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HiddenConditionalRandomFieldT Class

Hidden Conditional Random Field (HCRF).
Inheritance Hierarchy
SystemObject
  Accord.MachineLearningTransformBaseT, Int32
    Accord.MachineLearningClassifierBaseT, Int32
      Accord.MachineLearningMulticlassClassifierBaseT
        Accord.Statistics.Models.FieldsHiddenConditionalRandomFieldT

Namespace:  Accord.Statistics.Models.Fields
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.7.0
Syntax
[SerializableAttribute]
public class HiddenConditionalRandomField<T> : MulticlassClassifierBase<T[]>, 
	ICloneable
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Type Parameters

T
The type of the observations modeled by the field.

The HiddenConditionalRandomFieldT type exposes the following members.

Constructors
  NameDescription
Public methodHiddenConditionalRandomFieldT
Initializes a new instance of the HiddenConditionalRandomFieldT class.
Public methodHiddenConditionalRandomFieldT(IPotentialFunctionT)
Initializes a new instance of the HiddenConditionalRandomFieldT class.
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Properties
Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
Public methodCompute(T) Obsolete.
Computes the most likely output for the given observations.
Public methodCompute(T, Double) Obsolete.
Computes the most likely output for the given observations.
Public methodCompute(T, Double) Obsolete.
Computes the most likely output for the given observations.
Public methodDecide(TInput)
Computes class-label decisions for a given set of input vectors.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodDecide(T)
Computes a class-label decision for a given input.
(Overrides ClassifierBaseTInput, TClassesDecide(TInput).)
Public methodDecide(TInput, TClasses)
Computes a class-label decision for a given input.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodDecide(TInput, Boolean)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Double)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Int32)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Double)
Computes a class-label decision for a given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecode(T, Int32)
Computes the most likely state labels for the given observations, returning the overall sequence probability for this model.
Public methodDecode(T, Int32, Double)
Computes the most likely state labels for the given observations, returning the overall sequence probability for this model.
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodStatic memberLoad(Stream) Obsolete.
Loads a random field from a stream.
Public methodStatic memberLoad(String) Obsolete.
Loads a random field from a file.
Public methodLogLikelihood(T)
Computes the log-likelihood of the observations given this model.
Public methodLogLikelihood(T)
Computes the log-likelihood of the observations given this model.
Public methodLogLikelihood(T, Int32)
Computes the log-likelihood that the given observations belong to the desired output.
Public methodLogLikelihood(T, Int32)
Computes the log-likelihood that the given observations belong to the desired outputs.
Public methodLogLikelihood(T, Int32, Double)
Computes the log-likelihood that the given observations belong to the desired output.
Public methodLogLikelihood(T, Int32, Double)
Computes the log-likelihood that the given observations belong to the desired outputs.
Public methodLogPartition(T)
Computes the log-partition function ln Z(x).
Public methodLogPartition(T, Int32)
Computes the log-partition function ln Z(x,y).
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodPartition(T)
Computes the partition function Z(x).
Public methodPartition(T, Int32)
Computes the partition function Z(x,y).
Public methodSave(Stream) Obsolete.
Saves the random field to a stream.
Public methodSave(String) Obsolete.
Saves the random field to a stream.
Public methodToMultilabel
Views this instance as a multi-label classifier, giving access to more advanced methods, such as the prediction of one-hot vectors.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Public methodTransform(TInput)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodTransform(TInput)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from TransformBaseTInput, TOutput.)
Public methodTransform(TInput, TClasses)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
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

Conditional random fields (CRFs) are a class of statistical modeling method often applied in pattern recognition and machine learning, where they are used for structured prediction. Whereas an ordinary classifier predicts a label for a single sample without regard to "neighboring" samples, a CRF can take context into account; e.g., the linear chain CRF popular in natural language processing predicts sequences of labels for sequences of input samples.

While Conditional Random Fields can be seen as a generalization of Markov models, Hidden Conditional Random Fields can be seen as a generalization of Hidden Markov Model Classifiers. The (linear-chain) Conditional Random Field is the discriminative counterpart of the Markov model. An observable Markov Model assumes the sequences of states y to be visible, rather than hidden. Thus they can be used in a different set of problems than the hidden Markov models. Those models are often used for sequence component labeling, also known as part-of-sequence tagging. After a model has been trained, they are mostly used to tag parts of a sequence using the Viterbi algorithm. This is very handy to perform, for example, classification of parts of a speech utterance, such as classifying phonemes inside an audio signal.

