/usr/include/dlib/statistics/statistics_abstract.h is in libdlib-dev 18.18-1.
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// License: Boost Software License See LICENSE.txt for the full license.
#undef DLIB_STATISTICs_ABSTRACT_
#ifdef DLIB_STATISTICs_ABSTRACT_
#include <limits>
#include <cmath>
#include "../matrix/matrix_abstract.h"
#include "../svm/sparse_vector_abstract.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
template <
typename T,
typename alloc
>
double mean_sign_agreement (
const std::vector<T,alloc>& a,
const std::vector<T,alloc>& b
);
/*!
requires
- a.size() == b.size()
ensures
- returns the number of times a[i] has the same sign as b[i] divided by
a.size(). So we return the probability that elements of a and b have
the same sign.
!*/
// ----------------------------------------------------------------------------------------
template <
typename T,
typename alloc
>
double correlation (
const std::vector<T,alloc>& a,
const std::vector<T,alloc>& b
);
/*!
requires
- a.size() == b.size()
- a.size() > 1
ensures
- returns the correlation coefficient between all the elements of a and b.
(i.e. how correlated is a(i) with b(i))
!*/
// ----------------------------------------------------------------------------------------
template <
typename T,
typename alloc
>
double covariance (
const std::vector<T,alloc>& a,
const std::vector<T,alloc>& b
);
/*!
requires
- a.size() == b.size()
- a.size() > 1
ensures
- returns the covariance between all the elements of a and b.
(i.e. how does a(i) vary with b(i))
!*/
// ----------------------------------------------------------------------------------------
template <
typename T,
typename alloc
>
double r_squared (
const std::vector<T,alloc>& a,
const std::vector<T,alloc>& b
);
/*!
requires
- a.size() == b.size()
- a.size() > 1
ensures
- returns the R^2 coefficient of determination between all the elements of a and b.
This value is just the square of correlation(a,b).
!*/
// ----------------------------------------------------------------------------------------
template <
typename T,
typename alloc
>
double mean_squared_error (
const std::vector<T,alloc>& a,
const std::vector<T,alloc>& b
);
/*!
requires
- a.size() == b.size()
ensures
- returns the mean squared error between all the elements of a and b.
(i.e. mean(squared(mat(a)-mat(b))))
!*/
// ----------------------------------------------------------------------------------------
template <
typename T
>
class running_stats
{
/*!
REQUIREMENTS ON T
- T must be a float, double, or long double type
INITIAL VALUE
- mean() == 0
- current_n() == 0
WHAT THIS OBJECT REPRESENTS
This object represents something that can compute the running mean,
variance, skewness, and excess kurtosis of a stream of real numbers.
!*/
public:
running_stats(
);
/*!
ensures
- this object is properly initialized
!*/
void clear(
);
/*!
ensures
- this object has its initial value
- clears all memory of any previous data points
!*/
T current_n (
) const;
/*!
ensures
- returns the number of points given to this object so far.
!*/
void add (
const T& val
);
/*!
ensures
- updates the mean, variance, skewness, and kurtosis stored in this object
so that the new value is factored into them.
- #mean() == mean()*current_n()/(current_n()+1) + val/(current_n()+1).
(i.e. the updated mean value that takes the new value into account)
- #variance() == the updated variance that takes this new value into account.
- #skewness() == the updated skewness that takes this new value into account.
- #ex_kurtosis() == the updated kurtosis that takes this new value into account.
- #current_n() == current_n() + 1
!*/
T mean (
) const;
/*!
ensures
- returns the mean of all the values presented to this object
so far.
!*/
T variance (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample variance of all the values presented to this
object so far.
!*/
T stddev (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sampled standard deviation of all the values
presented to this object so far.
!*/
T skewness (
) const;
/*!
requires
- current_n() > 2
ensures
- returns the unbiased sample skewness of all the values presented
to this object so far.
!*/
T ex_kurtosis(
) const;
/*!
requires
- current_n() > 3
ensures
- returns the unbiased sample kurtosis of all the values presented
to this object so far.
!*/
T max (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the largest value presented to this object so far.
!*/
T min (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the smallest value presented to this object so far.
!*/
T scale (
const T& val
) const;
/*!
requires
- current_n() > 1
ensures
- return (val-mean())/stddev();
!*/
running_stats operator+ (
const running_stats& rhs
) const;
/*!
ensures
- returns a new running_stats object that represents the combination of all
the values given to *this and rhs. That is, this function returns a
running_stats object, R, that is equivalent to what you would obtain if
all calls to this->add() and rhs.add() had instead been done to R.
