Safe Haskell | None |
---|---|
Language | Haskell2010 |
- data T distr prob = Cons {
- initial :: Vector prob
- transition :: Matrix prob
- distribution :: distr
- data State
- state :: Int -> State
- type Discrete prob symbol = T (Discrete prob symbol) prob
- type DiscreteTrained prob symbol = Trained (DiscreteTrained prob symbol) prob
- type Gaussian a = T (Gaussian a) a
- type GaussianTrained a = Trained (GaussianTrained a) a
- uniform :: (Info distr, Probability distr ~ prob) => distr -> T distr prob
- generate :: (RandomGen g, Ord prob, Random prob, Generate distr, Probability distr ~ prob, Emission distr ~ emission) => T distr prob -> g -> [emission]
- logLikelihood :: (EmissionProb distr, Floating prob, Probability distr ~ prob, Emission distr ~ emission, Traversable f) => T distr prob -> T f emission -> prob
- reveal :: (EmissionProb distr, Probability distr ~ prob, Emission distr ~ emission, Traversable f, Reverse f) => T distr prob -> T f emission -> T f State
- data Trained distr prob = Trained {
- trainedInitial :: Vector prob
- trainedTransition :: Matrix prob
- trainedDistribution :: distr
- trainSupervised :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Int -> T [] (State, emission) -> Trained tdistr prob
- trainUnsupervised :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => T distr prob -> T [] emission -> Trained tdistr prob
- mergeTrained :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Trained tdistr prob -> Trained tdistr prob -> Trained tdistr prob
- finishTraining :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Trained tdistr prob -> T distr prob
- trainMany :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Foldable f) => (trainingData -> Trained tdistr prob) -> T f trainingData -> T distr prob
- deviation :: (Field prob, Ord prob) => T distr prob -> T distr prob -> prob
- toCSV :: (CSV distr, Field prob, Show prob) => T distr prob -> String
- fromCSV :: (CSV distr, Field prob, Read prob) => String -> Exceptional String (T distr prob)
Documentation
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.
Cons | |
|
type DiscreteTrained prob symbol = Trained (DiscreteTrained prob symbol) prob Source
type GaussianTrained a = Trained (GaussianTrained a) a Source
uniform :: (Info distr, Probability distr ~ prob) => distr -> T distr prob Source
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, Probability distr ~ prob, Emission distr ~ emission) => T distr prob -> g -> [emission] Source
logLikelihood :: (EmissionProb distr, Floating prob, Probability distr ~ prob, Emission distr ~ emission, Traversable f) => T distr prob -> T f emission -> prob Source
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, Probability distr ~ prob, Emission distr ~ emission, Traversable f, Reverse f) => T distr prob -> T f emission -> T f State Source
Reveal the state sequence that led most likely to the observed sequence of emissions. It is found using the Viterbi algorithm.
data Trained distr prob Source
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.
Trained | |
|
trainSupervised :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Int -> T [] (State, emission) -> Trained tdistr prob Source
Contribute a manually labeled emission sequence to a HMM training.
trainUnsupervised :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => T distr prob -> T [] emission -> Trained tdistr prob Source
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 tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Trained tdistr prob -> Trained tdistr prob -> Trained tdistr prob Source
finishTraining :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Emission distr ~ emission) => Trained tdistr prob -> T distr prob Source
trainMany :: (Estimate tdistr, Distribution tdistr ~ distr, Probability distr ~ prob, Foldable f) => (trainingData -> Trained tdistr prob) -> T f trainingData -> T distr prob Source
deviation :: (Field prob, Ord prob) => T distr prob -> T distr prob -> prob Source
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.