References:

Examples
// Let's say we would like to do a very simple mechanism for gesture recognition. 
// In this example, we will be trying to create a classifier that can distinguish 
// between the words "hello", "car", and "wardrobe". 

// Let's say we decided to acquire some data, and we asked some people to perform 
// those words in front of a Kinect camera, and, using Microsoft's SDK, we were able 
// to captured the x and y coordinates of each hand while the word was being performed.

// Let's say we decided to represent our frames as:
// 
//    double[] frame = { leftHandX, leftHandY, rightHandX, rightHandY }; // 4 dimensions
// 
// Since we captured words, this means we captured sequences of frames as we described 
// above. Let's write some of those as rough examples to explain how gesture recognition 
// can be done:

double[][] hello =
{
    new double[] { 1.0, 0.1, 0.0, 0.0 }, // let's say the word
    new double[] { 0.0, 1.0, 0.1, 0.1 }, // hello took 6 frames
    new double[] { 0.0, 1.0, 0.1, 0.1 }, // to be recorded.
    new double[] { 0.0, 0.0, 1.0, 0.0 },
    new double[] { 0.0, 0.0, 1.0, 0.0 },
    new double[] { 0.0, 0.0, 0.1, 1.1 },
};

double[][] car =
{
    new double[] { 0.0, 0.0, 0.0, 1.0 }, // the car word
    new double[] { 0.1, 0.0, 1.0, 0.1 }, // took only 4.
    new double[] { 0.0, 0.0, 0.1, 0.0 },
    new double[] { 1.0, 0.0, 0.0, 0.0 },
};

double[][] wardrobe =
{
    new double[] { 0.0, 0.0, 1.0, 0.0 }, // same for the
    new double[] { 0.1, 0.0, 1.0, 0.1 }, // wardrobe word.
    new double[] { 0.0, 0.1, 1.0, 0.0 },
    new double[] { 0.1, 0.0, 1.0, 0.1 },
};

// Please note that a real-world example would involve *lots* of samples for each word. 
// Here, we are considering just one from each class which is clearly sub-optimal and 
// should _never_ be done on practice. Please keep in mind that we are doing like this
// only to simplify this example on how to create and use HCRFs.

// These are the words we have in our vocabulary:
double[][][] words = { hello, car, wardrobe };

// Now, let's associate integer labels with them. This is needed
// for the case where there are multiple samples for each word.
int[] labels = { 0, 1, 2 };

// Create a new learning algorithm to train the hidden Markov model sequence classifier
var teacher = new HiddenMarkovClassifierLearning<Independent<NormalDistribution>, double[]>()
{
    // Train each model until the log-likelihood changes less than 0.001
    Learner = (i) => new BaumWelchLearning<Independent<NormalDistribution>, double[]>()
    {
        Topology = new Forward(5), // this value can be found by trial-and-error

        // We will create our classifiers assuming an independent Gaussian distribution 
        // for each component in our feature vectors (assuming a Naive Bayes assumption).
        Emissions = (s) => new Independent<NormalDistribution>(dimensions: 4), // 4 dimensions

        Tolerance = 0.001,
        Iterations = 100,

        // This is necessary so the code doesn't blow up when it realizes there is only one 
        // sample per word class. But this could also be needed in normal situations as well:
        FittingOptions = new IndependentOptions()
        {
            InnerOption = new NormalOptions() { Regularization = 1e-5 }
        }
    }
};

// PS: In case you find exceptions trying to configure your model, you might want 
//     to try disabling parallel processing to get more descriptive error messages:
// teacher.ParallelOptions.MaxDegreeOfParallelism = 1;

// Finally, we can run the learning algorithm!
var hmm = teacher.Learn(words, labels);
double logLikelihood = teacher.LogLikelihood;

// At this point, the classifier should be successfully 
// able to distinguish between our three word classes:
// 
int tc1 = hmm.Decide(hello);    // should be 0
int tc2 = hmm.Decide(car);      // should be 1
int tc3 = hmm.Decide(wardrobe); // should be 2
// Now, we can use the Markov classifier to initialize a HCRF
var baseline = HiddenConditionalRandomField.FromHiddenMarkov(hmm);

// We can check that both are equivalent, although they have
// formulations that can be learned with different methods:
int[] predictedLabels = baseline.Decide(words);
// Now we can learn the HCRF using one of the best learning
// algorithms available, Resilient Backpropagation learning:

// Create the Resilient Backpropagation learning algorithm
var rprop = new HiddenResilientGradientLearning<double[]>()
{
    Function = baseline.Function, // use the same HMM function