!*/
};
template <typename T>
void serialize (
const running_stats<T>& item,
std::ostream& out
);
/*!
provides serialization support
!*/
template <typename T>
void deserialize (
running_stats<T>& item,
std::istream& in
);
/*!
provides serialization support
!*/
// ----------------------------------------------------------------------------------------
template <
typename T
>
class running_scalar_covariance
{
/*!
REQUIREMENTS ON T
- T must be a float, double, or long double type
INITIAL VALUE
- mean_x() == 0
- mean_y() == 0
- current_n() == 0
WHAT THIS OBJECT REPRESENTS
This object represents something that can compute the running covariance
of a stream of real number pairs.
!*/
public:
running_scalar_covariance(
);
/*!
ensures
- this object is properly initialized
!*/
void clear(
);
/*!
ensures
- this object has its initial value
- clears all memory of any previous data points
!*/
void add (
const T& x,
const T& y
);
/*!
ensures
- updates the statistics stored in this object so that
the new pair (x,y) is factored into them.
- #current_n() == current_n() + 1
!*/
T current_n (
) const;
/*!
ensures
- returns the number of points given to this object so far.
!*/
T mean_x (
) const;
/*!
ensures
- returns the mean value of all x samples presented to this object
via add().
!*/
T mean_y (
) const;
/*!
ensures
- returns the mean value of all y samples presented to this object
via add().
!*/
T covariance (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the covariance between all the x and y samples presented
to this object via add()
!*/
T correlation (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the correlation coefficient between all the x and y samples
presented to this object via add()
!*/
T variance_x (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample variance value of all x samples presented
to this object via add().
!*/
T variance_y (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample variance value of all y samples presented
to this object via add().
!*/
T stddev_x (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample standard deviation of all x samples
presented to this object via add().
!*/
T stddev_y (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample standard deviation of all y samples
presented to this object via add().
!*/
running_scalar_covariance operator+ (
const running_covariance& rhs
) const;
/*!
ensures
- returns a new running_scalar_covariance object that represents the
combination of all the values given to *this and rhs. That is, this
function returns a running_scalar_covariance object, R, that is
equivalent to what you would obtain if all calls to this->add() and
rhs.add() had instead been done to R.
!*/
};
// ----------------------------------------------------------------------------------------
template <
typename matrix_type
>
class running_covariance
{
/*!
REQUIREMENTS ON matrix_type
Must be some type of dlib::matrix.
INITIAL VALUE
- in_vector_size() == 0
- current_n() == 0
WHAT THIS OBJECT REPRESENTS
This object is a simple tool for computing the mean and
covariance of a sequence of vectors.
!*/
public:
typedef typename matrix_type::mem_manager_type mem_manager_type;
typedef typename matrix_type::type scalar_type;
typedef typename matrix_type::layout_type layout_type;
typedef matrix<scalar_type,0,0,mem_manager_type,layout_type> general_matrix;
typedef matrix<scalar_type,0,1,mem_manager_type,layout_type> column_matrix;
running_covariance(
);
/*!
ensures
- this object is properly initialized
!*/
void clear(
);
/*!
ensures
- this object has its initial value
- clears all memory of any previous data points
!*/
long current_n (
) const;
/*!
ensures
- returns the number of samples that have been presented to this object
!*/
long in_vector_size (
) const;
/*!
ensures
- if (this object has been presented with any input vectors or
set_dimension() has been called) then
- returns the dimension of the column vectors used with this object
- else
- returns 0
!*/
void set_dimension (
long size
);
/*!
requires
- size > 0
ensures
- #in_vector_size() == size
- #current_n() == 0
!*/
template <typename T>
void add (
const T& val
);
/*!
requires
- val must represent a column vector. It can either be a dlib::matrix
object or some kind of unsorted sparse vector type. See the top of
dlib/svm/sparse_vector_abstract.h for a definition of unsorted sparse vector.
- val must have a number of dimensions which is compatible with the current
setting of in_vector_size(). In particular, this means that the
following must hold:
- if (val is a dlib::matrix) then
- in_vector_size() == 0 || val.size() == val_vector_size()
- else
- max_index_plus_one(val) <= in_vector_size()
- in_vector_size() > 0
(i.e. you must call set_dimension() prior to calling add() if
you want to use sparse vectors.)
ensures
- updates the mean and covariance stored in this object so that
the new value is factored into them.
