klDivergence
on mixed distributions works for one test case
Value: [1e-4 to 5e-2]
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@ -5,7 +5,6 @@ open GenericDist_Fixtures
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describe("klDivergence: continuous -> continuous -> float", () => {
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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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@ -59,6 +58,24 @@ describe("klDivergence: continuous -> continuous -> float", () => {
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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 =
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-.Js.Math.log((10.0 -. 9.0) /. Js.Math.sqrt(2.0 *. MagicNumbers.Math.pi *. 2.0 ** 2.0)) +.
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1.0 /.
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2.0 ** 2.0 *.
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(10.0 ** 2.0 -. (10.0 +. 9.0) *. 10.0 +. (9.0 ** 2.0 +. 10.0 *. 9.0 +. 10.0 ** 2.0) /. 3.0)
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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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@ -96,6 +113,47 @@ describe("klDivergence: discrete -> discrete -> float", () => {
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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 a' = [(floatDist, 1e0), (uniformDist, 1e0)]->mixture->run
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let b' = [(point3, 1e0), (floatDist, 1e0), (normalDist10, 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("finite klDivergence returns is correct", () => {
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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 =
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Js.Math.log(Js.Math.sqrt(2.0 *. MagicNumbers.Math.pi *. 2.0 ** 2.0) /. (10.0 -. 9.0)) +.
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1.0 /.
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2.0 ** 2.0 *.
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(10.0 ** 2.0 -. (10.0 +. 9.0) *. 10.0 +. (9.0 ** 2.0 +. 10.0 *. 9.0 +. 10.0 ** 2.0) /. 3.0)
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let analyticalKlDiscretePart = -2.0 /. 3.0 *. Js.Math.log(3.0 /. 2.0)
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switch kl {
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| Ok(kl') =>
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kl'->expect->toBeSoCloseTo(analyticalKlContinuousPart +. analyticalKlDiscretePart, ~digits=0)
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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("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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@ -302,10 +302,9 @@ module T = Dist({
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}
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let klDivergence = (prediction: t, answer: t) => {
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Error(Operation.NotYetImplemented)
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// combinePointwise(PointSetDist_Scoring.KLDivergence.integrand, prediction, answer) |> E.R.fmap(
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// integralEndY,
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// )
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let klDiscretePart = Discrete.T.klDivergence(prediction.discrete, answer.discrete)
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let klContinuousPart = Continuous.T.klDivergence(prediction.continuous, answer.continuous)
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E.R.merge(klDiscretePart, klContinuousPart)->E.R2.fmap(t => fst(t) +. snd(t))
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}
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})
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@ -200,6 +200,7 @@ module T = Dist({
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switch (t1, t2) {
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| (Continuous(t1), Continuous(t2)) => Continuous.T.klDivergence(t1, t2)
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| (Discrete(t1), Discrete(t2)) => Discrete.T.klDivergence(t1, t2)
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| (Mixed(t1), Mixed(t2)) => Mixed.T.klDivergence(t1, t2)
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| _ => Error(NotYetImplemented)
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}
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})
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