Bayes.Factor

Factors

Factor

class Factor f where

A factor as used in graphical model It may or not be a probability distribution. So it has no reason to be normalized to 1

Minimal complete definition

isScalarFactor, emptyFactor, containsVariable, factorVariables, factorWithVariables, factorValue, factorStringValue, variablePosition, factorDimension, factorNorm, factorScale, factorFromScalar, evidenceFrom, isUsingSameVariablesAs, factorToList, factorProduct, factorProjectOut

Methods

isScalarFactor :: f -> Bool

When all variables of a factor have been summed out, we have a scalar

emptyFactor :: f

An empty factor with no variable and no values

containsVariable :: f -> DV -> Bool

Check if a given discrete variable is contained in a factor

factorVariables :: f -> [DV]

Give the set of discrete variables used by the factor

factorMainVariable :: f -> DV

Return A in P(A | C D ...). It is making sense only if the factor is a conditional propbability table. It must always be in the vertex corresponding to A in the bayesian graph

factorWithVariables :: [DV] -> [Double] -> Maybe f

Create a new factors with given set of variables and a list of value for initialization. The creation may fail if the number of values is not coherent with the variables and their levels. For boolean variables ABC, the value must be given in order FFF, FFT, FTF, FTT ...

factorValue :: f -> [DVI] -> Double

Value of factor for a given set of variable instantitation. The variable instantion is like a multi-dimensional index.

factorStringValue :: f -> [DVI] -> String

String representation of a factor value

variablePosition :: f -> DV -> Maybe Int

Position of a discrete variable in te factor (p(AB) is differennt from p(BA) since values are not organized in same order in memory)

factorDimension :: f -> Int

Dimension of the factor (number of floating point values)

factorNorm :: f -> Double

Norm of the factor = sum of its values

factorScale :: Double -> f -> f

Scale the factor values by a given scaling factor

factorFromScalar :: Double -> f

Create a scalar factor with no variables

evidenceFrom :: [DVI] -> Maybe f

Create an evidence factor from an instantiation. If the instantiation is empty then we get nothing

isUsingSameVariablesAs :: f -> f -> Bool

Test if two factors are coding for the same probability dependence. It does not test if the factors are equal (same probabilities) but just if they involve the same variables so are linked to the same node in the Bayesian network

factorDivide :: f -> Double -> f

Divide all the factor values

factorToList :: f -> [Double]

factorProduct :: [f] -> f

Multiply factors.

factorProjectOut :: [DV] -> f -> f

Project out a factor. The variable in the DVSet are summed out

factorProjectTo :: [DV] -> f -> f

Project to. The variable are kept and other variables are removed

class Distribution d where

A distribution which can be used to create a factor

Methods

createFactor :: Factor f => [DV] -> d -> Maybe f

Create a factor from variables and a distributions for those variables

Instances

Real a => Distribution [a]

class MultiDimTable f where

Class used to display multidimensional tables

Methods

elementStringValue :: f -> [DVI] -> String

tableVariables :: f -> [DV]

isomorphicFactor :: Factor f => f -> f -> Bool

Test equality of two factors taking into account the fact that the variables may be in a different order. In case there is a distinction between conditionned variable and conditionning variables (imposed from the exterior) then this comparison may not make sense. It is a comparison of function of several variables which no special interpretation of the meaning of the variables according to their position.

normedFactor :: Factor f => f -> f

Norm the factor

displayFactorBody :: MultiDimTable f => f -> String

changeFactorInFunctor :: (Factor f, Functor m) => f -> m f -> m f

Change factor in a functor (only factor values should have been changed) It assumes that the variables of a factor are enough to identify it. If the functor is containing several factors with same set of variables then it won't give a meaningful result. So it should be used only on functor derived from a Bayesian Network.

class FactorContainer m where

Structure containing factors which can be replaced. It is making sense when the factors are related to the nodes of a Bayesian network.