- if (val is a dlib::matrix) then
- #in_vector_size() == val.size()
!*/
const column_matrix mean (
) const;
/*!
requires
- in_vector_size() != 0
ensures
- returns the mean of all the vectors presented to this object
so far.
!*/
const general_matrix covariance (
) const;
/*!
requires
- in_vector_size() != 0
- current_n() > 1
ensures
- returns the unbiased sample covariance matrix for all the vectors
presented to this object so far.
!*/
const running_covariance operator+ (
const running_covariance& item
) const;
/*!
requires
- in_vector_size() == 0 || item.in_vector_size() == 0 || in_vector_size() == item.in_vector_size()
(i.e. the in_vector_size() of *this and item must match or one must be zero)
ensures
- returns a new running_covariance object that represents the combination of all
the vectors given to *this and item. That is, this function returns a
running_covariance object, R, that is equivalent to what you would obtain if all
calls to this->add() and item.add() had instead been done to R.
!*/
};
// ----------------------------------------------------------------------------------------
template <
typename matrix_type
>
class running_cross_covariance
{
/*!
REQUIREMENTS ON matrix_type
Must be some type of dlib::matrix.
INITIAL VALUE
- x_vector_size() == 0
- y_vector_size() == 0
- current_n() == 0
WHAT THIS OBJECT REPRESENTS
This object is a simple tool for computing the mean and cross-covariance
matrices of a sequence of pairs of vectors.
!*/
public:
typedef typename matrix_type::mem_manager_type mem_manager_type;
typedef typename matrix_type::type scalar_type;
typedef typename matrix_type::layout_type layout_type;
typedef matrix<scalar_type,0,0,mem_manager_type,layout_type> general_matrix;
typedef matrix<scalar_type,0,1,mem_manager_type,layout_type> column_matrix;
running_cross_covariance(
);
/*!
ensures
- this object is properly initialized
!*/
void clear(
);
/*!
ensures
- This object has its initial value.
- Clears all memory of any previous data points.
!*/
long x_vector_size (
) const;
/*!
ensures
- if (this object has been presented with any input vectors or
set_dimensions() has been called) then
- returns the dimension of the x vectors given to this object via add().
- else
- returns 0
!*/
long y_vector_size (
) const;
/*!
ensures
- if (this object has been presented with any input vectors or
set_dimensions() has been called) then
- returns the dimension of the y vectors given to this object via add().
- else
- returns 0
!*/
void set_dimensions (
long x_size,
long y_size
);
/*!
requires
- x_size > 0
- y_size > 0
ensures
- #x_vector_size() == x_size
- #y_vector_size() == y_size
- #current_n() == 0
!*/
long current_n (
) const;
/*!
ensures
- returns the number of samples that have been presented to this object.
!*/
template <typename T, typename U>
void add (
const T& x,
const U& y
);
/*!
requires
- x and y must represent column vectors. They can either be dlib::matrix
objects or some kind of unsorted sparse vector type. See the top of
dlib/svm/sparse_vector_abstract.h for a definition of unsorted sparse vector.
- x and y must have a number of dimensions which is compatible with the
current setting of x_vector_size() and y_vector_size(). In particular,
this means that the following must hold:
- if (x or y is a sparse vector type) then
- x_vector_size() > 0 && y_vector_size() > 0
(i.e. you must call set_dimensions() prior to calling add() if
you want to use sparse vectors.)
- if (x is a dlib::matrix) then
- x_vector_size() == 0 || x.size() == x_vector_size()
- else
- max_index_plus_one(x) <= x_vector_size()
- if (y is a dlib::matrix) then
- y_vector_size() == 0 || y.size() == y_vector_size()
- else
- max_index_plus_one(y) <= y_vector_size()
ensures
- updates the mean and cross-covariance matrices stored in this object so
that the new (x,y) vector pair is factored into them.
- if (x is a dlib::matrix) then
- #x_vector_size() == x.size()
- if (y is a dlib::matrix) then
- #y_vector_size() == y.size()
!*/
const column_matrix mean_x (
) const;
/*!
requires
- current_n() != 0
ensures
- returns the mean of all the x vectors presented to this object so far.
- The returned vector will have x_vector_size() dimensions.
!*/
const column_matrix mean_y (
) const;
/*!
requires
- current_n() != 0
ensures
- returns the mean of all the y vectors presented to this object so far.
- The returned vector will have y_vector_size() dimensions.
