MCMC¶
MCMC¶

class
MCMC
(kernel, num_samples, warmup_steps=None, num_chains=1, mp_context=None, disable_progbar=False)[source]¶ Bases:
pyro.infer.abstract_infer.TracePosterior
Wrapper class for Markov Chain Monte Carlo algorithms. Specific MCMC algorithms are TraceKernel instances and need to be supplied as a
kernel
argument to the constructor.Note
The case of num_chains > 1 uses python multiprocessing to run parallel chains in multiple processes. This goes with the usual caveats around multiprocessing in python, e.g. the model used to initialize the
kernel
must be serializable via pickle, and the performance / constraints will be platform dependent (e.g. only the “spawn” context is available in Windows). This has also not been extensively tested on the Windows platform.Parameters:  kernel – An instance of the
TraceKernel
class, which when given an execution trace returns another sample trace from the target (posterior) distribution.  num_samples (int) – The number of samples that need to be generated, excluding the samples discarded during the warmup phase.
 warmup_steps (int) – Number of warmup iterations. The samples generated during the warmup phase are discarded. If not provided, default is half of num_samples.
 num_chains (int) – Number of MCMC chains to run in parallel. Depending on whether num_chains is 1 or more than 1, this class internally dispatches to either _SingleSampler or _ParallelSampler.
 mp_context (str) – Multiprocessing context to use when num_chains > 1. Only applicable for Python 3.5 and above. Use mp_context=”spawn” for CUDA.
 disable_progbar (bool) – Disable progress bar and diagnostics update.

marginal
(sites=None)[source]¶ Marginalizes latent sites from the sampler.
Parameters: sites (list) – optional list of sites for which we need to generate the marginal distribution. Returns: A MCMCMarginals
class instance.Return type: MCMCMarginals
.
 kernel – An instance of the
HMC¶

class
HMC
(model, step_size=1, trajectory_length=None, num_steps=None, adapt_step_size=True, adapt_mass_matrix=True, full_mass=False, transforms=None, max_plate_nesting=None, jit_compile=False, jit_options=None, ignore_jit_warnings=False, target_accept_prob=0.8)[source]¶ Bases:
pyro.infer.mcmc.trace_kernel.TraceKernel
Simple Hamiltonian Monte Carlo kernel, where
step_size
andnum_steps
need to be explicitly specified by the user.References
[1] MCMC Using Hamiltonian Dynamics, Radford M. Neal
Parameters:  model – Python callable containing Pyro primitives.
 step_size (float) – Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1.
 trajectory_length (float) – Length of a MCMC trajectory. If not
specified, it will be set to
step_size x num_steps
. In casenum_steps
is not specified, it will be set to \(2\pi\).  num_steps (int) – The number of discrete steps over which to simulate
Hamiltonian dynamics. The state at the end of the trajectory is
returned as the proposal. This value is always equal to
int(trajectory_length / step_size)
.  adapt_step_size (bool) – A flag to decide if we want to adapt step_size during warmup phase using Dual Averaging scheme.
 adapt_mass_matrix (bool) – A flag to decide if we want to adapt mass matrix during warmup phase using Welford scheme.
 full_mass (bool) – A flag to decide if mass matrix is dense or diagonal.
 transforms (dict) – Optional dictionary that specifies a transform
for a sample site with constrained support to unconstrained space. The
transform should be invertible, and implement log_abs_det_jacobian.
If not specified and the model has sites with constrained support,
automatic transformations will be applied, as specified in
torch.distributions.constraint_registry
.  max_plate_nesting (int) – Optional bound on max number of nested
pyro.plate()
contexts. This is required if model contains discrete sample sites that can be enumerated over in parallel.  jit_compile (bool) – Optional parameter denoting whether to use the PyTorch JIT to trace the log density computation, and use this optimized executable trace in the integrator.
 jit_options (dict) – A dictionary contains optional arguments for
torch.jit.trace()
function.  ignore_jit_warnings (bool) – Flag to ignore warnings from the JIT
tracer when
jit_compile=True
. Default is False.  target_accept_prob (float) – Increasing this value will lead to a smaller step size, hence the sampling will be slower and more robust. Default to 0.8.
Note
Internally, the mass matrix will be ordered according to the order of the names of latent variables, not the order of their appearance in the model.
Example:
>>> true_coefs = torch.tensor([1., 2., 3.]) >>> data = torch.randn(2000, 3) >>> dim = 3 >>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(1)).sample() >>> >>> def model(data): ... coefs_mean = torch.zeros(dim) ... coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(3))) ... y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(1)), obs=labels) ... return y >>> >>> hmc_kernel = HMC(model, step_size=0.0855, num_steps=4) >>> mcmc_run = MCMC(hmc_kernel, num_samples=500, warmup_steps=100).run(data) >>> posterior = mcmc_run.marginal('beta').empirical['beta'] >>> posterior.mean tensor([ 0.9819, 1.9258, 2.9737])

