Merge pull request #402 from quantified-uncertainty/algebraic-combination-refactor

Algebraic combination refactor
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Ozzie Gooen 2022-04-28 08:19:02 -04:00 committed by GitHub
commit 20685ea8cb
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3 changed files with 166 additions and 144 deletions

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@ -92,11 +92,11 @@ describe("eval on distribution functions", () => {
testEval("log(2, uniform(5,8))", "Ok(Sample Set Distribution)")
testEval(
"log(normal(5,2), 3)",
"Error(Distribution Math Error: Logarithm of input error: First input must completely greater than 0)",
"Error(Distribution Math Error: Logarithm of input error: First input must be completely greater than 0)",
)
testEval(
"log(normal(5,2), normal(10,1))",
"Error(Distribution Math Error: Logarithm of input error: First input must completely greater than 0)",
"Error(Distribution Math Error: Logarithm of input error: First input must be completely greater than 0)",
)
testEval("log(uniform(5,8))", "Ok(Sample Set Distribution)")
testEval("log10(uniform(5,8))", "Ok(Sample Set Distribution)")

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@ -150,144 +150,143 @@ let truncate = Truncate.run
of a new variable that is the result of the operation on A and B.
For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
In general, this is implemented via convolution.
TODO: It would be useful to be able to pass in a paramater to get this to run either with convolution or monte carlo.
*/
module AlgebraicCombination = {
let runConvolution = (
toPointSet: toPointSetFn,
arithmeticOperation: Operation.convolutionOperation,
t1: t,
t2: t,
) =>
E.R.merge(toPointSet(t1), toPointSet(t2))->E.R2.fmap(((a, b)) =>
PointSetDist.combineAlgebraically(arithmeticOperation, a, b)
)
let runMonteCarlo = (
toSampleSet: toSampleSetFn,
arithmeticOperation: Operation.algebraicOperation,
t1: t,
t2: t,
): result<t, error> => {
let fn = Operation.Algebraic.toFn(arithmeticOperation)
E.R.merge(toSampleSet(t1), toSampleSet(t2))
->E.R.bind(((t1, t2)) => {
SampleSetDist.map2(~fn, ~t1, ~t2)->E.R2.errMap(x => DistributionTypes.OperationError(x))
})
->E.R2.fmap(r => DistributionTypes.SampleSet(r))
}
/*
module InputValidator = {
/*
It would be good to also do a check to make sure that probability mass for the second
operand, at value 1.0, is 0 (or approximately 0). However, we'd ideally want to check
that both the probability mass and the probability density are greater than zero.
Right now we don't yet have a way of getting probability mass, so I'll leave this for later.
*/
let getLogarithmInputError = (t1: t, t2: t, ~toPointSetFn: toPointSetFn): option<error> => {
let firstOperandIsGreaterThanZero =
toFloatOperation(
t1,
~toPointSetFn,
~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
) |> E.R.fmap(r => r > 0.)
let secondOperandIsGreaterThanZero =
toFloatOperation(
t2,
~toPointSetFn,
~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
) |> E.R.fmap(r => r > 0.)
let items = E.A.R.firstErrorOrOpen([
firstOperandIsGreaterThanZero,
secondOperandIsGreaterThanZero,
])
switch items {
| Error(r) => Some(r)
| Ok([true, _]) =>
Some(LogarithmOfDistributionError("First input must completely greater than 0"))
| Ok([false, true]) =>
Some(LogarithmOfDistributionError("Second input must completely greater than 0"))
| Ok([false, false]) => None
| Ok(_) => Some(Unreachable)
let getLogarithmInputError = (t1: t, t2: t, ~toPointSetFn: toPointSetFn): option<error> => {
let firstOperandIsGreaterThanZero =
toFloatOperation(
t1,
~toPointSetFn,
~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
) |> E.R.fmap(r => r > 0.)
let secondOperandIsGreaterThanZero =
toFloatOperation(
t2,
~toPointSetFn,
~distToFloatOperation=#Cdf(MagicNumbers.Epsilon.ten),
) |> E.R.fmap(r => r > 0.)
