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c#machine-learninghiddenmarkov-models
Petrus Theron
Petrus Theron

Reputation: 28886

Applying hidden Markov model to multiple simultaneous bit sequences

This excellent article on implementing a Hidden Markov Model in C# does a fair job of classifying a single bit sequence based on training data.

How to modify the algorithm, or build it out (multiple HMMs?) to support the classification of multiple simultaneous bit sequences?

Example

Instead of classifying just one stream:

double t1 = hmm.Evaluate(new int[] { 0,1 });      // 0.49999423004045024  
double t2 = hmm.Evaluate(new int[] { 0,1,1,1 });  // 0.11458685045803882

Rather classify a dual bit stream:

double t1 = hmm.Evaluate(new int[] { [0, 0], [0, 1] });
double t2 = hmm.Evaluate(new int[] { [0, 0], [1, 1], [0, 1], [1, 1] });

Or even better, three streams:

double t1 = hmm.Evaluate(new int[] { [0, 0, 1], [0, 0, 1] });
double t2 = hmm.Evaluate(new int[] { [0, 0, 1], [1, 1, 0], [0, 1, 1], [1, 1, 1] });

Obviously the training data would also be expanded.

Upvotes: 3

Views: 2601

Answers (2)

Cesar
Cesar

Reputation: 2118

The article mentioned deals with the hidden Markov model implementation in the Accord.NET Framework. When using the complete version of the framework, and not just the subproject available in that article, one can use the generic HiddenMarkovModel model and use any suitable emission symbol distribution. If the user would like to express the joint probability between two or three discrete variables, it would be worth to use the JointDistribution class.

If, however, there are many symbol variables, such that expression all possible variable combinations is not practical, it should be better to use a continuous representation for the features and use a Multivariate Normal distribution instead.

An example would be:

// Specify a initial normal distribution for the samples.
var initialDensity = MultivariateNormalDistribution(3); // 3 dimensions

// Create a continuous hidden Markov Model with two states organized in a forward
//  topology and an underlying multivariate Normal distribution as probability density.
var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Ergodic(2), density);

// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
{
    Tolerance = 0.0001,
    Iterations = 0,
};

// Fit the model
double likelihood = teacher.Run(sequences);

Upvotes: 1

Amro
Amro

Reputation: 124553

The trick is to model the set of observations as the n-ary cartesian product of all possible values of each sequence, in your case the HMM will have 2^n output symbol where n is the number of bit sequences.

Example: for three bit sequences, the 8 symbols are: 000 001 010 011 100 101 110 111, as if we created a megavariable whose values are all the possible tuples of values of the individual observation sequences (0/1 of each bit sequence)

Upvotes: 1

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