Merge pull request #533 from Vasilev-Ilya/STUD-7_metropolis_hastings_sampler
Draft: STUD-7: Metropolis-Hastings sampler implementation
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/*
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* Copyright 2018-2024 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.samplers
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import space.kscience.kmath.chains.BlockingDoubleChain
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import space.kscience.kmath.distributions.Distribution1D
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import space.kscience.kmath.distributions.NormalDistribution
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import space.kscience.kmath.random.RandomGenerator
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import space.kscience.kmath.structures.Float64Buffer
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import kotlin.math.*
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/**
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* [Metropolis–Hastings algorithm](https://en.wikipedia.org/wiki/Metropolis-Hastings_algorithm) for sampling
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* target distribution [targetDist].
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*
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* The normal distribution is used as the proposal function.
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*
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* params:
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* - targetDist: function close to the density of the sampled distribution;
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* - initialState: initial value of the chain of sampled values;
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* - proposalStd: standard deviation of the proposal function.
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*/
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public class MetropolisHastingsSampler(
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public val targetDist: (arg : Double) -> Double,
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public val initialState : Double = 0.0,
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public val proposalStd : Double = 1.0,
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) : BlockingDoubleSampler {
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override fun sample(generator: RandomGenerator): BlockingDoubleChain = object : BlockingDoubleChain {
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var currentState = initialState
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fun proposalDist(arg : Double) = NormalDistribution(arg, proposalStd)
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override fun nextBufferBlocking(size: Int): Float64Buffer {
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val acceptanceProb = generator.nextDoubleBuffer(size)
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return Float64Buffer(size) {index ->
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val newState = proposalDist(currentState).sample(generator).nextBufferBlocking(1).get(0)
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val acceptanceRatio = min(1.0, targetDist(newState) / targetDist(currentState))
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currentState = if (acceptanceProb[index] <= acceptanceRatio) newState else currentState
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currentState
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}
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}
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override suspend fun fork(): BlockingDoubleChain = sample(generator.fork())
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}
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}
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/*
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* Copyright 2018-2024 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.samplers
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import space.kscience.kmath.distributions.NormalDistribution
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import space.kscience.kmath.operations.Float64Field
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import space.kscience.kmath.random.DefaultGenerator
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import space.kscience.kmath.stat.invoke
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import space.kscience.kmath.stat.mean
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import kotlin.math.exp
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import kotlin.math.pow
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import kotlin.test.Test
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import kotlin.test.assertEquals
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class TestMetropolisHastingsSampler {
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@Test
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fun samplingNormalTest() {
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fun normalDist1(arg : Double) = NormalDistribution(0.5, 1.0).probability(arg)
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var sampler = MetropolisHastingsSampler(::normalDist1, proposalStd = 1.0)
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var sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(1_000_000)
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assertEquals(0.5, Float64Field.mean(sampledValues), 1e-2)
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fun normalDist2(arg : Double) = NormalDistribution(68.13, 1.0).probability(arg)
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sampler = MetropolisHastingsSampler(::normalDist2, initialState = 63.0, proposalStd = 1.0)
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sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(1_000_000)
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assertEquals(68.13, Float64Field.mean(sampledValues), 1e-2)
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}
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@Test
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fun samplingExponentialTest() {
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fun expDist(arg : Double, param : Double) : Double {
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if (arg < 0.0) { return 0.0 }
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return param * exp(-param * arg)
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}
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fun expDist1(arg : Double) = expDist(arg, 0.5)
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var sampler = MetropolisHastingsSampler(::expDist1, initialState = 2.0, proposalStd = 1.0)
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var sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(1_000_000)
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assertEquals(2.0, Float64Field.mean(sampledValues), 1e-2)
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fun expDist2(arg : Double) = expDist(arg, 2.0)
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sampler = MetropolisHastingsSampler(::expDist2, initialState = 9.0, proposalStd = 1.0)
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sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(1_000_000)
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assertEquals(0.5, Float64Field.mean(sampledValues), 1e-2)
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}
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@Test
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fun samplingRayleighTest() {
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fun rayleighDist(arg : Double, sigma : Double) : Double {
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if (arg < 0.0) { return 0.0 }
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val expArg = (arg / sigma).pow(2)
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return arg * exp(-expArg / 2.0) / sigma.pow(2)
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}
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fun rayleighDist1(arg : Double) = rayleighDist(arg, 1.0)
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var sampler = MetropolisHastingsSampler(::rayleighDist1, initialState = 2.0, proposalStd = 1.0)
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var sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(1_000_000)
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assertEquals(1.25, Float64Field.mean(sampledValues), 1e-2)
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fun rayleighDist2(arg : Double) = rayleighDist(arg, 2.0)
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sampler = MetropolisHastingsSampler(::rayleighDist2, proposalStd = 1.0)
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sampledValues = sampler.sample(DefaultGenerator()).nextBufferBlocking(10_000_000)
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assertEquals(2.5, Float64Field.mean(sampledValues), 1e-2)
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}
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}
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