From 52393979e6597b22b898c29d8c60377e52d115fe Mon Sep 17 00:00:00 2001 From: shermanlo77 Date: Wed, 7 Apr 2021 17:10:07 +0100 Subject: [PATCH] Added elliptical slice sampling HMC accepted step is green rather than blue --- README.md | 28 +-- pom.xml | 2 +- .../ac/warwick/sip/mcmc/EllipticalSlice.java | 172 ++++++++++++++++++ src/uk/ac/warwick/sip/mcmc/Global.java | 2 + .../warwick/sip/mcmc/NormalDistribution.java | 13 ++ .../sip/mcmcprocessing/EllipticalSlice.java | 151 +++++++++++++++ .../mcmcprocessing/HamiltonianMonteCarlo.java | 2 +- .../sip/mcmcprocessing/McmcApplet.java | 4 +- .../sip/mcmcprocessing/NoUTurnSampler.java | 6 +- tex/processing_slice.png | Bin 0 -> 203623 bytes 10 files changed, 362 insertions(+), 18 deletions(-) create mode 100644 src/uk/ac/warwick/sip/mcmc/EllipticalSlice.java create mode 100644 src/uk/ac/warwick/sip/mcmcprocessing/EllipticalSlice.java create mode 100644 tex/processing_slice.png diff --git a/README.md b/README.md index efab48b..c4d1969 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ # oxwasp_exchange_mcmc -*Java* implementations of the **Metropolis-Hastings** (Metropolis et al., 1953) (Hastings, 1970), **Adaptive Metropolis-Hastings** (Haario et al., 2001) (Roberts and Rosenthal, 2009), **Hamiltonian Monte Carlo** (Neal, 2011) and **No U-Turn Sampler** (Hoffman and Gelman, 2014) including the dual averaging version. +*Java* implementations of the **Metropolis-Hastings** (Metropolis et al., 1953) (Hastings, 1970), **Adaptive Metropolis-Hastings** (Haario et al., 2001) (Roberts and Rosenthal, 2009), **Hamiltonian Monte Carlo** (Neal, 2011), **No U-Turn Sampler** (Hoffman and Gelman, 2014) including the dual averaging version and **Elliptical Slice Sampler** (Murray et al., 2010). Also included are *Processing* implementations of the algorithms for visualising these algorithms sampling a 2D Normal distribution. @@ -11,18 +11,10 @@ For dependencies, see the `pom.xml` file or: * `org.apache.commons.math3` [Commons Math: The Apache Commons Mathematics Library](http://commons.apache.org/proper/commons-math/) * `org.ejml` [Efficient Java Matrix Library](http://ejml.org/wiki/index.php?title=Main_Page) -## References -* Haario, H., Saksman, E., Tamminen, J., et al. (2001). An adaptive Metropolis algorithm. _Bernoulli_, 7(2):223-242. -* Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. _Biometrika_ 57(1):97-109. -* Hoffman, M. D. and Gelman, A. (2014). The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. _Journal of Machine Learning Research_, 15(1):1593-1623. -* Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. _The Journal of Chemical Physics_, 21(6):1087–1092. -* Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., editors, _Handbook of Markov Chain Monte Carlo_, chapter 5, pages 113–162. CRC press. -* Roberts, G. O. and Rosenthal, J. S. (2009). Examples of adaptive MCMC. _Journal of Computational and Graphical Statistics_, 18(2):349–367. - ## How to use (Linux recommended) Call the `.jar` file using ``` -java -jar oxwasp_exchange_mcmc-0.0.1-jar-with-dependencies.jar -option +java -jar oxwasp_exchange_mcmc-1.0.0-jar-with-dependencies.jar -option ``` where `-option` can be one of the following options below. Click on `pause` to pause the simulation, once paused, click on `step` to run the simulation one step at a time. Click on `quit` to quit the simulation. @@ -48,6 +40,11 @@ Click on the screen to start a No U-Turn Sampler. The yellow dots show the leap ![alt text](tex/processing_nuts.png "No U-Turn Sampler") +### `-slice` Elliptical Slice Sampler +Click on the screen to start an elliptical slice sampler. The next step of the chain is searched for on the ellipse. The yellow sections show acceptable regions of the ellipse. The