ObservationDistribution types are used for states of generative models. Such a type can be trained from a set of examples, and can evaluate a similarity measure over observation types.

Refinement of
Notation

The following expressions are used in this document:

OD

A ObservationDistribution type.

od

An object of type OD

O

The Observation type associated with OD

o

An object of type O

Requirements

Name

Expression

Result Type

Semantics

Observation Type

OD::observation_type

O

The Observation type associated with OD.

Observation Similarity

od(o)

double

For probabilistic models, this typically returns the probability that o was generated by the state modeled by od. In practice, any similarity measure might work.

Example

The below example uses a normal distribution to model a state. The training consists of calculating the mean and standard deviation of the provided example observations. The trained distribution is then used to provide a similarity measure with observations. 

#include <ame/range/standard_deviation.hpp>
#include <ame/utility/serialize/normal_distribution.hpp>
#include <boost/math/distributions/normal.hpp>

namespace ame { namespace patterns {

class normal_model_state
{
public:
    typedef double observation_type;
    
    normal_model_state(double min_st_dev=std::numeric_limits<double>::min())
        : m_min_st_dev(min_st_dev)
    {}
    double operator()(double a) const
    {
        return pdf(m_distribution,a);
    }
    template<typename Range>
    void train_with_examples(const Range &examples)
    {
        if (examples.size()==0)
            return;
        double mean=ame::range::mean(examples);
        double st_dev=ame::range::standard_deviation(examples, mean);

        m_distribution = boost::math::normal_distribution<>(mean, (std::max)(st_dev, m_min_st_dev));
    }
    const boost::math::normal_distribution<> distribution() const
    {   return m_distribution; }
    bool operator == (const normal_model_state &rhs) const
    {
        return
                m_min_st_dev == rhs.m_min_st_dev
            &&  mean(m_distribution) == mean(rhs.m_distribution)
            && standard_deviation(m_distribution) == standard_deviation(rhs.m_distribution);
    }
private:
    double m_min_st_dev;
    boost::math::normal_distribution<> m_distribution;
    
    friend class boost::serialization::access;
    template<class Archive>
    void serialize(Archive & ar, const unsigned int version)
    {
        ar & m_min_st_dev;
        ar & m_distribution;
    }
};

}}