Math.HiddenMarkovModel.Private

Documentation

data T typ sh prob

A Hidden Markov model consists of a number of (hidden) states and a set of emissions. There is a vector for the initial probability of each state and a matrix containing the probability for switching from one state to another one. The distribution field points to probability distributions that associate every state with emissions of different probability. Famous distribution instances are discrete and Gaussian distributions. See Math.HiddenMarkovModel.Distribution for details.

The transition matrix is transposed with respect to popular HMM descriptions. But I think this is the natural orientation, because this way you can write "transition matrix times probability column vector".

Constructors

Cons

Fields

• initial :: Vector sh prob
• transition :: Square sh prob
• distribution :: T typ sh prob

Instances

(C sh, Storable prob, Show sh, Show prob, Show typ) => Show (T typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

showsPrec :: Int -> T typ sh prob -> ShowS

show :: T typ sh prob -> String

showList :: [T typ sh prob] -> ShowS

(NFData typ, NFData sh, C sh, NFData prob, Storable prob) => NFData (T typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

rnf :: T typ sh prob -> ()

(Format typ, FormatArray sh, Real prob) => Format (T typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

format :: Output out => Config -> T typ sh prob -> out

mapStatesShape :: (EmissionProb typ, C sh0, C sh1) => (sh0 -> sh1) -> T typ sh0 prob -> T typ sh1 prob

emission :: (EmissionProb typ, C sh, Eq sh, Real prob) => T typ sh prob -> Emission typ prob -> Vector sh prob

forward :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission, Traversable f) => T typ sh prob -> T f emission -> prob

alpha :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission, Traversable f) => T typ sh prob -> T f emission -> T f (Vector sh prob)

backward :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission, Traversable f) => T typ sh prob -> T f emission -> prob

beta :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission, Traversable f) => T typ sh prob -> f emission -> T f (Vector sh prob)

alphaBeta :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission, Traversable f) => T typ sh prob -> T f emission -> (prob, T f (Vector sh prob), T f (Vector sh prob))

biscaleTransition :: (EmissionProb typ, C sh, Eq sh, Real prob) => T typ sh prob -> Emission typ prob -> Vector sh prob -> Vector sh prob -> Square sh prob

xiFromAlphaBeta :: (EmissionProb typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission) => T typ sh prob -> prob -> T [] emission -> T [] (Vector sh prob) -> T [] (Vector sh prob) -> [Square sh prob]

zetaFromXi :: (C sh, Eq sh, Real prob) => [Square sh prob] -> [Vector sh prob]

zetaFromAlphaBeta :: (C sh, Eq sh, Real prob) => prob -> T [] (Vector sh prob) -> T [] (Vector sh prob) -> T [] (Vector sh prob)

reveal :: (EmissionProb typ, InvIndexed sh, Eq sh, Index sh ~ state, Emission typ prob ~ emission, Real prob, Traversable f) => T typ sh prob -> T f emission -> T f state

In constrast to Math.HiddenMarkovModel.reveal this does not normalize the vector. This is slightly simpler but for long sequences the product of probabilities might be smaller than the smallest representable number.

revealGen :: (EmissionProb typ, InvIndexed sh, Eq sh, Index sh ~ state, Emission typ prob ~ emission, Real prob, Traversable f) => (Vector (Deferred sh) prob -> Vector (Deferred sh) prob) -> T typ sh prob -> T f emission -> T f state

revealStorable :: (EmissionProb typ, InvIndexed sh, Eq sh, Index sh ~ state, Storable state, Emission typ prob ~ emission, Real prob, Traversable f) => (Vector sh prob -> Vector sh prob) -> T typ sh prob -> T f emission -> T f state

matrixMaxMul :: (InvIndexed sh, Eq sh, Index sh ~ ix, Storable ix, Real a) => Square sh a -> Vector sh a -> (Vector sh ix, Vector sh a)

data Trained typ sh prob

A trained model is a temporary form of a Hidden Markov model that we need during the training on multiple training sequences. It allows to collect knowledge over many sequences with mergeTrained, even with mixed supervised and unsupervised training. You finish the training by converting the trained model back to a plain modul using finishTraining.

You can create a trained model in three ways:

• supervised training using an emission sequence with associated states,
• unsupervised training using an emission sequence and an existing Hidden Markov Model,
• derive it from state sequence patterns, cf. Math.HiddenMarkovModel.Pattern.

Constructors

Trained

Fields

• trainedInitial :: Vector sh prob
• trainedTransition :: Square sh prob
• trainedDistribution :: Trained typ sh prob

Instances

(C sh, Storable prob, Show sh, Show prob, Show typ) => Show (Trained typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

showsPrec :: Int -> Trained typ sh prob -> ShowS

show :: Trained typ sh prob -> String

showList :: [Trained typ sh prob] -> ShowS

(Estimate typ, C sh, Eq sh, Real prob) => Semigroup (Trained typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

(<>) :: Trained typ sh prob -> Trained typ sh prob -> Trained typ sh prob

sconcat :: NonEmpty (Trained typ sh prob) -> Trained typ sh prob

stimes :: Integral b => b -> Trained typ sh prob -> Trained typ sh prob

(NFData typ, NFData sh, C sh, NFData prob, Storable prob) => NFData (Trained typ sh prob)

Defined in Math.HiddenMarkovModel.Private

Methods

rnf :: Trained typ sh prob -> ()

sumTransitions :: (C sh, Eq sh, Real e) => T typ sh e -> [Square sh e] -> Square sh e

trainUnsupervised :: (Estimate typ, C sh, Eq sh, Real prob, Emission typ prob ~ emission) => T typ sh prob -> T [] emission -> Trained typ sh prob

Baum-Welch algorithm

mergeTrained :: (Estimate typ, C sh, Eq sh, Real prob) => Trained typ sh prob -> Trained typ sh prob -> Trained typ sh prob

toCells :: (ToCSV typ, Indexed sh, Real prob, Show prob) => T typ sh prob -> [[String]]

parseCSV :: (FromCSV typ, C stateSh, Eq stateSh, Real prob, Read prob) => (Int -> stateSh) -> CSVParser (T typ stateSh prob)