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

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open Jest
open Expect
open TestHelpers
describe("kl divergence", () => {
let klDivergence = DistributionOperation.Constructors.klDivergence(~env)
exception KlFailed
let testUniform = (lowAnswer, highAnswer, lowPrediction, highPrediction) => {
test("of two uniforms is equal to the analytic expression", () => {
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)
switch kl {
| Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
| Error(err) => {
Js.Console.log(DistributionTypes.Error.toString(err))
raise(KlFailed)
}
}
})
}
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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.
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
testUniform(0.0, 1.0, -1.0, 1.0) // equal rightendpoints
testUniform(0.0, 1e1, 0.0, 1e1) // equal (klDivergence = 0)
// testUniform(-1.0, 1.0, 0.0, 2.0)
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 = 4.0
let stdev2 = 1.0
let prediction =
normalMakeR(mean1, stdev1)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
let answer = normalMakeR(mean2, stdev2)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
// https://stats.stackexchange.com/questions/7440/kl-divergence-between-two-univariate-gaussians
let analyticalKl =
Js.Math.log(stdev1 /. stdev2) +.
(stdev2 ** 2.0 +. (mean2 -. mean1) ** 2.0) /. (2.0 *. stdev1 ** 2.0) -. 0.5
let kl = E.R.liftJoin2(klDivergence, prediction, answer)
switch kl {
| Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
| Error(err) => {
Js.Console.log(DistributionTypes.Error.toString(err))
raise(KlFailed)
}
}
})
})
describe("combine along support test", () => {
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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.
test("combine along support test", _ => {
let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument0
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,
))
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
}
result
->expect
->toEqual(
Some(
Ok({
xs: [
0.0,
MagicNumbers.Epsilon.ten,
2.0 *. MagicNumbers.Epsilon.ten,
1.0 -. MagicNumbers.Epsilon.ten,
1.0,
],
ys: [
-0.34657359027997264,
-0.34657359027997264,
-0.34657359027997264,
-0.34657359027997264,
-0.34657359027997264,
],
}),
),
)
})
})