HiddenQuasiNewtonLearningT Class 
Namespace: Accord.Statistics.Models.Fields.Learning
public class HiddenQuasiNewtonLearning<T> : BaseHiddenGradientOptimizationLearning<T, BoundedBroydenFletcherGoldfarbShanno>, ISupervisedLearning<HiddenConditionalRandomField<T>, T[], int>, IParallel, ISupportsCancellation, IHiddenConditionalRandomFieldLearning<T>, IConvergenceLearning, IDisposable
The HiddenQuasiNewtonLearningT type exposes the following members.
Name  Description  

HiddenQuasiNewtonLearningT 
Constructs a new LBFGS learning algorithm.
 
HiddenQuasiNewtonLearningT(HiddenConditionalRandomFieldT) 
Constructs a new LBFGS learning algorithm.

Name  Description  

CurrentIteration 
Gets the current iteration number.
 
Function 
Gets or sets the potential function to be used if this learning algorithm
needs to create a new HiddenConditionalRandomFieldT.
(Inherited from BaseHiddenConditionalRandomFieldLearningT.)  
HasConverged 
Gets or sets whether the algorithm has converged.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
MaxIterations 
Gets or sets the maximum number of iterations
performed by the learning algorithm.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Model 
Gets or sets the model being trained.
(Inherited from BaseHiddenConditionalRandomFieldLearningT.)  
Optimizer 
Gets the optimization algorithm being used.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
ParallelOptions 
Gets or sets the parallelization options for this algorithm.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Regularization 
Gets or sets the amount of the parameter weights
which should be included in the objective function.
Default is 0 (do not include regularization).
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Token 
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
(Inherited from BaseHiddenConditionalRandomFieldLearningT.)  
Tolerance 
Gets or sets the tolerance value used to determine
whether the algorithm has converged.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.) 
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.
(Inherited from BaseHiddenConditionalRandomFieldLearningT.)  
CreateOptimizer 
Inheritors of this class should create the optimization algorithm in this
method, using the current MaxIterations and Tolerance
settings.
(Overrides BaseHiddenGradientOptimizationLearningTData, TOptimizerCreateOptimizer.)  
Dispose 
Performs applicationdefined tasks associated with freeing,
releasing, or resetting unmanaged resources.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Dispose(Boolean) 
Releases unmanaged and  optionally  managed resources
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize 
Releases unmanaged resources and performs other cleanup operations before
the HiddenQuasiNewtonLearningT is reclaimed by garbage
collection.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
InnerRun 
Runs the learning algorithm.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Learn 
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseHiddenConditionalRandomFieldLearningT.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
Run(TData, Int32) 
Online learning is not supported.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
Run(TData, Int32)  Obsolete.
Runs the learning algorithm with the specified input
training observations and corresponding output labels.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
RunEpoch  Obsolete.
Online learning is not supported.
(Inherited from BaseHiddenGradientOptimizationLearningTData, TOptimizer.)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
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.) 
// 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 realworld example would involve *lots* of samples for each word. // Here, we are considering just one from each class which is clearly suboptimal 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 loglikelihood changes less than 0.001 Learner = (i) => new BaumWelchLearning<Independent<NormalDistribution>, double[]>() { Topology = new Forward(5), // this value can be found by trialanderror // 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 = 1e5 } } } }; // 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 = 1e5 }; // 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 realworld 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: localDownloadPath); // Get and preprocess the training set double[][][] trainInputs = pendigits.Training.Item1; int[] trainOutputs = pendigits.Training.Item2; // Preprocess 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 loglikelihood is less than 1e6 between iterations Tolerance = 1e6, 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 positivedefinite again: FittingOptions = new NormalOptions() { Regularization = 1e6 } } }; // 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 HiddenQuasiNewtonLearning<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 groundtruth: var m1 = new GeneralConfusionMatrix(predicted: trainPredicted, expected: trainOutputs); double trainAcc = m1.Accuracy; // should be 0.66523727844482561 // 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 groundtruth: var m2 = new GeneralConfusionMatrix(predicted: testPredicted, expected: testOutputs); double testAcc = m2.Accuracy; // should be 0.66506538564184681