Methods

changeFactor :: (IsBucketItem f, Factor f) => f -> m f -> m f

Instances

FactorContainer []

Set of variables

class Set s where

A Set of variables used in a factor. s is the set and a the variable

Minimal complete definition

emptySet, union, intersection, difference, isEmpty, isElem, addElem, nbElements, subset

Methods

emptySet :: s a

Empty set

union :: Eq a => s a -> s a -> s a

Union of two sets

intersection :: Eq a => s a -> s a -> s a

Intersection of two sets

difference :: Eq a => s a -> s a -> s a

Difference of two sets

isEmpty :: s a -> Bool

Check if the set is empty

isElem :: Eq a => a -> s a -> Bool

Check if an element is member of the set

addElem :: Eq a => a -> s a -> s a

Add an element to the set

nbElements :: s a -> Int

Number of elements in the set

subset :: Eq a => s a -> s a -> Bool

Check if a set is subset of another one

equal :: Eq a => s a -> s a -> Bool

Check set equality

Instances

Set []

class BayesianVariable v => BayesianDiscreteVariable v where

A discrete variable has a number of levels which is required to size the factors

Methods

dimension :: v -> Int

dv :: v -> DV

Instances

BayesianDiscreteVariable DVI

BayesianDiscreteVariable DV

BayesianDiscreteVariable DEV

BayesianDiscreteVariable (TDV s)

class BayesianVariable v where

A Bayesian Variable is a variable part of Bayesian network and so which knows its position : the vertex.

Methods

vertex :: v -> Vertex

Instances

BayesianVariable DVI

BayesianVariable DV

BayesianVariable CVI

BayesianVariable CV

BayesianVariable Vertex

BayesianVariable DEV

BayesianVariable DN

BayesianVariable (TDV s)

Implementation

newtype Vertex

Vertex type used to identify a vertex in a graph

Constructors

Vertex

Fields

vertexId :: Int

Instances

Eq Vertex

Ord Vertex

Show Vertex

BayesianVariable Vertex

Discrete variables and instantiations

data DV

A discrete variable

Constructors

DV !Vertex !Int

Instances

Eq DV

Ord DV

Show DV

BayesianDiscreteVariable DV

BayesianVariable DV

(Bounded b, Enum b) => Instantiable DV b DVI

data TDV s

A typed discrete variable

Instances

Eq (TDV s)

Ord (TDV s)

Show (TDV s)

BayesianDiscreteVariable (TDV s)

BayesianVariable (TDV s)

(Bounded b, Enum b) => Instantiable (TDV b) b DVI

newtype DVSet s

A set of discrete variables The tag is used to check that an index is used with the right set of DV

Constructors

DVSet [DV]

Instances

Eq (DVSet s)

Show (DVSet s)

Arbitrary (DVSet s)

data DVI

Discrete Variable instantiation. A variable and its value

Instances

Eq DVI

Show DVI

BayesianDiscreteVariable DVI

BayesianVariable DVI

InstantiationValue DVI Int

(Bounded b, Enum b) => Instantiable DV b DVI

Instantiable DEV Int DVI

(Bounded b, Enum b) => Instantiable (TDV b) b DVI

type DVISet = [DVI]

class InstantiationValue i v | i -> v where

Methods

instantiationValue :: i -> v

toDouble :: i -> Double

Instances

InstantiationValue DVI Int

InstantiationValue CVI Double

tdvi :: Enum s => DVI -> (TDV s, s)

Typed instantiation

tdv :: DV -> TDV s

Typed discrete variable

setDVValue :: DV -> Int -> DVI

Create a discrete variable instantiation for a given discrete variable

instantiationVariable :: DVI -> DV

Discrete variable from the instantiation

variableVertex :: LabeledVertex l => l -> Vertex

(=:) :: Instantiable d v r => d -> v -> r

Create a variable instantiation using values from an enumeration

forAllInstantiations :: DVSet s -> [[DVI]]

Generate all instantiations of variables The DVInt can be in any order so the tag s is not used

factorFromInstantiation :: Factor f => DVI -> f

Convert a variable instantation to a factor Useful to create evidence factors