Math.HiddenMarkovModel

Documentation

data T distr 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".

The type has two type parameters, although the one for the distribution would be enough. However, replacing prob by Distr.Probability distr would prohibit the derived Show and Read instances.

Constructors

Cons

Fields

initial :: Vector sh prob

transition :: SquareMatrix sh prob

distribution :: distr

Instances

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

(NFData distr, NFData sh, NFData prob, Storable prob) => NFData (T distr sh prob)

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

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

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

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

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

uniform :: (Info distr, StateShape distr ~ sh, C sh, Probability distr ~ prob) => distr -> T distr 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 :: (RandomGen g, Ord prob, Random prob, Generate distr, StateShape distr ~ sh, Indexed sh, Index sh ~ state, Probability distr ~ prob, Emission distr ~ emission) => T distr sh prob -> g -> [emission]

generateLabeled :: (RandomGen g, Ord prob, Random prob, Generate distr, StateShape distr ~ sh, Indexed sh, Index sh ~ state, Probability distr ~ prob, Emission distr ~ emission) => T distr sh prob -> g -> [(state, emission)]

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

logLikelihood :: (EmissionProb distr, StateShape distr ~ sh, Eq sh, Floating prob, Probability distr ~ prob, Emission distr ~ emission, Traversable f) => T distr 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 distr, StateShape distr ~ sh, InvIndexed sh, Eq sh, Index sh ~ state, Probability distr ~ prob, Emission distr ~ emission, Traversable f, Reverse f) => T distr 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 distr 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 :: SquareMatrix sh prob

trainedDistribution :: distr

Instances

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

(NFData distr, NFData sh, NFData prob, Storable prob) => NFData (Trained distr sh prob)

(C sh, Eq sh, Estimate tdistr distr, ~ * (Probability distr) prob) => Semigroup (Trained tdistr sh prob)

trainSupervised :: (StateShape distr ~ sh, Index sh ~ state, Estimate tdistr distr, Probability distr ~ prob, Emission distr ~ emission) => sh -> T [] (state, emission) -> Trained tdistr sh prob

Contribute a manually labeled emission sequence to a HMM training.

trainUnsupervised :: (Estimate tdistr distr, StateShape distr ~ sh, Eq sh, Probability distr ~ prob, Emission distr ~ emission) => T distr sh prob -> T [] emission -> Trained tdistr 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 :: (C sh, Eq sh, Estimate tdistr distr, Probability distr ~ prob) => Trained tdistr sh prob -> Trained tdistr sh prob -> Trained tdistr sh prob

finishTraining :: (C sh, Eq sh, Estimate tdistr distr, Probability distr ~ prob) => Trained tdistr sh prob -> T distr sh prob

trainMany :: (C sh, Eq sh, Estimate tdistr distr, Probability distr ~ prob, Foldable f) => (trainingData -> Trained tdistr sh prob) -> T f trainingData -> T distr sh prob

deviation :: (InvIndexed sh, Eq sh, Real prob, Ord prob) => T distr sh prob -> T distr 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 distr, Indexed sh, Real prob, Show prob) => T distr sh prob -> String

fromCSV :: (FromCSV distr, StateShape distr ~ stateSh, Indexed stateSh, Index stateSh ~ state, Real prob, Read prob) => (Int -> stateSh) -> String -> Exceptional String (T distr stateSh prob)