bnmf_algs::alloc_model Namespace Reference

Namespace that contains functions related to Allocation Model [5]. More...

Classes
struct	Params
	Structure to hold the parameters for the Allocation Model [5]. More...

Functions
template<typename T , typename Scalar >
double	log_marginal_S (const tensor_t< T, 3 > &S, const Params< Scalar > &model_params)
	Compute the log marginal of tensor S with respect to the given distribution parameters. More...
template<typename T , typename Scalar >
std::tuple< matrix_t< T >, matrix_t< T >, vector_t< T > >	bnmf_priors (const shape< 3 > &tensor_shape, const Params< Scalar > &model_params)
	Return prior matrices W, H and vector L according to the Bayesian NMF allocation model using distribution parameters. More...
template<typename T >
tensor_t< T, 3 >	sample_S (const matrix_t< T > &prior_W, const matrix_t< T > &prior_H, const vector_t< T > &prior_L)
	Sample a tensor S from generative Bayesian NMF model using the given priors. More...
template<typename Integer , typename Scalar >
double	total_log_marginal (const matrix_t< Integer > &X, const Params< Scalar > &model_params)
	Calculate total marginal value, \(p(X|\Theta) = \sum_S p(X|S)p(S|\Theta)\) where \(Theta\) is model parameters. More...
template<typename Scalar >
Params< Scalar >	make_bld_params (const shape< 3 > &tensor_shape)
	Make default BLD solver parameters. More...
template<typename Scalar >
std::vector< Params< Scalar > >	make_EM_params (const shape< 3 > &tensor_shape)
	Make default EM solver parameters. More...

Detailed Description

Namespace that contains functions related to Allocation Model [5].

Function Documentation

template<typename T , typename Scalar >

std::tuple<matrix_t<T>, matrix_t<T>, vector_t<T> > bnmf_algs::alloc_model::bnmf_priors	(	const shape< 3 > &	tensor_shape,
		const Params< Scalar > &	model_params
	)

Return prior matrices W, H and vector L according to the Bayesian NMF allocation model using distribution parameters.

According to the Bayesian NMF allocation model [5],

\(L_j \sim \mathcal{G}(a, b) \qquad W_{:k} \sim \mathcal{D}(\alpha) \qquad H_{:j} \sim \mathcal{D}(\beta)\).

Template Parameters

T	Value type of the matrix/vector objects.
Scalar	Type of the model parameters.

Parameters

tensor_shape	Shape of the sample tensor \(x \times y \times z\).
model_params	Allocation Model parameters. See bnmf_algs::alloc_model::Params<double>.

Returns

std::tuple of \(<W_{x \times z}, H_{z \times y}, L_y>\).

Exceptions

assertion

error if number of alpha parameters is not \(x\), if number of beta parameters is not \(z\).

template<typename T , typename Scalar >

double bnmf_algs::alloc_model::log_marginal_S	(	const tensor_t< T, 3 > &	S,
		const Params< Scalar > &	model_params
	)

Compute the log marginal of tensor S with respect to the given distribution parameters.

According to the Bayesian NMF allocation model [5],

\(\log{p(S)} = \log{p(W, H, L, S)} - \log{p(W, H, L | S)}\).

Template Parameters

T	value type of tensor S.
Scalar	Type of the model parameters.

Parameters

S	Tensor \(S\) of size \(x \times y \times z \).
model_params	Allocation model parameters. See bnmf_algs::alloc_model::Params<double>.

Returns

log marginal \(\log{p(S)}\).

Exceptions

assertion

error if number of alpha parameters is not equal to S.dimension(0), if number of beta parameters is not equal to S.dimension(2).

template<typename Scalar >

Params<Scalar> bnmf_algs::alloc_model::make_bld_params

(

const shape< 3 > &

tensor_shape

)

Make default BLD solver parameters.

This function makes default BLD parameters as specified in Params::Params.

Template Parameters

Scalar

Type of the parameters.

Parameters

tensor_shape

Shape of tensor \(S_{x \times y \times z}\).

Returns

Default parameters to be used with any BLD algorithm.

template<typename Scalar >

std::vector<Params<Scalar> > bnmf_algs::alloc_model::make_EM_params

(

const shape< 3 > &

tensor_shape

)

Make default EM solver parameters.

This function makes default EM algorithm (such as online_EM) parameters. Note that EM algorithms have a different parametrization than BLD solvers, i.e. there is a parameter for each entry of \(W\) and \(H\) matrices. Therefore, this function returns a vector of \(z\) Params objects where \(z\) is the rank of the decomposition (depth of the hidden tensor \(S\).)

Template Parameters

Scalar

Type of the parameters.

Parameters

tensor_shape

Shape of tensor \(S_{x \times y \times z}\).

Returns

Default parameters to be used with EM algorithms.

template<typename T >

tensor_t<T, 3> bnmf_algs::alloc_model::sample_S	(	const matrix_t< T > &	prior_W,
		const matrix_t< T > &	prior_H,
		const vector_t< T > &	prior_L
	)

Sample a tensor S from generative Bayesian NMF model using the given priors.

According to the generative Bayesian NMF model [5],

\(S_{ijk} \sim \mathcal{PO}(W_{ik}H_{kj}L_{j})\).

Template Parameters

T	Value type of the matrix/vector/tensor objects.

Parameters

prior_W	Prior matrix for \(W\) of shape \(x \times z\).
prior_H	Prior matrix for \(H\) of shape \(z \times y\).
prior_L	Prior vector for \(L\) of size \(y\).

Returns

A sample tensor of size \(x \times y \times z\) from generative Bayesian NMF model.

Exceptions

assertion

error if number of columns of prior_W is not equal to number of rows of prior_H, if number of columns of prior_H is not equal to number of columns of prior_L

template<typename Integer , typename Scalar >

double bnmf_algs::alloc_model::total_log_marginal	(	const matrix_t< Integer > &	X,
		const Params< Scalar > &	model_params
	)

Calculate total marginal value, \(p(X|\Theta) = \sum_S p(X|S)p(S|\Theta)\) where \(Theta\) is model parameters.

Template Parameters

Integer	Type of the matrix entries (must be an integer type).
Scalar	Type of the model parameters.

Parameters

X	Integer matrix whose every possible tensor allocation will be tried.
model_params	Model parameters.

Returns

Total marginal value \(p(X|\Theta)\).