Computes the variational autoencoder error function. More...

#include <shark/ObjectiveFunctions/VariationalAutoencoderError.h>

Inheritance diagram for shark::VariationalAutoencoderError< SearchPointType >:

Public Types
typedef UnlabeledData< SearchPointType >	DatasetType

typedef AbstractModel< SearchPointType, SearchPointType, SearchPointType >	ModelType

Public Types inherited from shark::AbstractObjectiveFunction< SearchPointType, double >
enum	Feature
	List of features that are supported by an implementation. More...

typedef SearchPointType	SearchPointType

typedef double	ResultType

typedef boost::mpl::if_< std::is_arithmetic< double >, SearchPointType, RealMatrix >::type	FirstOrderDerivative

typedef TypedFlags< Feature >	Features
	This statement declares the member m_features. See Core/Flags.h for details.

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Public Member Functions
	VariationalAutoencoderError (DatasetType const &data, ModelType encoder, ModelType decoder, AbstractLoss< SearchPointType, SearchPointType > *visible_loss, double lambda=1.0)

std::string	name () const
	From INameable: return the class name.

SearchPointType	proposeStartingPoint () const
	Proposes a starting point in the feasible search space of the function.

std::size_t	numberOfVariables () const
	Accesses the number of variables.

MatrixType	sampleZ (SearchPointType const &parameters, MatrixType const &batch) const

double	eval (SearchPointType const &parameters) const
	Evaluates the objective function for the supplied argument.

double	evalDerivative (SearchPointType const &parameters, SearchPointType &derivative) const

Public Member Functions inherited from shark::AbstractObjectiveFunction< SearchPointType, double >
const Features &	features () const

virtual void	updateFeatures ()

bool	hasValue () const
	returns whether this function can calculate it's function value

bool	hasFirstDerivative () const
	returns whether this function can calculate the first derivative

bool	hasSecondDerivative () const
	returns whether this function can calculate the second derivative

bool	canProposeStartingPoint () const
	returns whether this function can propose a starting point.

bool	isConstrained () const
	returns whether this function can return

bool	hasConstraintHandler () const
	returns whether this function can return

bool	canProvideClosestFeasible () const
	Returns whether this function can calculate thee closest feasible to an infeasible point.

bool	isThreadSafe () const
	Returns true, when the function can be usd in parallel threads.

bool	isNoisy () const
	Returns true, when the function can be usd in parallel threads.

	AbstractObjectiveFunction ()
	Default ctor.

virtual	~AbstractObjectiveFunction ()
	Virtual destructor.

virtual void	init ()

void	setRng (random::rng_type *rng)
	Sets the Rng used by the objective function.

virtual bool	hasScalableDimensionality () const

virtual void	setNumberOfVariables (std::size_t numberOfVariables)
	Adjusts the number of variables if the function is scalable.

virtual std::size_t	numberOfObjectives () const

virtual bool	hasScalableObjectives () const

virtual void	setNumberOfObjectives (std::size_t numberOfObjectives)
	Adjusts the number of objectives if the function is scalable.

std::size_t	evaluationCounter () const
	Accesses the evaluation counter of the function.

AbstractConstraintHandler< SearchPointType > const &	getConstraintHandler () const
	Returns the constraint handler of the function if it has one.

virtual bool	isFeasible (const SearchPointType &input) const
	Tests whether a point in SearchSpace is feasible, e.g., whether the constraints are fulfilled.

virtual void	closestFeasible (SearchPointType &input) const
	If supported, the supplied point is repaired such that it satisfies all of the function's constraints.

ResultType	operator() (SearchPointType const &input) const
	Evaluates the function. Useful together with STL-Algorithms like std::transform.

virtual ResultType	evalDerivative (SearchPointType const &input, FirstOrderDerivative &derivative) const
	Evaluates the objective function and calculates its gradient.

virtual ResultType	evalDerivative (SearchPointType const &input, SecondOrderDerivative &derivative) const
	Evaluates the objective function and calculates its gradient.

Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Additional Inherited Members
Protected Member Functions inherited from shark::AbstractObjectiveFunction< SearchPointType, double >
void	announceConstraintHandler (AbstractConstraintHandler< SearchPointType > const *handler)
	helper function which is called to announce the presence of an constraint handler.

Protected Attributes inherited from shark::AbstractObjectiveFunction< SearchPointType, double >
Features	m_features

std::size_t	m_evaluationCounter
	Evaluation counter, default value: 0.

AbstractConstraintHandler< SearchPointType > const *	m_constraintHandler

random::rng_type *	mep_rng

Detailed Description

template<class SearchPointType>
class shark::VariationalAutoencoderError< SearchPointType >

Computes the variational autoencoder error function.

We want to optimize a model \( p(x) = \int p(x|z) p(z) dz \) where we choose p(z) as a multivariate normal distribution and p(x|z) is an arbitrary model, e.g. a deep neural entwork. The naive solution is sampling from p(z) and then compute the sample average. This will fail when p(z|x) is a very localized distribution and we might need many samples from p(z) to find a sample which is likely under p(z|x). p(z|x) is assumed to be intractable to compute, so we introduce a second model q(z|x), modeling p(z|x) and we want to train it such that it learns the unknown p(z|x). For this a variational lower bound on the likelihood is used and we maximize

\[ log p(x) \leq E_{q(z|x)}[\log p(x|z)] - KL[q(z|x) || p(z)] \]

The first term explains the meaning of variational autoencoder: we first sample z given x using the encoder model q and then decode z to obtain an estimate for x. The only difference to normal autoencoders is that we now have a probabilistic z. The second term ensures that q is learning p(z|x), assuming that we have enough modeling capacity to actually learn it. See https://arxiv.org/abs/1606.05908 for more background.

Implementation notice: we assume q(z|x) to be a set of independent gaussian distributions parameterized as \( q(z| mu(x), \log \sigma^2(x)) \). The provided encoder model q must therefore have twice as many outputs as the decvoder has inputs as the second half of outputs is interpreted as the log of the variance. So if z should be a 100 dimensional variable, q must have 200 outputs. The outputs and loss function used for the encoder p is arbitrary, but a SquaredLoss will work well, however also other losses like pixel probabilities can be used.

Definition at line 63 of file VariationalAutoencoderError.h.

Member Typedef Documentation

◆ DatasetType

template<class SearchPointType >

typedef UnlabeledData<SearchPointType> shark::VariationalAutoencoderError< SearchPointType >::DatasetType

Definition at line 70 of file VariationalAutoencoderError.h.

◆ ModelType

template<class SearchPointType >

typedef AbstractModel<SearchPointType,SearchPointType, SearchPointType> shark::VariationalAutoencoderError< SearchPointType >::ModelType

Definition at line 71 of file VariationalAutoencoderError.h.

Constructor & Destructor Documentation

◆ VariationalAutoencoderError()

template<class SearchPointType >

shark::VariationalAutoencoderError< SearchPointType >::VariationalAutoencoderError	(	DatasetType const &	data,
		ModelType *	encoder,
		ModelType *	decoder,
		AbstractLoss< SearchPointType, SearchPointType > *	visible_loss,
		double	lambda = `1.0`
	)