red sections show unacceptable regions of the ellipse. Red dots shows rejected samples. + +![alt text](tex/processing_slice.png "Elliptical Slice Sampler") + ## How to compile (Linux recommended) *Maven* required. @@ -62,4 +59,13 @@ Go to the repository and run ``` mvn package ``` -and the `.jar` files are located in `/target/`. +and the `.jar` files are located in `target/`. + +## References +* Haario, H., Saksman, E., Tamminen, J., et al. (2001). An adaptive Metropolis algorithm. _Bernoulli_, 7(2):223-242. +* Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. _Biometrika_ 57(1):97-109. +* Hoffman, M. D. and Gelman, A. (2014). The No-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. _Journal of Machine Learning Research_, 15(1):1593-1623. +* Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. _The Journal of Chemical Physics_, 21(6):1087–1092. +* Murray, I., Adams, R. P., and MacKay, D. J. (2010). Elliptical slice sampling. _In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics_. +* Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., editors, _Handbook of Markov Chain Monte Carlo_, chapter 5, pages 113–162. CRC press. +* Roberts, G. O. and Rosenthal, J. S. (2009). Examples of adaptive MCMC. _Journal of Computational and Graphical Statistics_, 18(2):349–367. diff --git a/pom.xml b/pom.xml index d894cf4..50ccdc7 100644 --- a/pom.xml +++ b/pom.xml @@ -2,7 +2,7 @@ 4.0.0 uk.ac.warwick.sip oxwasp_exchange_mcmc - 0.0.1 + 1.0.0 jar UTF-8 diff --git a/src/uk/ac/warwick/sip/mcmc/EllipticalSlice.java b/src/uk/ac/warwick/sip/mcmc/EllipticalSlice.java new file mode 100644 index 0000000..2a21aaf --- /dev/null +++ b/src/uk/ac/warwick/sip/mcmc/EllipticalSlice.java @@ -0,0 +1,172 @@ +/* + * Copyright 2018-2021 Sherman Lo + + 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 uk.ac.warwick.sip.mcmc; + +import java.util.ArrayList; +import java.util.Iterator; + +import org.apache.commons.math3.random.MersenneTwister; +import org.ejml.dense.row.CommonOps_DDRM; +import org.ejml.simple.SimpleMatrix; + +/**CLASS: ELLIPTICAL SLICE SAMPLER + * Sampler which uses elliptical slice sampling + * Reference: Elliptical slice sampling (Murray, I., Adams, R. P., and MacKay, D. J. (2010). + * Elliptical slice sampling. In Proceedings of the 13th International Conference on Artificial + * Intelligence and Statistics.) + * At a step, a sample from the prior is taken. A weighted average between the current step and that + * sample is used as the next step in the MCMC according to the slice sampling scheme. + */ +public class EllipticalSlice extends Mcmc{ + + //the likelihood of the model, elliptical slice sampling works on the likelihood rather than the + //posterior + protected TargetDistribution likelihood; + //the prior distribution + protected NormalDistribution prior; + //position vector of the start of the ellipse (the current step) + protected SimpleMatrix ellipse0; + //position vector of the end of the ellipse (the sample from the prior) + protected SimpleMatrix proposal; + //after a step, an array of points looked at on the ellipse + protected ArrayList ellipticalPositions; + //slice variable, log uniform number plus log likelihood + protected double sliceVariable; + + /**CONSTRUCTOR + * Elliptical slice sampling algorithm. Samples from the prior (called the proposal in this code) + * and then uses slice sampling to find a weighted combination of the proposed and the current + * value, which turns out to make an ellipse. + * @param target Object which has a method to call the pdf + * @param likelihood the likelihood of the model + * @param prior NormalDistribution representing the prior + * @param chainLength Length of the chain to be obtained + * @param rng Random number