.Math.log(4.0 /. 3.0)
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switch kl {
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| Ok(kl') =>
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kl'->expect->toBeSoCloseTo(analyticalKlContinuousPart +. analyticalKlDiscretePart, ~digits=1)
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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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describe("combineAlongSupportOfSecondArgument0", () => {
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// This tests the version of the function that we're NOT using. Haven't deleted the test in case we use the code later.
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test("test on two uniforms", _ => {
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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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1.0 +. MagicNumbers.Epsilon.ten,
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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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infinity,
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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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