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-// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
-/*
-
- This is an example illustrating the use of the machine learning
- tools for sequence labeling in the dlib C++ Library.
-
- The general problem addressed by these tools is the following.
- Suppose you have a set of sequences of some kind and you want to
- learn to predict a label for each element of a sequence. So for
- example, you might have a set of English sentences where each
- word is labeled with its part of speech and you want to learn a
- model which can predict the part of speech for each word in a new
- sentence.
-
- Central to these tools is the sequence_labeler object. It is the
- object which represents the label prediction model. In particular,
- the model used by this object is the following. Given an input
- sequence x, predict an output label sequence y such that:
- y == argmax_y dot(weight_vector, PSI(x,y))
- where PSI() is supplied by the user and defines the form of the
- model. In this example program we will define it such that we
- obtain a simple Hidden Markov Model. However, it's possible to
- define much more sophisticated models. You should take a look
- at the following papers for a few examples:
- - Hidden Markov Support Vector Machines by
- Y. Altun, I. Tsochantaridis, T. Hofmann
- - Shallow Parsing with Conditional Random Fields by
- Fei Sha and Fernando Pereira
-
-
-
- In the remainder of this example program we will show how to
- define your own PSI(), as well as how to learn the "weight_vector"
- parameter. Once you have these two items you will be able to
- use the sequence_labeler to predict the labels of new sequences.
-*/
-
-
-#include <iostream>
-#include <dlib/svm_threaded.h>
-#include <dlib/rand.h>
-
-using namespace std;
-using namespace dlib;
-
-
-/*
- In this example we will be working with a Hidden Markov Model where
- the hidden nodes and observation nodes both take on 3 different states.
- The task will be to take a sequence of observations and predict the state
- of the corresponding hidden nodes.
-*/
-
-const unsigned long num_label_states = 3;
-const unsigned long num_sample_states = 3;
-
-// ----------------------------------------------------------------------------------------
-
-class feature_extractor
-{
- /*
- This object is where you define your PSI(). To ensure that the argmax_y
- remains a tractable problem, the PSI(x,y) vector is actually a sum of vectors,
- each derived from the entire input sequence x but only part of the label
- sequence y. This allows the argmax_y to be efficiently solved using the
- well known Viterbi algorithm.
- */
-
-public:
- // This defines the type used to represent the observed sequence. You can use
- // any type here so long as it has a .size() which returns the number of things
- // in the sequence.
- typedef std::vector<unsigned long> sequence_type;
-
- unsigned long num_features() const
- /*!
- ensures
- - returns the dimensionality of the PSI() feature vector.
- !*/
- {
- // Recall that we are defining a HMM. So in this case the PSI() vector
- // should have the same dimensionality as the number of parameters in the HMM.
- return num_label_states*num_label_states + num_label_states*num_sample_states;
- }
-
- unsigned long order() const
- /*!
- ensures
- - This object represents a Markov model on the output labels.
- This parameter defines the order of the model. That is, this
- value controls how many previous label values get to be taken
- into consideration when performing feature extraction for a
- particular element of the input sequence. Note that the runtime
- of the algorithm is exponential in the order. So don't make order
- very large.
- !*/
- {
- // In this case we are using a HMM model that only looks at the
- // previous label.
- return 1;
- }
-
- unsigned long num_labels() const
- /*!
- ensures
- - returns the number of possible output labels.
- !*/
- {
- return num_label_states;
- }
-
- template <typename feature_setter, typename EXP>
- void get_features (
- feature_setter& set_feature,
- const sequence_type& x,
- const matrix_exp<EXP>& y,
- unsigned long position
- ) const
- /*!
- requires
- - EXP::type == unsigned long
- (i.e. y contains unsigned longs)
- - position < x.size()
- - y.size() == min(position, order) + 1
- - is_vector(y) == true
- - max(y) < num_labels()
- - set_feature is a function object which allows expressions of the form:
- - set_features((unsigned long)feature_index, (double)feature_value);
- - set_features((unsigned long)feature_index);
- ensures
- - for all valid i:
- - interprets y(i) as the label corresponding to x[position-i]
- - This function computes the part of PSI() corresponding to the x[position]
- element of the input sequence. Moreover, this part of PSI() is returned as
- a sparse vector by invoking set_feature(). For example, to set the feature
- with an index of 55 to the value of 1 this method would call:
- set_feature(55);
- Or equivalently:
- set_feature(55,1);
- Therefore, the first argument to set_feature is the index of the feature
- to be set while the second argument is the value the feature should take.
- Additionally, note that calling set_feature() multiple times with the same
- feature index does NOT overwrite the old value, it adds to the previous
- value. For example, if you call set_feature(55) 3 times then it will
- result in feature 55 having a value of 3.
