tuneSampler
Class: HamiltonianSampler
Tune Hamiltonian Monte Carlo (HMC) sampler
Syntax
tunedSmp = tuneSampler(smp)
[tunedSmp,tuningInfo]
= tuneSampler(smp)
[tunedSmp,tuningInfo]
= tuneSampler(___,Name,Value)
Description
tunedSmp = tuneSampler(smp)
First, tuneSampler tunes the mass vector of
the HMC sampler smp. Then, it tunes the step
size and number of steps of the leapfrog integrations to achieve a
certain target acceptance ratio.
You can use the tuned sampler to create Markov chains using
the drawSamples method.
[ returns additional
tuning information in tunedSmp,tuningInfo]
= tuneSampler(smp)tuningInfo.
[ specifies
additional options using one or more name-value pair arguments. Specify
name-value pair arguments after all other input arguments. tunedSmp,tuningInfo]
= tuneSampler(___,Name,Value)
Input Arguments
Name-Value Arguments
Output Arguments
Examples
Tune the parameters of a Hamiltonian Monte Carlo (HMC) sampler.
Define the number of parameters to sample and their means.
NumParams = 9; means = [1:NumParams]'; standevs = 1;
First, save a function normalDistGrad on the MATLAB® path that returns the multivariate normal log probability density and its gradient (normalDistGrad is defined at the end of this example). Then, call the function with arguments to define the logpdf input argument to the hmcSampler function.
logpdf = @(theta)normalDistGrad(theta,means,standevs);
Choose a starting point and create the HMC sampler.
startpoint = randn(NumParams,1); smp = hmcSampler(logpdf,startpoint);
It is important to select good values for the sampler parameters to get efficient sampling. The best way to find good values is to automatically tune the MassVector, StepSize, and NumSteps parameters using tuneSampler. The method:
1. Tunes the MassVector of the sampler.
2. Tunes StepSize and NumSteps for a fixed simulation length to achieve a certain acceptance ratio. The default target acceptance ratio of 0.65 is good in most cases.
[smp,info] = tuneSampler(smp,'NumStepSizeTuningIterations',50,'VerbosityLevel',1,'NumPrint',10);
o Tuning mass vector using method: iterative-sampling Finished mass vector tuning iteration 1 of 5. Finished mass vector tuning iteration 2 of 5. Finished mass vector tuning iteration 3 of 5. Finished mass vector tuning iteration 4 of 5. Finished mass vector tuning iteration 5 of 5. o Tuning step size using method: dual-averaging. Target acceptance ratio = 0.65 o Initial step size for dual-averaging = 2 |==================================================================================| | ITER | LOG PDF | STEP SIZE | NUM STEPS | ACC RATIO | DIVERGENT | |==================================================================================| | 10 | -1.710457e+01 | 1.193e+00 | 4 | 5.000e-01 | 0 | | 20 | -9.152514e+00 | 9.527e-01 | 5 | 5.500e-01 | 0 | | 30 | -1.068923e+01 | 8.856e-01 | 6 | 5.333e-01 | 0 | | 40 | -1.290816e+01 | 8.506e-01 | 6 | 5.750e-01 | 0 | | 50 | -1.770386e+01 | 8.581e-01 | 6 | 6.000e-01 | 0 |
Plot the evolution of the step size during tuning to ensure that the step size tuning has converged. Display the achieved acceptance ratio.
figure; plot(info.StepSizeTuningInfo.StepSizeProfile); xlabel('Iteration'); ylabel('Step Size');
accratio = info.StepSizeTuningInfo.AcceptanceRatio
accratio = 0.6000
The normalDistGrad function returns the logarithm of the multivariate normal probability density with means in Mu and standard deviations in Sigma, specified as scalars or columns vectors the same length as startpoint. The second output argument is the corresponding gradient.
function [lpdf,glpdf] = normalDistGrad(X,Mu,Sigma) Z = (X - Mu)./Sigma; lpdf = sum(-log(Sigma) - .5*log(2*pi) - .5*(Z.^2)); glpdf = -Z./Sigma; end
Tips
After creating an HMC sampler using the
hmcSamplerfunction, you can compute MAP (maximum-a-posteriori) point estimates, tune the sampler, draw samples, and check convergence diagnostics using the methods of theHamiltonianSamplerclass. For an example of this workflow, see Bayesian Linear Regression Using Hamiltonian Monte Carlo.
Version History
Introduced in R2017a
