Neal3 Class Reference

Implementation of Neal's Algorithm 3 for collapsed Gibbs sampling. More...

#include <neal.hpp>

Inheritance diagram for Neal3:

Public Member Functions
	Neal3 (Data &d, Params &p, Likelihood &l, Process &pr)
	Constructor for Neal's Algorithm 3 sampler.
void	step () override
	Perform one complete iteration of Neal's Algorithm 3.
Public Member Functions inherited from Sampler
	Sampler (Data &d, const Params &p, const Likelihood &l, Process &pr)
	Constructor initializing sampler with required components.
virtual	~Sampler ()=default
	Virtual destructor for proper cleanup of derived classes.

Private Member Functions
void	step_1_observation (int index)
	Sample cluster assignment for a single observation.
int	sample_from_log_probs (int num_clusters)
	Sample an index from log-probabilities using the log-sum-exp trick.

Private Attributes
std::mt19937	gen
	Mersenne Twister random number generator for sampling operations.
std::vector< int >	indices
std::vector< double >	log_likelihoods
std::vector< double >	weights
int	n_data

Additional Inherited Members
Protected Attributes inherited from Sampler
Data &	data
	Reference to the data object containing observations and current allocations.
const Params &	params
	Reference to the parameters object containing model hyperparameters and MCMC settings.
const Likelihood &	likelihood
	Reference to the likelihood computation object for evaluating cluster assignments.
Process &	process
	Reference to the stochastic process object (DP, NGGP, DPW, NGGPW).
std::random_device	rd
	Random device for generating random numbers across sampling algorithms.

Detailed Description

Implementation of Neal's Algorithm 3 for collapsed Gibbs sampling.

This class implements Neal's Algorithm 3, a standard collapsed Gibbs sampler for Bayesian nonparametric mixture models. The algorithm sequentially updates cluster assignments by sampling from the full conditional distribution of each observation, integrating out the cluster parameters.

Algorithm 3 is characterized by:

• Sequential updates: One observation at a time
• Collapsed sampling: Cluster parameters are integrated out analytically
• Full conditionals: Each assignment is sampled from its exact posterior
• Automatic cluster creation/deletion: Clusters are created when needed and deleted when empty

The algorithm is particularly effective for models where the likelihood can be computed in closed form after integrating out cluster-specific parameters.

Note

reference Neal, R. M. (2000). "Markov Chain Sampling Methods for Dirichlet Process Mixture Models"

See also

Sampler, Process, Likelihood

Constructor & Destructor Documentation

Neal3()

Neal3::Neal3 ( Data & d, Params & p, Likelihood & l, Process & pr )

inline

Constructor for Neal's Algorithm 3 sampler.

Parameters

d	Reference to Data object containing observations
p	Reference to Params object with hyperparameters
l	Reference to Likelihood object for probability computations
pr	Reference to Process object (DP, NGGP, etc.) defining the prior

Initializes the Gibbs sampler with all required components. The random number generator is seeded from the inherited random device. Pre-allocates vectors to maximum possible size to avoid resizing during sampling.

Member Function Documentation

sample_from_log_probs()

int Neal3::sample_from_log_probs ( int num_clusters )

private

Sample an index from log-probabilities using the log-sum-exp trick.

Parameters

num_clusters

Number of clusters (including new cluster)

Returns

Index sampled according to the probabilities

This method performs sampling from a discrete distribution defined by log-probabilities. It uses the log-sum-exp trick for numerical stability and implements roulette wheel selection.

step()

void Neal3::step ( )

overridevirtual

Perform one complete iteration of Neal's Algorithm 3.

Executes one full sweep of the collapsed Gibbs sampler by sequentially updating the cluster assignment of each observation. The order of updates is typically randomized to avoid systematic bias.

After each full sweep:

• All observations have been considered for reassignment
• Cluster structure may have changed (clusters created/destroyed)
• The Markov chain has advanced by one step

See also

step_1_observation()

Performs a single step of the Neal 3 algorithm for all the dataset.

Implements Sampler.

step_1_observation()

void Neal3::step_1_observation ( int index )

private

Sample cluster assignment for a single observation.

Parameters

index

Index of the observation to update

This method implements the core of Algorithm 3:

1. Remove the observation from its current cluster
2. Compute probabilities for all existing clusters plus a new cluster
3. Sample new assignment from the full conditional distribution
4. Update cluster assignments and clean up empty clusters

The probabilities combine prior information from the Process with likelihood information computed by integrating out cluster parameters.

Performs a step in the DPNeal2 sampling process.

This method is responsible for updating the allocations of the data points based on the current state of the model.

Parameters

index

The index of the data point to update.

Member Data Documentation

gen

std::mt19937 Neal3::gen

mutableprivate

Mersenne Twister random number generator for sampling operations.

indices

std::vector<int> Neal3::indices

private

log_likelihoods

std::vector<double> Neal3::log_likelihoods

private

n_data

int Neal3::n_data

private

weights

std::vector<double> Neal3::weights

private

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The documentation for this class was generated from the following files:

• src/samplers/neal.hpp
• src/samplers/neal.cpp