generator all the random numbers + */ + public EllipticalSlice(TargetDistribution target, TargetDistribution likelihood, + NormalDistribution prior, int chainLength, MersenneTwister rng) { + super(target, chainLength, rng); + this.likelihood = likelihood; + this.prior = prior; + this.ellipticalPositions = new ArrayList(); + } + + /**CONSTRUCTOR + * Constructor for extending the length of the chain and resume running it + * Does a shallow copy of the provided chain and extending the member variable chainArray + * @param chain Chain to be extended + * @param nMoreSteps Number of steps to be extended + */ + public EllipticalSlice(EllipticalSlice chain, int nMoreSteps) { + //shallow copies of member variables + super(chain, nMoreSteps); + this.likelihood = chain.likelihood; + this.prior = chain.prior; + this.proposal = chain.proposal; + this.ellipticalPositions = chain.ellipticalPositions; + this.sliceVariable = chain.sliceVariable; + } + + @Override + public void step(SimpleMatrix position) { + //elliptical slice sampling is a weighted sum of position and a sample from the prior + this.ellipse0 = new SimpleMatrix(position); //start of ellipse + this.proposal = this.prior.sample(this.rng); //end of ellipse + //array to store all points looked at on the ellipse + this.ellipticalPositions = new ArrayList(); + + double angle = this.sampleAngle(0, 2*Math.PI); + double angleMin = angle - 2*Math.PI; + double angleMax = angle; + + //sliceVariable is compared with the likelihood at points on the ellipse + this.sliceVariable = Math.log(this.rng.nextDouble()) - this.likelihood.getPotential(position); + boolean gotSample = false; + + //look through the ellipse until got valid sample + while (!gotSample) { + position.set(this.getPointOnEllipse(angle)); + if (this.isValidPointOnEllipse(position)) { + gotSample = true; + } else { + //else this is not a valid point, look elsewhere on the ellipse + this.ellipticalPositions.add(new SimpleMatrix(position)); + if (angle < 0) { + angleMin = angle; + } else { + angleMax = angle; + } + angle = this.sampleAngle(angleMin, angleMax); + } + } + this.updateStatistics(position); + } + + /**METHOD: IS VALID POINT ON ELLIPSE + * Check if this position vector would be accepted under the slice sampling scheme. This would + * require the member variable sliceVariable initalised with the correct value. + * @param position position vector (on the ellipse) + * @return boolean if the position vector is valid under slice sampling + */ + public boolean isValidPointOnEllipse(SimpleMatrix position) { + return -this.likelihood.getPotential(position) > this.sliceVariable; + } + + /**METHOD: GET POINT ON ELLIPSE + * Return a weighted sum of initial and proposal, the weight using cosine and sine of angle + * @param initial vector of current position of chain + * @param proposal vector of sample from prior + * @param angle of the ellipse + * @return vector, weighted sum of initial and proposal + */ + public SimpleMatrix getPointOnEllipse(double angle) { + SimpleMatrix initialWeighted = new SimpleMatrix(this.ellipse0); + SimpleMatrix proposalWeighted = new SimpleMatrix(this.proposal); + + //centre the position vectors at the prior mean + CommonOps_DDRM.subtractEquals(initialWeighted.getDDRM(), this.prior.mean.getDDRM()); + CommonOps_DDRM.subtractEquals(proposalWeighted.getDDRM(), this.prior.mean.getDDRM()); + + CommonOps_DDRM.scale(Math.cos(angle), initialWeighted.getDDRM()); + CommonOps_DDRM.scale(Math.sin(angle), proposalWeighted.getDDRM()); + + CommonOps_DDRM.addEquals(proposalWeighted.getDDRM(), initialWeighted.getDDRM()); + CommonOps_DDRM.addEquals(proposalWeighted.getDDRM(), this.prior.mean.getDDRM()); + + return proposalWeighted; + } + + /**METHOD: GET ELLIPTICAL