NUTS#

class cuqi.sampler.NUTS(target, x0=None, max_depth=15, adapt_step_size=True, opt_acc_rate=0.6, **kwargs)#

No-U-Turn Sampler (Hoffman and Gelman, 2014).

Samples a distribution given its logpdf and gradient using a Hamiltonian Monte Carlo (HMC) algorithm with automatic parameter tuning.

For more details see: See Hoffman, M. D., & Gelman, A. (2014). The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15, 1593-1623.

Parameters:

  • target (cuqi.distribution.Distribution) – The target distribution to sample. Must have logpdf and gradient method. Custom logpdfs and gradients are supported by using a cuqi.distribution.UserDefinedDistribution.

  • x0 (ndarray) – Initial parameters. Optional

  • max_depth (int) – Maximum depth of the tree.

  • adapt_step_size (Bool or float) – Whether to adapt the step size. If True, the step size is adapted automatically. If False, the step size is fixed to the initially estimated value. If set to a scalar, the step size will be given by user and not adapted.

  • opt_acc_rate (float) – The optimal acceptance rate to reach if using adaptive step size. Suggested values are 0.6 (default) or 0.8 (as in stan).

  • callback (callable, Optional) – If set this function will be called after every sample. The signature of the callback function is callback(sample, sample_index), where sample is the current sample and sample_index is the index of the sample. An example is shown in demos/demo31_callback.py.

Example

# Import cuqi
import cuqi

# Define a target distribution
tp = cuqi.testproblem.WangCubic()
target = tp.posterior

# Set up sampler
sampler = cuqi.sampler.NUTS(target)

# Sample
samples = sampler.sample(10000, 5000)

# Plot samples
samples.plot_pair()

After running the NUTS sampler, run diagnostics can be accessed via the following attributes:

# Number of tree nodes created each NUTS iteration
sampler.num_tree_node_list

# Step size used in each NUTS iteration
sampler.epsilon_list

# Suggested step size during adaptation (the value of this step size is
# only used after adaptation). The suggested step size is None if
# adaptation is not requested.
sampler.epsilon_bar_list

# Additionally, iterations' number can be accessed via
sampler.iteration_list
__init__(target, x0=None, max_depth=15, adapt_step_size=True, opt_acc_rate=0.6, **kwargs)#

Methods

__init__(target[, x0, max_depth, ...])

sample(N[, Nb])

sample_adapt(N[, Nb])

step(x)

Perform a single MCMC step

step_tune(x, *args, **kwargs)

Perform a single MCMC step and tune the sampler.

tune()

Tune the sampler parameters.

Attributes

dim

geometry

target