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ImportanceSample.scala
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ImportanceSample.scala
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/*
* Copyright 2021 Arman Bilge
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package schrodinger.montecarlo
import algebra.ring.Semifield
import cats.Monad
import cats.data.NonEmptyList
import cats.kernel.Eq
import cats.syntax.all.*
import schrodinger.kernel.Categorical
import schrodinger.math.syntax.*
import schrodinger.stats.Density
trait ImportanceSample[F[_], G[_], A]:
def importanceSample(target: F[A], proposal: G[A], sampleCount: Int): G[A]
object ImportanceSample:
inline def apply[F[_], G[_], A](using
is: ImportanceSample[F, G, A],
)(target: F[A], proposal: G[A], sampleCount: Int): G[A] =
is.importanceSample(target, proposal, sampleCount)
given [F[_]: Monad, P: Eq, A](using
P: Semifield[P],
c: Categorical[F, NonEmptyList[P], Long],
): ImportanceSample[Density[F, P, _], WeightedT[F, P, _], A] with
def importanceSample(
target: Density[F, P, A],
proposal: WeightedT[F, P, A],
sampleCount: Int,
) = WeightedT {
proposal.importanceF(target).value.replicateA(sampleCount).flatMap { samples =>
val marginal = P.sum(samples.view.map(_.weight)) / P.fromInt(sampleCount)
Categorical(NonEmptyList.fromListUnsafe(samples).fproduct(_.weight)).map {
case Weighted.Heavy(_, d, a) => Weighted(d / marginal, a)
case weightless @ Weighted.Weightless(_) => weightless
}
}
}