Bayes.Factor

Conditional probability table

Conditional Probability Tables and Probability tables

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

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 Int] -> Double

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

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 Int] -> Maybe f

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

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

Instances

Factor CPT

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

Set of variables

class Set s where

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

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 BayesianDiscreteVariable v where

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

Methods

dimension :: v -> Int

Instances

BayesianDiscreteVariable DV

BayesianDiscreteVariable (DVI a)

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

Discrete variables and instantiations

data DV

A discrete variable

Instances

Eq DV

Ord DV

Show DV

BayesianDiscreteVariable DV

LabeledVertex DV

IsCluster [DV]

data DVI a

Discrete Variable instantiation. A variable and its value

Instances

Eq a => Eq (DVI a)

Show a => Show (DVI a)

BayesianDiscreteVariable (DVI a)

LabeledVertex (DVI a)

setDVValue :: DV -> a -> DVI a

Create a discrete variable instantiation for a given discrete variable

instantiationValue :: DVI t -> t

Extract value of the instantiation

instantiationVariable :: DVI t -> DV

Discrete variable from the instantiation

variableVertex :: LabeledVertex l => l -> Vertex

(=:) :: (Bounded b, Enum b) => DV -> b -> DVI Int

Create a variable instantiation using values from an enumeration

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

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

factorFromInstantiation :: Factor f => DVI Int -> f

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

changeVariableOrder

Arguments

:: DVSet s

Old order

-> DVSet s'

New order

-> [Double]

Old values

-> [Double]

New values

Change the layout of values in the factor to correspond to a new variable order Used to import external files

Factor

data CPT

Mainly used for conditional probability table like p(A B | C D E) but the normalization to 1 is not imposed. And the conditionned variables are not different from the conditionning ones. The dimensions for each variables are listed. The variables on the left or right of the condition bar are not tracked. What's matter is that it is encoding a function of several variables. Marginalization of variables will be computed from the bayesian graph where the knowledge of the dependencies is. So, this same structure is used for a probability too (conditioned on nothing)

Instances

Show CPT

Arbitrary CPT

Factor CPT

Tests

testProductProject_prop :: CPT -> CPT -> Property

testAssocProduct_prop :: CPT -> CPT -> CPT -> Bool

testScale_prop :: Double -> CPT -> Bool

testProjectCommut_prop :: CPT -> Property

testScalarProduct_prop :: Double -> CPT -> Bool

testProjectionToScalar_prop :: CPT -> Bool