Math.HiddenMarkovModel

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 => String -> T typ sh prob -> out

type Discrete symbol sh prob = T (Discrete symbol) sh prob

type DiscreteTrained symbol sh prob = Trained (Discrete symbol) sh prob

type Gaussian emiSh stateSh a = T (Gaussian emiSh) stateSh a

type GaussianTrained emiSh stateSh a = Trained (Gaussian emiSh) stateSh a

uniform :: (Info typ, C sh, Real prob) => T typ sh prob -> T typ sh prob

Create a model with uniform probabilities for initial vector and transition matrix given a distribution for the emissions. You can use this as a starting point for trainUnsupervised.

generate :: (Generate typ, Indexed sh, Real prob, RandomGen g, Random prob, Emission typ prob ~ emission) => T typ sh prob -> g -> [emission]

generateLabeled :: (Generate typ, Indexed sh, Index sh ~ state, RandomGen g, Random prob, Real prob, Emission typ prob ~ emission) => T typ sh prob -> g -> [(state, emission)]

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

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

Logarithm of the likelihood to observe the given sequence. We return the logarithm because the likelihood can be so small that it may be rounded to zero in the choosen number type.

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

Reveal the state sequence that led most likely to the observed sequence of emissions. It is found using the Viterbi algorithm.

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 -> ()

trainSupervised :: (Estimate typ, Indexed sh, Index sh ~ state, Real prob, Emission typ prob ~ emission) => sh -> T [] (state, emission) -> Trained typ sh prob

Contribute a manually labeled emission sequence to a HMM training.

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

Consider a superposition of all possible state sequences weighted by the likelihood to produce the observed emission sequence. Now train the model with respect to all of these sequences with respect to the weights. This is done by the Baum-Welch algorithm.

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

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

trainMany :: (Estimate typ, C sh, Eq sh, Real prob, Foldable f) => (trainingData -> Trained typ sh prob) -> T f trainingData -> T typ sh prob

deviation :: (C sh, Eq sh, Real prob) => T typ sh prob -> T typ sh prob -> prob

Compute maximum deviation between initial and transition probabilities. You can use this as abort criterion for unsupervised training. We omit computation of differences between the emission probabilities. This simplifies matters a lot and should suffice for defining an abort criterion.

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

fromCSV :: (FromCSV typ, Indexed sh, Eq sh, Real prob, Read prob) => (Int -> sh) -> String -> Exceptional String (T typ sh prob)