let items = E.A.R.firstErrorOrOpen([
firstOperandIsGreaterThanZero,
secondOperandIsGreaterThanZero,
])
switch items {
| Error(r) => Some(r)
| Ok([true, _]) =>
Some(LogarithmOfDistributionError("First input must be completely greater than 0"))
| Ok([false, true]) =>
Some(LogarithmOfDistributionError("Second input must be completely greater than 0"))
| Ok([false, false]) => None
| Ok(_) => Some(Unreachable)
}
}
let run = (t1: t, t2: t, ~toPointSetFn: toPointSetFn, ~arithmeticOperation): option<error> => {
if arithmeticOperation == #Logarithm {
getLogarithmInputError(t1, t2, ~toPointSetFn)
} else {
None
}
}
}
let getInvalidOperationError = (
t1: t,
t2: t,
~toPointSetFn: toPointSetFn,
module StrategyCallOnValidatedInputs = {
let convolution = (
toPointSet: toPointSetFn,
arithmeticOperation: Operation.convolutionOperation,
t1: t,
t2: t,
): result<t, error> =>
E.R.merge(toPointSet(t1), toPointSet(t2))
->E.R2.fmap(((a, b)) => PointSetDist.combineAlgebraically(arithmeticOperation, a, b))
->E.R2.fmap(r => DistributionTypes.PointSet(r))
let monteCarlo = (
toSampleSet: toSampleSetFn,
arithmeticOperation: Operation.algebraicOperation,
t1: t,
t2: t,
): result<t, error> => {
let fn = Operation.Algebraic.toFn(arithmeticOperation)
E.R.merge(toSampleSet(t1), toSampleSet(t2))
->E.R.bind(((t1, t2)) => {
SampleSetDist.map2(~fn, ~t1, ~t2)->E.R2.errMap(x => DistributionTypes.OperationError(x))
})
->E.R2.fmap(r => DistributionTypes.SampleSet(r))
}
let symbolic = (
arithmeticOperation: Operation.algebraicOperation,
t1: t,
t2: t,
): SymbolicDistTypes.analyticalSimplificationResult => {
switch (t1, t2) {
| (DistributionTypes.Symbolic(d1), DistributionTypes.Symbolic(d2)) =>
SymbolicDist.T.tryAnalyticalSimplification(d1, d2, arithmeticOperation)
| _ => #NoSolution
}
}
}
module StrategyChooser = {
type specificStrategy = [#AsSymbolic | #AsMonteCarlo | #AsConvolution]
//I'm (Ozzie) really just guessing here, very little idea what's best
let expectedConvolutionCost: t => int = x =>
switch x {
| Symbolic(#Float(_)) => MagicNumbers.OpCost.floatCost
| Symbolic(_) => MagicNumbers.OpCost.symbolicCost
| PointSet(Discrete(m)) => m.xyShape->XYShape.T.length
| PointSet(Mixed(_)) => MagicNumbers.OpCost.mixedCost
| PointSet(Continuous(_)) => MagicNumbers.OpCost.continuousCost
| _ => MagicNumbers.OpCost.wildcardCost
}
let run = (~t1: t, ~t2: t, ~arithmeticOperation): specificStrategy => {
switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
| #AnalyticalSolution(_)
| #Error(_) =>
#AsSymbolic
| #NoSolution =>
if Operation.Convolution.canDoAlgebraicOperation(arithmeticOperation) {
expectedConvolutionCost(t1) * expectedConvolutionCost(t2) >
MagicNumbers.OpCost.monteCarloCost
? #AsMonteCarlo
: #AsConvolution
} else {
#AsMonteCarlo
}
}
}
}
let runStrategyOnValidatedInputs = (
~t1: t,
~t2: t,
~arithmeticOperation,
): option<error> => {
if arithmeticOperation == #Logarithm {
getLogarithmInputError(t1, t2, ~toPointSetFn)
} else {
None
}
}
//I'm (Ozzie) really just guessing here, very little idea what's best
let expectedConvolutionCost: t => int = x =>
switch x {
| Symbolic(#Float(_)) => MagicNumbers.OpCost.floatCost
| Symbolic(_) => MagicNumbers.OpCost.symbolicCost
| PointSet(Discrete(m)) => m.xyShape->XYShape.T.length
| PointSet(Mixed(_)) => MagicNumbers.OpCost.mixedCost
| PointSet(Continuous(_)) => MagicNumbers.OpCost.continuousCost
| _ => MagicNumbers.OpCost.wildcardCost
}
type calculationStrategy = MonteCarloStrat | ConvolutionStrat(Operation.convolutionOperation)
let chooseConvolutionOrMonteCarloDefault = (
op: Operation.algebraicOperation,
t2: t,
t1: t,
): calculationStrategy =>
switch op {
| #Divide
| #Power
| #Logarithm =>
MonteCarloStrat
| (#Add | #Subtract | #Multiply) as convOp =>
expectedConvolutionCost(t1) * expectedConvolutionCost(t2) > MagicNumbers.OpCost.monteCarloCost
? MonteCarloStrat
: ConvolutionStrat(convOp)
}
let tryAnalyticalSimplification = (
arithmeticOperation: Operation.algebraicOperation,
t1: t,
t2: t,
): option<SymbolicDistTypes.analyticalSimplificationResult> => {
switch (t1, t2) {
| (DistributionTypes.Symbolic(d1), DistributionTypes.Symbolic(d2)) =>
Some(SymbolicDist.T.tryAnalyticalSimplification(d1, d2, arithmeticOperation))
| _ => None
}
}