- - This function only calls set_feature() with feature_index values < num_features()
- !*/
- {
- // Again, the features below only define a simple HMM. But in general, you can
- // use a wide variety of sophisticated feature extraction methods here.
-
- // Pull out an indicator feature for the type of transition between the
- // previous label and the current label.
- if (y.size() > 1)
- set_feature(y(1)*num_label_states + y(0));
-
- // Pull out an indicator feature for the type of observed node given
- // the current label.
- set_feature(num_label_states*num_label_states +
- y(0)*num_sample_states + x[position]);
- }
-};
-
-// We need to define serialize() and deserialize() for our feature extractor if we want
-// to be able to serialize and deserialize our learned models. In this case the
-// implementation is empty since our feature_extractor doesn't have any state. But you
-// might define more complex feature extractors which have state that needs to be saved.
-void serialize(const feature_extractor&, std::ostream&) {}
-void deserialize(feature_extractor&, std::istream&) {}
-
-// ----------------------------------------------------------------------------------------
-
-void make_dataset (
- const matrix<double>& transition_probabilities,
- const matrix<double>& emission_probabilities,
- std::vector<std::vector<unsigned long> >& samples,
- std::vector<std::vector<unsigned long> >& labels,
- unsigned long dataset_size
-);
-/*!
- requires
- - transition_probabilities.nr() == transition_probabilities.nc()
- - transition_probabilities.nr() == emission_probabilities.nr()
- - The rows of transition_probabilities and emission_probabilities must sum to 1.
- (i.e. sum_cols(transition_probabilities) and sum_cols(emission_probabilities)
- must evaluate to vectors of all 1s.)
- ensures
- - This function randomly samples a bunch of sequences from the HMM defined by
- transition_probabilities and emission_probabilities.
- - The HMM is defined by:
- - The probability of transitioning from hidden state H1 to H2
- is given by transition_probabilities(H1,H2).
- - The probability of a hidden state H producing an observed state
- O is given by emission_probabilities(H,O).
- - #samples.size() == #labels.size() == dataset_size
- - for all valid i:
- - #labels[i] is a randomly sampled sequence of hidden states from the
- given HMM. #samples[i] is its corresponding randomly sampled sequence
- of observed states.
-!*/
-
-// ----------------------------------------------------------------------------------------
-
-int main()
-{
- // We need a dataset to test the machine learning algorithms. So we are going to
- // define a HMM based on the following two matrices and then randomly sample a
- // set of data from it. Then we will see if the machine learning method can
- // recover the HMM model from the training data.
-
-
- matrix<double> transition_probabilities(num_label_states, num_label_states);
- transition_probabilities = 0.05, 0.90, 0.05,
- 0.05, 0.05, 0.90,
- 0.90, 0.05, 0.05;
-
- matrix<double> emission_probabilities(num_label_states,num_sample_states);
- emission_probabilities = 0.5, 0.5, 0.0,
- 0.0, 0.5, 0.5,
- 0.5, 0.0, 0.5;
-
- std::vector<std::vector<unsigned long> > samples;
- std::vector<std::vector<unsigned long> > labels;
- // sample 1000 labeled sequences from the HMM.
- make_dataset(transition_probabilities,emission_probabilities,
- samples, labels, 1000);
-
- // print out some of the randomly sampled sequences
- for (int i = 0; i < 10; ++i)
- {
- cout << "hidden states: " << trans(mat(labels[i]));
- cout << "observed states: " << trans(mat(samples[i]));
- cout << "******************************" << endl;
- }
-
- // Next we use the structural_sequence_labeling_trainer to learn our
- // prediction model based on just the samples and labels.
- structural_sequence_labeling_trainer<feature_extractor> trainer;
- // This is the common SVM C parameter. Larger values encourage the
- // trainer to attempt to fit the data exactly but might overfit.
- // In general, you determine this parameter by cross-validation.
- trainer.set_c(4);
- // This trainer can use multiple CPU cores to speed up the training.
- // So set this to the number of available CPU cores.
- trainer.set_num_threads(4);
-
-
- // Learn to do sequence labeling from the dataset
- sequence_labeler<feature_extractor> labeler = trainer.train(samples, labels);
-
- // Test the learned labeler on one of the training samples. In this
- // case it will give the correct sequence of labels.
- std::vector<unsigned long> predicted_labels = labeler(samples[0]);
- cout << "true hidden states: "<< trans(mat(labels[0]));
- cout << "predicted hidden states: "<< trans(mat(predicted_labels));
-
-
-
- // We can also do cross-validation. The confusion_matrix is defined as:
- // - confusion_matrix(T,P) == the number of times a sequence element with label T
- // was predicted to have a label of P.
- // So if all predictions are perfect then only diagonal elements of this matrix will
- // be non-zero.
