Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ > Class Template Reference

An emission table: the probability of each observed value given each value of the state. More...

#include <EmrysFilter/Models/Emission.h>

Classes
class	Observation
	The emission model of one observed value: the column of the table it selects. More...

Public Types
using	Scalar = Scalar_
	the scalar type of the probabilities
using	SpaceType = Space_
	the discrete space of the state
using	ObservationSpaceType = ObservationSpace_
	the discrete space of the observation
using	MatrixType
	The emission matrix's type: a row per value of the state, a column per observed value.

Public Member Functions
template<MatrixExpression Matrix>
	EmissionTable (Space_ space, ObservationSpace_ observations, Matrix &&matrix)
	The table over space and observations with emission matrix matrix: nonnegative, with each row summing to one.
Space_ const &	space () const
ObservationSpace_ const &	observationSpace () const
MatrixType const &	matrix () const
Observation	observe (Eigen::Index observed) const &
void	observe (Eigen::Index observed) const &&=delete
	observe() of a temporary table is deleted: the observation refers to the table, which would be gone at the end of the full expression (hidden-markov-filter.md Q4).

Detailed Description

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>
class Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >

An emission table: the probability of each observed value given each value of the state.

The emission matrix \( B \) of a hidden Markov model with a finite observation space (Rabiner (1989), §II), a right stochastic matrix with a row per value of the state and a column per observed value, \( B_{vz} = P(z \mid v) \). The table itself is not an emission model: observe() names what was observed and borrows the table, so a filter updated every step doesn't copy the matrix.

auto const table =
    EmissionTable{Weather{}, Activity{}, Eigen::Matrix<double, 2, 3>{{0.1, 0.4, 0.5}, {0.6, 0.3, 0.1}}};
auto const evidence = update(prior, table.observe(Activity::index<Walk>()));

Template Parameters

Space_	the discrete space of the state
ObservationSpace_	the discrete space of the observation
Scalar_	scalar type of the probabilities, double by default

Member Typedef Documentation

MatrixType

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>

using Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >::MatrixType

Initial value:

Eigen::Matrix<
       Scalar_,
       Space_::Cardinality,
       ObservationSpace_::Cardinality,
       Eigen::RowMajor,
       Space_::MaxCardinality,
       ObservationSpace_::MaxCardinality>

The emission matrix's type: a row per value of the state, a column per observed value.

Member Function Documentation

matrix()

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>

MatrixType const & Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >::matrix ( ) const

inlinenodiscard

Returns

the emission matrix \( B \), with \( B_{vz} = P(z \mid v) \)

observationSpace()

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>

ObservationSpace_ const & Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >::observationSpace ( ) const

inlinenodiscard

Returns

the discrete space of the observation

observe()

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>

Observation Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >::observe ( Eigen::Index observed ) const &

inlinenodiscard

Returns

the emission model of observing the value with flat index observed

space()

template<DiscreteSpace Space_, DiscreteSpace ObservationSpace_, RealScalar Scalar_ = double>

Space_ const & Emrys::EmissionTable< Space_, ObservationSpace_, Scalar_ >::space ( ) const

inlinenodiscard

Returns

the discrete space of the state

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

• EmrysFilter/Models/Emission.h