NUTS#

class cuqi.experimental.mcmc.NUTS(target=None, initial_point=None, max_depth=None, step_size=None, 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.
initial_point (ndarray) – Initial parameters. Optional. If not provided, the initial point is an array of ones.
max_depth (int) – Maximum depth of the tree >=0 and the default is 15.
step_size (None or float) – If step_size is provided (as positive float), it will be used as initial step size. If None, the step size will be estimated by the sampler.
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). In principle, opt_acc_rate should be in (0, 1), however, choosing a value that is very close to 1 or 0 might lead to poor performance of the sampler.
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.experimental.mcmc.NUTS(target)

# Sample
sampler.warmup(5000)
sampler.sample(10000)

# Get samples
samples = sampler.get_samples()

# 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).
sampler.epsilon_bar_list

__init__(target=None, initial_point=None, max_depth=None, step_size=None, opt_acc_rate=0.6, **kwargs)#

Initializer for abstract base class for all samplers.

Any subclassing samplers should simply store input parameters as part of the __init__ method.

The actual initialization of the sampler should be done in the _initialize method.

Parameters:

target (cuqi.density.Density) – The target density.
initial_point (array-like, optional) – The initial point for the sampler. If not given, the sampler will choose an initial point.
callback (callable, optional) – A function that will be called after each sample is drawn. The function should take two arguments: the sample and the index of the sample. The sample is a 1D numpy array and the index is an integer. The callback function is useful for monitoring the sampler during sampling.

Methods

`__init__`([target, initial_point, max_depth, ...])	Initializer for abstract base class for all samplers.
`get_history`()	Return the history of the sampler.
`get_samples`()	Return the samples.
`get_state`()	Return the state of the sampler.
`initialize`()	Initialize the sampler by setting and allocating the state and history before sampling starts.
`load_checkpoint`(path)	Load the state of the sampler from a file.
`reinitialize`()	Re-initialize the sampler.
`sample`(Ns[, batch_size, sample_path])	Sample Ns samples from the target density.
`save_checkpoint`(path)	Save the state of the sampler to a file.
`set_history`(history)	Set the history of the sampler.
`set_state`(state)	Set the state of the sampler.
`step`()	Perform one step of the sampler by transitioning the current point to a new point according to the sampler's transition kernel.
`tune`(skip_len, update_count)	adapt epsilon during burn-in using dual averaging
`validate_target`()	Validate the target is compatible with the sampler.
`warmup`(Nb[, tune_freq])	Warmup the sampler by drawing Nb samples.

Attributes

`dim`	Dimension of the target density.
`geometry`	Geometry of the target density.
`max_depth`
`opt_acc_rate`
`step_size`
`target`	Return the target density.