feat: Get KL divergence working except in case of numerical errors ()

- Quinn was of great help here.
- I also left some dead code, which still has to be cleaned up
- There are still very annoying numerical errors, so I left one test
failing. These are due to how the interpolation is done
- Quinn to pick up from here

Value: [0.6 to 2]

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

@@ -8,7 +8,7 @@ describe("kl divergence", () => {
   test("of two uniforms is equal to the analytic expression", () => {
     let lowAnswer = 0.0
     let highAnswer = 1.0
-    let lowPrediction = 0.0
+    let lowPrediction = -1.0
     let highPrediction = 2.0
     let answer =
       uniformMakeR(lowAnswer, highAnswer)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
@@ -29,20 +29,50 @@ describe("kl divergence", () => {
       }
     }
   })
+  test(
+    "of two uniforms is equal to the analytic expression, part 2 (annoying numerical errors)",
+    () => {
+      Js.Console.log(
+        "This will fait because of extremely annoying numerical errors. Will not fail if the two uniforms are a bit different. Very annoying",
+      )
+      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 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))
     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
+      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)
 
     Js.Console.log2("Analytical: ", analyticalKl)
@@ -59,10 +89,12 @@ describe("kl divergence", () => {
 })
 
 describe("combine along support test", () => {
+  Skip.test("combine along support test", _ => {
+    // doesn't matter
     let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument
     let lowAnswer = 0.0
     let highAnswer = 1.0
-  let lowPrediction = -1.0
+    let lowPrediction = 0.0
     let highPrediction = 2.0
 
     let answer =
@@ -82,7 +114,6 @@ describe("combine along support test", () => {
       Some(combineAlongSupportOfSecondArgument(integrand, interpolator, a.xyShape, b.xyShape))
     | _ => None
     }
-  test("combine along support test", _ => {
     Js.Console.log2("combineAlongSupportOfSecondArgument", result)
     false->expect->toBe(true)
   })

packages/squiggle-lang/package.json

@@ -15,6 +15,7 @@
     "test": "jest",
     "test:ts": "jest __tests__/TS/",
     "test:rescript": "jest --modulePathIgnorePatterns=__tests__/TS/*",
+    "test:kldivergence": "jest __tests__/Distributions/KlDivergence_test.*",
     "test:watch": "jest --watchAll",
     "coverage:rescript": "rm -f *.coverage; yarn clean; BISECT_ENABLE=yes yarn build; yarn test:rescript; bisect-ppx-report html",
     "coverage:ts": "yarn clean; yarn build; nyc --reporter=lcov yarn test:ts",

packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res

@@ -271,7 +271,7 @@ module T = Dist({
   let variance = (t: t): float =>
     XYShape.Analysis.getVarianceDangerously(t, mean, Analysis.getMeanOfSquares)
 
-  let klDivergence = (prediction: t, answer: t) => {
+  let klDivergence0 = (prediction: t, answer: t) => {
     combinePointwise(
       ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument,
       PointSetDist_Scoring.KLDivergence.integrand,
@@ -281,6 +281,29 @@ module T = Dist({
     |> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
     |> E.R.fmap(integralEndY)
   }
+
+  let klDivergence = (prediction: t, answer: t) => {
+    let newShape = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument2(
+      PointSetDist_Scoring.KLDivergence.integrand,
+      prediction.xyShape,
+      answer.xyShape,
+    )
+    let generateContinuousDistFromXYShape: XYShape.xyShape => t = xyShape => {
+      xyShape: xyShape,
+      interpolation: #Linear,
+      integralSumCache: None,
+      integralCache: None,
+    }
+    let _ = Js.Console.log2("prediction", prediction)
+    let _ = Js.Console.log2("answer", answer)
+    let _ = Js.Console.log2("newShape", newShape)
+    switch newShape {
+    | Ok(tshape) => Ok(integralEndY(generateContinuousDistFromXYShape(tshape)))
+    | Error(errormessage) => Error(errormessage)
+    }
+    //|> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
+    //|> E.R.fmap(integralEndY)
+  }
 })
 
 let isNormalized = (t: t): bool => {

packages/squiggle-lang/src/rescript/Utility/XYShape.res

@@ -391,7 +391,7 @@ module PointwiseCombination = {
     `)
 
   // This function is used for kl divergence
-  let combineAlongSupportOfSecondArgument0: (
+  let combineAlongSupportOfSecondArgument: (
     (float, float) => result<float, Operation.Error.t>,
     interpolator,
     T.t,
@@ -489,12 +489,11 @@ module PointwiseCombination = {
     result
   }
 
-  let combineAlongSupportOfSecondArgument: (
+  let combineAlongSupportOfSecondArgument2: (
     (float, float) => result<float, Operation.Error.t>,
-    interpolator,
     T.t,
     T.t,
-  ) => result<T.t, Operation.Error.t> = (fn, interpolator, prediction, answer) => {
+  ) => result<T.t, Operation.Error.t> = (fn, prediction, answer) => {
     let combineWithFn = (x: float, i: int) => {
       let answerX = x
       let answerY = answer.ys[i]