initial_trace
¶ Find a valid trace to initiate the MCMC sampler. This is also used as a prototype trace to interconvert between Pyro’s trace object and dict object used by the integrator.

inverse_mass_matrix
¶

num_steps
¶

step_size
¶
NUTS¶

class
NUTS
(model, step_size=1, adapt_step_size=True, adapt_mass_matrix=True, full_mass=False, use_multinomial_sampling=True, transforms=None, max_plate_nesting=None, jit_compile=False, jit_options=None, ignore_jit_warnings=False, target_accept_prob=0.8, max_tree_depth=10)[source]¶ Bases:
pyro.infer.mcmc.hmc.HMC
NoUTurn Sampler kernel, which provides an efficient and convenient way to run Hamiltonian Monte Carlo. The number of steps taken by the integrator is dynamically adjusted on each call to
sample
to ensure an optimal length for the Hamiltonian trajectory [1]. As such, the samples generated will typically have lower autocorrelation than those generated by theHMC
kernel. Optionally, the NUTS kernel also provides the ability to adapt step size during the warmup phase.Refer to the baseball example to see how to do Bayesian inference in Pyro using NUTS.
References
 [1] The NoUturn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo,
 Matthew D. Hoffman, and Andrew Gelman.
 [2] A Conceptual Introduction to Hamiltonian Monte Carlo,
 Michael Betancourt
 [3] Slice Sampling,
 Radford M. Neal
Parameters:  model – Python callable containing Pyro primitives.
 step_size (float) – Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1.
 adapt_step_size (bool) – A flag to decide if we want to adapt step_size during warmup phase using Dual Averaging scheme.
 adapt_mass_matrix (bool) – A flag to decide if we want to adapt mass matrix during warmup phase using Welford scheme.
 full_mass (bool) – A flag to decide if mass matrix is dense or diagonal.
 use_multinomial_sampling (bool) – A flag to decide if we want to sample candidates along its trajectory using “multinomial sampling” or using “slice sampling”. Slice sampling is used in the original NUTS paper [1], while multinomial sampling is suggested in [2]. By default, this flag is set to True. If it is set to False, NUTS uses slice sampling.
 transforms (dict) – Optional dictionary that specifies a transform
for a sample site with constrained support to unconstrained space. The
transform should be invertible, and implement log_abs_det_jacobian.
If not specified and the model has sites with constrained support,
automatic transformations will be applied, as specified in
torch.distributions.constraint_registry
.  max_plate_nesting (int) – Optional bound on max number of nested
pyro.plate()
contexts. This is required if model contains discrete sample sites that can be enumerated over in parallel.  jit_compile (bool) – Optional parameter denoting whether to use the PyTorch JIT to trace the log density computation, and use this optimized executable trace in the integrator.
 jit_options (dict) – A dictionary contains optional arguments for
torch.jit.trace()
function.  ignore_jit_warnings (bool) – Flag to ignore warnings from the JIT
tracer when
jit_compile=True
. Default is False.  target_accept_prob (float) – Target acceptance probability of step size adaptation scheme. Increasing this value will lead to a smaller step size, so the sampling will be slower but more robust. Default to 0.8.
 max_tree_depth (int) – Max depth of the binary tree created during the doubling scheme of NUTS sampler. Default to 10.
Example:
>>> true_coefs = torch.tensor([1., 2., 3.]) >>> data = torch.randn(2000, 3) >>> dim = 3 >>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(1)).sample() >>> >>> def model(data): ... coefs_mean = torch.zeros(dim) ... coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(3))) ... y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(1)), obs=labels) ... return y >>> >>> nuts_kernel = NUTS(model, adapt_step_size=True) >>> mcmc_run = MCMC(nuts_kernel, num_samples=500, warmup_steps=300).run(data) >>> posterior = mcmc_run.marginal('beta').empirical['beta'] >>> posterior.mean tensor([ 0.9221, 1.9464, 2.9228])