MaximumLikelihoodLearning Class

Maximum Likelihood learning algorithm for discrete-density Hidden Markov Models.

Inheritance Hierarchy

SystemObject
Accord.Statistics.Models.Markov.LearningBaseMaximumLikelihoodLearningHiddenMarkovModel, GeneralDiscreteDistribution, Int32, GeneralDiscreteOptions
Accord.Statistics.Models.Markov.LearningMaximumLikelihoodLearning

Namespace: Accord.Statistics.Models.Markov.Learning
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

Syntax

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public class MaximumLikelihoodLearning : BaseMaximumLikelihoodLearning<HiddenMarkovModel, GeneralDiscreteDistribution, int, GeneralDiscreteOptions>, 
	ISupervisedLearning, ISupervisedLearning<HiddenMarkovModel, int[], int[]>

Public Class MaximumLikelihoodLearning
	Inherits BaseMaximumLikelihoodLearning(Of HiddenMarkovModel, GeneralDiscreteDistribution, Integer, GeneralDiscreteOptions)
	Implements ISupervisedLearning, ISupervisedLearning(Of HiddenMarkovModel, Integer(), Integer())

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The MaximumLikelihoodLearning type exposes the following members.

Constructors

	Name	Description
	MaximumLikelihoodLearning	Creates a new instance of the Maximum Likelihood learning algorithm.
	MaximumLikelihoodLearning(HiddenMarkovModel)	Creates a new instance of the Maximum Likelihood learning algorithm.

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Properties

	Name	Description
	Emissions	Gets or sets the function that initializes the emission distributions in the hidden Markov Models. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	FittingOptions	Gets or sets the distribution fitting options to use when estimating distribution densities during learning. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	Model	Gets the model being trained. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	Token	Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	UseLaplaceRule	Gets or sets whether to use Laplace's rule of succession to avoid zero probabilities. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	UseWeights	Gets or sets whether the emission fitting algorithm should present weighted samples or simply the clustered samples to the density estimation methods. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)

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Methods

	Name	Description
	Create	Creates an instance of the model to be learned. Inheritors of this abstract class must define this method so new models can be created from the training data. (Overrides BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptionsCreate(TObservation, Int32).)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Learn	Learns a model that can map the given inputs to the given outputs. (Inherited from BaseMaximumLikelihoodLearningTModel, TDistribution, TObservation, TOptions.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Run	Obsolete. Runs the Maximum Likelihood learning algorithm for hidden Markov models.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

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Remarks

The maximum likelihood estimate is a supervised learning algorithm. It considers both the sequence of observations as well as the sequence of states in the Markov model are visible and thus during training.

Often, the Maximum Likelihood Estimate can be used to give a starting point to a unsupervised algorithm, making possible to use semi-supervised techniques with HMMs. It is possible, for example, to use MLE to guess initial values for an HMM given a small set of manually labeled labels, and then further estimate this model using the Viterbi learning algorithm.

Examples

The following example comes from Prof. Yechiam Yemini slides on Hidden Markov Models, available at http://www.cs.columbia.edu/4761/notes07/chapter4.3-HMM.pdf. In this example, we will be specifying both the sequence of observations and the sequence of states assigned to each observation in each sequence to learn our Markov model.

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// Example from
// http://www.cs.columbia.edu/4761/notes07/chapter4.3-HMM.pdf

// Inputs
int[][] observations = 
{
    new int[] { 0,0,0,1,0,0 }, 
    new int[] { 1,0,0,1,0,0 },
    new int[] { 0,0,1,0,0,0 },
    new int[] { 0,0,0,0,1,0 },
    new int[] { 1,0,0,0,1,0 },
    new int[] { 0,0,0,1,1,0 },
    new int[] { 1,0,0,0,0,0 },
    new int[] { 1,0,1,0,0,0 },
};

// Outputs
int[][] paths =
{
    new int[] { 0,0,1,0,1,0 },
    new int[] { 1,0,1,0,1,0 },
    new int[] { 1,0,0,1,1,0 },
    new int[] { 1,0,1,1,1,0 },
    new int[] { 1,0,0,1,0,1 },
    new int[] { 0,0,1,0,0,1 },
    new int[] { 0,0,1,1,0,1 },
    new int[] { 0,1,1,1,0,0 },
};

// Create a hidden Markov model with 2 states for 2 symbols
var model = new HiddenMarkovModel(states: 2, symbols: 2);

// Create a Maximum Likelihood learning algorithm
var target = new MaximumLikelihoodLearning(model)
{
    UseLaplaceRule = false // don't use Laplace smoothing (to reproduce the example)
};

// Learn the Markov model
target.Learn(observations, paths);

// Recover the learned parameters
var pi = model.LogInitial.Exp();
var A = model.LogTransitions.Exp();
var B = model.LogEmissions.Exp();

Reference

Accord.Statistics.Models.Markov.Learning Namespace

Accord.Statistics.Models.Markov.LearningMaximumLikelihoodLearning

Accord.Statistics.Models.Markov.LearningViterbiLearning

Accord.Statistics.Models.MarkovHiddenMarkovModel