POSITIONS ITERATOR + * Return an iterator which iterates through all the points looked at on the ellipse + */ + public Iterator getEllipticalPositionsIterator(){ + return this.ellipticalPositions.iterator(); + } + + /**METHOD: SAMPLE ANGLE` + * Sample from the uniform distribution + * @param min minimun value + * @param max maximum value + */ + protected double sampleAngle(double min, double max) { + double angle = this.rng.nextDouble(); + angle *= max - min; + angle += min; + return angle; + } + +} diff --git a/src/uk/ac/warwick/sip/mcmc/Global.java b/src/uk/ac/warwick/sip/mcmc/Global.java index 02fec6c..345054f 100644 --- a/src/uk/ac/warwick/sip/mcmc/Global.java +++ b/src/uk/ac/warwick/sip/mcmc/Global.java @@ -48,6 +48,8 @@ public static void main(String[] args) { uk.ac.warwick.sip.mcmcprocessing.NoUTurnSampler.main(args); } else if (userArg.equals("-rwmh")) { uk.ac.warwick.sip.mcmcprocessing.RandomWalkMetropolisHastings.main(args); + } else if (userArg.equals("-slice")) { + uk.ac.warwick.sip.mcmcprocessing.EllipticalSlice.main(args); } else if (userArg.equals("-example")) { example(); } else if (userArg.equals("-test")) { diff --git a/src/uk/ac/warwick/sip/mcmc/NormalDistribution.java b/src/uk/ac/warwick/sip/mcmc/NormalDistribution.java index 755913d..3b43e7b 100644 --- a/src/uk/ac/warwick/sip/mcmc/NormalDistribution.java +++ b/src/uk/ac/warwick/sip/mcmc/NormalDistribution.java @@ -18,6 +18,7 @@ import java.lang.Math; +import org.apache.commons.math3.random.MersenneTwister; import org.ejml.dense.row.CommonOps_DDRM; import org.ejml.dense.row.decomposition.TriangularSolver_DDRM; import org.ejml.simple.SimpleMatrix; @@ -98,7 +99,19 @@ public SimpleMatrix getDPotential(SimpleMatrix x) { SimpleMatrix covariance = new SimpleMatrix(this.nDim, this.nDim); CommonOps_DDRM.multInner(covarianceCholInverse.getDDRM(), covariance.getDDRM()); return covariance.mult(x.minus(this.mean)); + } + /**METHOD: SAMPLE + * Sample a Gaussian distribution with a mean and covariance + * @return vector, sample from Gaussian distribution + */ + public SimpleMatrix sample(MersenneTwister rng) { + double [] xArray = new double[this.nDim]; + for (int i=0; i ellipticalPoints = this.chain.getEllipticalPositionsIterator(); + this.stroke(255, 0, 0); + this.fill(255, 0, 0); + float x, y; + while(ellipticalPoints.hasNext()) { + SimpleMatrix point = ellipticalPoints.next(); + x = (float) point.get(0); + y = (float) point.get(1); + //draw the first sample + this.ellipse(x, y , CIRCLE_SIZE, CIRCLE_SIZE); + } + + //draw the ellipse as a parametric plot, using angle as a parameter + //yellow line for acceptable region of the ellipse + //red line for rejected region of the ellipse, according to slice sampling + double angle = -Math.PI; + double angleDiff = 2*Math.PI/N_PLOT; + float x0 = Float.NaN; + float y0 = Float.NaN; + SimpleMatrix ellipticalPoint; + this.strokeWeight(2); + if (this.chain.getNStep() > 0) { + for (int i=0; i 0) { + + if (this.chain.isValidPointOnEllipse(ellipticalPoint)) { + this.stroke(255, 255, 0); + } else { + this.stroke(255, 0, 0); + } + + this.line(x0, y0, x, y); + } + + x0 = x; + y0 = y; + angle += angleDiff; + } + } + this.strokeWeight(1); + + //draw the latest sample + this.stroke(0,255,0); + this.fill(0,255,0); + x = (float) chainArray[this.chain.getNStep()*2]; + y = (float) chainArray[this.chain.getNStep()*2 + 1]; + this.ellipse(x, y , CIRCLE_SIZE, CIRCLE_SIZE); + } + + /**OVERRIDE: MOUSE RELEASED + * Instantiate a new chain, if the mouse of not or clicked on a gui + */ + @Override + public void mouseReleased() { + //if the mouse hasn't clicked on a gui or on one + if (!this.isMouseClickOnGui) { + if (!this.isMouseOnGui()) { + //get mouse position + double [] mousePosition = new double [2]; + mousePosition[0] = (double) this.mouseX; + mousePosition[1] = (double) this.mouseY; + //instantiate chain + MersenneTwister rng = new MersenneTwister(this.millis()); + this.chain = new uk.ac.warwick.sip.mcmc.EllipticalSlice(this.target, this.likelihood, + this.prior, CHAIN_LENGTH, rng); + this.chain.setInitialValue(mousePosition); + super.chain = this.chain; //save copy to the superclass + this.isInit = true; + } + } + super.mouseReleased(); + } + + /**METHOD: GET LIKELIHOOD + * Return the default likelihood function + */ + private NormalDistribution getLikelihood() { + //instantiate the covariance + SimpleMatrix targetCovariance = new SimpleMatrix(2, 2); + targetCovariance.set(0, 0, 2*NORMAL_TARGET_VARIANCE); + targetCovariance.set(1, 1, 2*NORMAL_TARGET_VARIANCE); + //instantiate the mean + SimpleMatrix mean = new SimpleMatrix(2, 1, true, this.getCentre()); + return new NormalDistribution(2, mean, targetCovariance); + } + + /**METHOD: GET PRIOR + * Return the default prior distribution + */ + private NormalDistribution getPrior() { + return this.getLikelihood(); + } + + public static void main(String[] args) { + PApplet.main("uk.ac.warwick.sip.mcmcprocessing.EllipticalSlice"); + } +} diff --git a/src/uk/ac/warwick/sip/mcmcprocessing/HamiltonianMonteCarlo.java b/src/uk/ac/warwick/sip/mcmcprocessing/HamiltonianMonteCarlo.java index a1d1f86..3726736 100644 --- a/src/uk/ac/warwick/sip/mcmcprocessing/HamiltonianMonteCarlo.java +++ b/src/uk/ac/warwick/sip/mcmcprocessing/HamiltonianMonteCarlo.java @@ -50,7 +50,7 @@ public class HamiltonianMonteCarlo extends McmcApplet{ @Override public void setup() { super.setup(); - target = this.getNormalDistribution(); + this.target = this.getNormalDistribution(); //instantiate slider bar this.nLeapFrogSlider = new GSlider(this, 110, 150, 300, 150, 30); diff --git a/src/uk/ac/warwick/sip/mcmcprocessing/McmcApplet.java b/src/uk/ac/warwick/sip/mcmcprocessing/McmcApplet.java index 5c2da20..7a20b8c 100644 --- a/src/uk/ac/warwick/sip/mcmcprocessing/McmcApplet.java +++ b/src/uk/ac/warwick/sip/mcmcprocessing/McmcApplet.java @@ -69,8 +69,8 @@ public void settings() { */ @Override public void setup() { - this.pauseButton = new GButton(this, 10,10,50,50,"pause"); - this.stepButton = new GButton(this, 10,80,50,50,"step"); + this.pauseButton = new GButton(this, 10, 10, 50,50, "pause"); + this.stepButton = new GButton(this, 10, 80, 50, 50, "step"); this.quitButton = new GButton(this, 10, this.height-80, 50, 50, "quit"); } diff --git a/src/uk/ac/warwick/sip/mcmcprocessing/NoUTurnSampler.java b/src/uk/ac/warwick/sip/mcmcprocessing/NoUTurnSampler.java index 45221d0..93a5a9f 100644 --- a/src/uk/ac/warwick/sip/mcmcprocessing/NoUTurnSampler.java +++ b/src/uk/ac/warwick/sip/mcmcprocessing/NoUTurnSampler.java @@ -80,9 +80,9 @@ protected void drawMcmc() { x1 = x2; y1 = y2; } - //draw in blue the accepted sample - this.stroke(0,0,255); - this.fill(0,0,255); + //draw in green the accepted sample + this.stroke(0,255,0); + this.fill(0,255,0); x2 = (float) chainArray[this.chain.getNStep()*2]; y2 = (float) chainArray[this.chain.getNStep()*2+1]; this.ellipse(x2, y2 , CIRCLE_SIZE, CIRCLE_SIZE); diff --git a/tex/processing_slice.png b/tex/processing_slice.png new file mode 100644 index 0000000000000000000000000000000000000000..6398e8983682d179f6bc2096653127f2d98d6762 GIT binary patch literal 203623 zcma&O1yq!6)Gkblv`V*1Np}q;ARwIzC}j{M-Gj8!2q-Bn-Hmi3ARw(E-7xgfL!V~` ze82DLf7be4%Qb*^?zr}~_r5VmT~!_*hY|+`1qEN>@gq$X6fAEP6b#CnH-Mj{Rhf7K z9~chO3feb;KkheQ2Lj(yILhieYT1}Ny1cMAK{2zou`=Oscx7*5V(nmV3Hv>}NbQ?8Ii7mw}pBlEaH>#>+c#;5h)?e262R~2jsa7JlDUCps8B-A4+b60u% z{O^7#FafuGwtc_}x1-Y^f6ro-N=%T+q4FcyufzFHS6KSDFrs!P2ClN#9DMY>VqTNe 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