let runDefault = (
t1: t,
~strategy: StrategyChooser.specificStrategy,
~toPointSetFn: toPointSetFn,
~toSampleSetFn: toSampleSetFn,
~arithmeticOperation,
~t2: t,
): result<t, error> => {
switch tryAnalyticalSimplification(arithmeticOperation, t1, t2) {
| Some(#AnalyticalSolution(symbolicDist)) => Ok(Symbolic(symbolicDist))
| Some(#Error(e)) => Error(OperationError(e))
| Some(#NoSolution)
| None =>
switch getInvalidOperationError(t1, t2, ~toPointSetFn, ~arithmeticOperation) {
| Some(e) => Error(e)
| None =>
switch chooseConvolutionOrMonteCarloDefault(arithmeticOperation, t1, t2) {
| MonteCarloStrat => runMonteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
| ConvolutionStrat(convOp) =>
runConvolution(toPointSetFn, convOp, t1, t2)->E.R2.fmap(r => DistributionTypes.PointSet(
r,
))
}
switch strategy {
| #AsMonteCarlo =>
StrategyCallOnValidatedInputs.monteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
| #AsSymbolic =>
switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
| #AnalyticalSolution(symbolicDist) => Ok(Symbolic(symbolicDist))
| #Error(e) => Error(OperationError(e))
| #NoSolution => Error(Unreachable)
}
| #AsConvolution =>
switch Operation.Convolution.fromAlgebraicOperation(arithmeticOperation) {
| Some(convOp) => StrategyCallOnValidatedInputs.convolution(toPointSetFn, convOp, t1, t2)
| None => Error(Unreachable)
}
}
}
@ -300,27 +299,38 @@ module AlgebraicCombination = {
~arithmeticOperation: Operation.algebraicOperation,
~t2: t,
): result<t, error> => {
switch strategy {
| AsDefault => runDefault(t1, ~toPointSetFn, ~toSampleSetFn, ~arithmeticOperation, ~t2)
| AsSymbolic =>
switch tryAnalyticalSimplification(arithmeticOperation, t1, t2) {
| Some(#AnalyticalSolution(symbolicDist)) => Ok(Symbolic(symbolicDist))
| Some(#NoSolution) => Error(RequestedStrategyInvalidError(`No analytical solution`))
| None => Error(RequestedStrategyInvalidError("Inputs were not even symbolic"))
| Some(#Error(err)) => Error(OperationError(err))
let invalidOperationError = InputValidator.run(t1, t2, ~arithmeticOperation, ~toPointSetFn)
switch (invalidOperationError, strategy) {
| (Some(e), _) => Error(e)
| (None, AsDefault) => {
let chooseStrategy = StrategyChooser.run(~arithmeticOperation, ~t1, ~t2)
runStrategyOnValidatedInputs(
~t1,
~t2,
~strategy=chooseStrategy,
~arithmeticOperation,
~toPointSetFn,
~toSampleSetFn,
)
}
| AsConvolution => {
let errString = opString => `Can't convolve on ${opString}`
switch arithmeticOperation {
| (#Add | #Subtract | #Multiply) as convOp =>
runConvolution(toPointSetFn, convOp, t1, t2)->E.R2.fmap(r => DistributionTypes.PointSet(
r,
))
| (#Divide | #Power | #Logarithm) as op =>
op->Operation.Algebraic.toString->errString->RequestedStrategyInvalidError->Error
| (None, AsMonteCarlo) =>
StrategyCallOnValidatedInputs.monteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
| (None, AsSymbolic) =>
switch StrategyCallOnValidatedInputs.symbolic(arithmeticOperation, t1, t2) {
| #AnalyticalSolution(symbolicDist) => Ok(Symbolic(symbolicDist))
| #NoSolution => Error(RequestedStrategyInvalidError(`No analytic solution for inputs`))
| #Error(err) => Error(OperationError(err))
}
| (None, AsConvolution) =>
switch Operation.Convolution.fromAlgebraicOperation(arithmeticOperation) {
| None => {
let errString = `Convolution not supported for ${Operation.Algebraic.toString(
arithmeticOperation,
)}`
Error(RequestedStrategyInvalidError(errString))
}
| Some(convOp) => StrategyCallOnValidatedInputs.convolution(toPointSetFn, convOp, t1, t2)
}
| AsMonteCarlo => runMonteCarlo(toSampleSetFn, arithmeticOperation, t1, t2)
}
}
}

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@ -29,6 +29,18 @@ type distToFloatOperation = [
module Convolution = {
type t = convolutionOperation
//Only a selection of operations are supported by convolution.
let fromAlgebraicOperation = (op: algebraicOperation): option<convolutionOperation> =>
switch op {
| #Add => Some(#Add)
| #Subtract => Some(#Subtract)
| #Multiply => Some(#Multiply)
| #Divide | #Power | #Logarithm => None
}
let canDoAlgebraicOperation = (op: algebraicOperation): bool =>
fromAlgebraicOperation(op)->E.O.isSome
let toFn: (t, float, float) => float = x =>
switch x {
| #Add => \"+."