UGLA#

class cuqi.experimental.mcmc.UGLA(target=None, initial_point=None, maxit=50, tol=0.0001, beta=1e-05, **kwargs)#

Unadjusted (Gaussian) Laplace Approximation sampler

Samples an approximate posterior where the prior is approximated by a Gaussian distribution. The likelihood must be Gaussian.

Currently only works for LMRF priors.

The inner solver is Conjugate Gradient Least Squares (CGLS) solver.

For more details see: Uribe, Felipe, et al. A hybrid Gibbs sampler for edge-preserving tomographic reconstruction with uncertain view angles. SIAM/ASA Journal on UQ, https://doi.org/10.1137/21M1412268 (2022).

Parameters:

  • target (cuqi.distribution.Posterior) – The target posterior distribution to sample.

  • initial_point (ndarray, Optional) – Initial parameters. If not provided, it defaults to zeros.

  • maxit (int) – Maximum number of inner iterations for solver when generating one sample. If not provided, it defaults to 50.

  • tol (float) – Tolerance for inner solver. The inner solvers will stop before maxit if convergence check reaches tol. If not provided, it defaults to 1e-4.

  • beta (float) – Smoothing parameter for the Gaussian approximation of the Laplace distribution. A small value in the range of 1e-7 to 1e-3 is recommended, though values out of this range might give better results in some cases. Generally, a larger beta value makes sampling easier but results in a worse approximation. See details in Section 3.3 of the paper. If not provided, it defaults to 1e-5.

  • 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.

__init__(target=None, initial_point=None, maxit=50, tol=0.0001, beta=1e-05, **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, maxit, ...])

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)

Tune the parameters of the sampler.

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.

likelihood

model

prior

target

Return the target density.