    Iterations = 50,
    Tolerance = 1e-5
};

// Run the algorithm and learn the models
var hcrf = rprop.Learn(words, labels);

// At this point, the HCRF should be successfully 
// able to distinguish between our three word classes:
// 
int hc1 = hcrf.Decide(hello);    // should be 0
int hc2 = hcrf.Decide(car);      // should be 1
int hc3 = hcrf.Decide(wardrobe); // should be 2

The next example shows how to use the learning algorithms in a real-world dataset, including training and testing in separate sets and evaluating its performance:

// Ensure we get reproducible results
Accord.Math.Random.Generator.Seed = 0;

// Download the PENDIGITS dataset from UCI ML repository
var pendigits = new Pendigits(path: Path.GetTempPath());

// Get and pre-process the training set
double[][][] trainInputs = pendigits.Training.Item1;
int[] trainOutputs = pendigits.Training.Item2;

// Pre-process the digits so each of them is centered and scaled
trainInputs = trainInputs.Apply(Accord.Statistics.Tools.ZScores);
trainInputs = trainInputs.Apply((x) => x.Subtract(x.Min())); // make them positive

// Create some prior distributions to help initialize our parameters
var priorC = new WishartDistribution(dimension: 2, degreesOfFreedom: 5);
var priorM = new MultivariateNormalDistribution(dimension: 2);

// Create a new learning algorithm for creating continuous hidden Markov model classifiers
var teacher1 = new HiddenMarkovClassifierLearning<MultivariateNormalDistribution, double[]>()
{
    // This tells the generative algorithm how to train each of the component models. Note: The learning
    // algorithm is more efficient if all generic parameters are specified, including the fitting options
    Learner = (i) => new BaumWelchLearning<MultivariateNormalDistribution, double[], NormalOptions>()
    {
        Topology = new Forward(5), // Each model will have a forward topology with 5 states

        // Their emissions will be multivariate Normal distributions initialized using the prior distributions
        Emissions = (j) => new MultivariateNormalDistribution(mean: priorM.Generate(), covariance: priorC.Generate()),

        // We will train until the relative change in the average log-likelihood is less than 1e-6 between iterations
        Tolerance = 1e-6,
        MaxIterations = 1000, // or until we perform 1000 iterations (which is unlikely for this dataset)

        // We will prevent our covariance matrices from becoming degenerate by adding a small 
        // regularization value to their diagonal until they become positive-definite again:
        FittingOptions = new NormalOptions()
        {
            Regularization = 1e-6
        }
    }
};

//// The following line is only needed to ensure reproducible results. Please remove it to enable full parallelization
//teacher1.ParallelOptions.MaxDegreeOfParallelism = 1; // (Remove, comment, or change this line to enable full parallelism)

// Use the learning algorithm to create a classifier
var hmmc = teacher1.Learn(trainInputs, trainOutputs);

// Create a new learning algorithm for creating HCRFs
var teacher2 = new HiddenResilientGradientLearning<double[]>()
{
    Function = new MarkovMultivariateFunction(hmmc),

    MaxIterations = 10
};

//// The following line is only needed to ensure reproducible results. Please remove it to enable full parallelization
//teacher2.ParallelOptions.MaxDegreeOfParallelism = 1; // (Remove, comment, or change this line to enable full parallelism)

// Use the learning algorithm to create a classifier
var hcrf = teacher2.Learn(trainInputs, trainOutputs);

// Compute predictions for the training set
int[] trainPredicted = hcrf.Decide(trainInputs);

// Check the performance of the classifier by comparing with the ground-truth:
var m1 = new GeneralConfusionMatrix(predicted: trainPredicted, expected: trainOutputs);
double trainAcc = m1.Accuracy; // should be 0.81532304173813608


// Prepare the testing set
double[][][] testInputs = pendigits.Testing.Item1;
int[] testOutputs = pendigits.Testing.Item2;

// Apply the same normalizations
testInputs = testInputs.Apply(Accord.Statistics.Tools.ZScores);
testInputs = testInputs.Apply((x) => x.Subtract(x.Min())); // make them positive

// Compute predictions for the test set
int[] testPredicted = hcrf.Decide(testInputs);

// Check the performance of the classifier by comparing with the ground-truth:
var m2 = new GeneralConfusionMatrix(predicted: testPredicted, expected: testOutputs);
double testAcc = m2.Accuracy; // should be 0.77061649319455561
See Also