- matrix<double> confusion_matrix;
- confusion_matrix = cross_validate_sequence_labeler(trainer, samples, labels, 4);
- cout << "\ncross-validation: " << endl;
- cout << confusion_matrix;
- cout << "label accuracy: "<< sum(diag(confusion_matrix))/sum(confusion_matrix) << endl;
-
- // In this case, the label accuracy is about 88%. At this point, we want to know if
- // the machine learning method was able to recover the HMM model from the data. So
- // to test this, we can load the true HMM model into another sequence_labeler and
- // test it out on the data and compare the results.
-
- matrix<double,0,1> true_hmm_model_weights = log(join_cols(reshape_to_column_vector(transition_probabilities),
- reshape_to_column_vector(emission_probabilities)));
- // With this model, labeler_true will predict the most probable set of labels
- // given an input sequence. That is, it will predict using the equation:
- // y == argmax_y dot(true_hmm_model_weights, PSI(x,y))
- sequence_labeler<feature_extractor> labeler_true(true_hmm_model_weights);
-
- confusion_matrix = test_sequence_labeler(labeler_true, samples, labels);
- cout << "\nTrue HMM model: " << endl;
- cout << confusion_matrix;
- cout << "label accuracy: "<< sum(diag(confusion_matrix))/sum(confusion_matrix) << endl;
-
- // Happily, we observe that the true model also obtains a label accuracy of 88%.
-
-
-
-
-
-
- // Finally, the labeler can be serialized to disk just like most dlib objects.
- serialize("labeler.dat") << labeler;
-
- // recall from disk
- deserialize("labeler.dat") >> labeler;
-}
-
-// ----------------------------------------------------------------------------------------
-// ----------------------------------------------------------------------------------------
-// Code for creating a bunch of random samples from our HMM.
-// ----------------------------------------------------------------------------------------
-// ----------------------------------------------------------------------------------------
-
-void sample_hmm (
- dlib::rand& rnd,
- const matrix<double>& transition_probabilities,
- const matrix<double>& emission_probabilities,
- unsigned long previous_label,
- unsigned long& next_label,
- unsigned long& next_sample
-)
-/*!
- requires
- - previous_label < transition_probabilities.nr()
- - transition_probabilities.nr() == transition_probabilities.nc()
- - transition_probabilities.nr() == emission_probabilities.nr()
- - The rows of transition_probabilities and emission_probabilities must sum to 1.
- (i.e. sum_cols(transition_probabilities) and sum_cols(emission_probabilities)
- must evaluate to vectors of all 1s.)
- ensures
- - This function randomly samples the HMM defined by transition_probabilities
- and emission_probabilities assuming that the previous hidden state
- was previous_label.
- - The HMM is defined by:
- - P(next_label |previous_label) == transition_probabilities(previous_label, next_label)
- - P(next_sample|next_label) == emission_probabilities (next_label, next_sample)
- - #next_label == the sampled value of the hidden state
- - #next_sample == the sampled value of the observed state
-!*/
-{
- // sample next_label
- double p = rnd.get_random_double();
- for (long c = 0; p >= 0 && c < transition_probabilities.nc(); ++c)
- {
- next_label = c;
- p -= transition_probabilities(previous_label, c);
- }
-
- // now sample next_sample
- p = rnd.get_random_double();
- for (long c = 0; p >= 0 && c < emission_probabilities.nc(); ++c)
- {
- next_sample = c;
- p -= emission_probabilities(next_label, c);
- }
-}
-
-// ----------------------------------------------------------------------------------------
-
-void make_dataset (
- const matrix<double>& transition_probabilities,
- const matrix<double>& emission_probabilities,
- std::vector<std::vector<unsigned long> >& samples,
- std::vector<std::vector<unsigned long> >& labels,
- unsigned long dataset_size
-)
-{
- samples.clear();
- labels.clear();
-
- dlib::rand rnd;
-
- // now randomly sample some labeled sequences from our Hidden Markov Model
- for (unsigned long iter = 0; iter < dataset_size; ++iter)
- {
- const unsigned long sequence_size = rnd.get_random_32bit_number()%20+3;
- std::vector<unsigned long> sample(sequence_size);
- std::vector<unsigned long> label(sequence_size);
-
- unsigned long previous_label = rnd.get_random_32bit_number()%num_label_states;
- for (unsigned long i = 0; i < sample.size(); ++i)
- {
- unsigned long next_label = 0, next_sample = 0;
- sample_hmm(rnd, transition_probabilities, emission_probabilities,
- previous_label, next_label, next_sample);
-
- label[i] = next_label;
- sample[i] = next_sample;
-
- previous_label = next_label;
- }
-
- samples.push_back(sample);
- labels.push_back(label);
- }
-}
-
-// ----------------------------------------------------------------------------------------
-