!*/
const general_matrix covariance_xy (
) const;
/*!
requires
- current_n() > 1
ensures
- returns the unbiased sample cross-covariance matrix for all the vector
pairs presented to this object so far. In particular, returns a matrix
M such that:
- M.nr() == x_vector_size()
- M.nc() == y_vector_size()
- M == the cross-covariance matrix of the data given to add().
!*/
const running_cross_covariance operator+ (
const running_cross_covariance& item
) const;
/*!
requires
- x_vector_size() == 0 || item.x_vector_size() == 0 || x_vector_size() == item.x_vector_size()
(i.e. the x_vector_size() of *this and item must match or one must be zero)
- y_vector_size() == 0 || item.y_vector_size() == 0 || y_vector_size() == item.y_vector_size()
(i.e. the y_vector_size() of *this and item must match or one must be zero)
ensures
- returns a new running_cross_covariance object that represents the
combination of all the vectors given to *this and item. That is, this
function returns a running_cross_covariance object, R, that is equivalent
to what you would obtain if all calls to this->add() and item.add() had
instead been done to R.
!*/
};
// ----------------------------------------------------------------------------------------
template <
typename matrix_type
>
class vector_normalizer
{
/*!
REQUIREMENTS ON matrix_type
- must be a dlib::matrix object capable of representing column
vectors
INITIAL VALUE
- in_vector_size() == 0
- out_vector_size() == 0
- means().size() == 0
- std_devs().size() == 0
WHAT THIS OBJECT REPRESENTS
This object represents something that can learn to normalize a set
of column vectors. In particular, normalized column vectors should
have zero mean and a variance of one.
Also, if desired, this object can use principal component
analysis for the purposes of reducing the number of elements in a
vector.
THREAD SAFETY
Note that this object contains a cached matrix object it uses
to store intermediate results for normalization. This avoids
needing to reallocate it every time this object performs normalization
but also makes it non-thread safe. So make sure you don't share
instances of this object between threads.
!*/
public:
typedef typename matrix_type::mem_manager_type mem_manager_type;
typedef typename matrix_type::type scalar_type;
typedef matrix_type result_type;
template <typename vector_type>
void train (
const vector_type& samples
);
/*!
requires
- samples.size() > 0
- samples == a column matrix or something convertible to a column
matrix via mat(). Also, x should contain
matrix_type objects that represent nonempty column vectors.
- samples does not contain any infinite or NaN values
ensures
- #in_vector_size() == samples(0).nr()
- #out_vector_size() == samples(0).nr()
- This object has learned how to normalize vectors that look like
vectors in the given set of samples.
- #means() == mean(samples)
- #std_devs() == reciprocal(sqrt(variance(samples)));
!*/
long in_vector_size (
) const;
/*!
ensures
- returns the number of rows that input vectors are
required to contain if they are to be normalized by
this object.
!*/
long out_vector_size (
) const;
/*!
ensures
- returns the number of rows in the normalized vectors
that come out of this object.
!*/
const matrix_type& means (
) const;
/*!
ensures
- returns a matrix M such that:
- M.nc() == 1
- M.nr() == in_vector_size()
- M(i) == the mean of the ith input feature shown to train()
!*/
const matrix_type& std_devs (
) const;
/*!
ensures
- returns a matrix SD such that:
- SD.nc() == 1
- SD.nr() == in_vector_size()
- SD(i) == the reciprocal of the standard deviation of the ith
input feature shown to train()
!*/
const result_type& operator() (
const matrix_type& x
) const;
/*!
requires
- x.nr() == in_vector_size()
- x.nc() == 1
ensures
- returns a normalized version of x, call it Z, that has the
following properties:
- Z.nr() == out_vector_size()
- Z.nc() == 1
- the mean of each element of Z is 0
- the variance of each element of Z is 1
- Z == pointwise_multiply(x-means(), std_devs());
!*/
void swap (
vector_normalizer& item
);
/*!
ensures
- swaps *this and item
!*/
};
template <
typename matrix_type
>
inline void swap (
vector_normalizer<matrix_type>& a,
vector_normalizer<matrix_type>& b
) { a.swap(b); }
/*!
provides a global swap function
!*/
template <
typename matrix_type,
>
void deserialize (
vector_normalizer<matrix_type>& item,
std::istream& in
);
/*!
provides deserialization support
!*/
template <
typename matrix_type,
>
void serialize (
const vector_normalizer<matrix_type>& item,
std::ostream& out
);
/*!
provides serialization support
!*/
// ----------------------------------------------------------------------------------------
template <
typename matrix_type
>
class vector_normalizer_pca
{
/*!
REQUIREMENTS ON matrix_type
- must be a dlib::matrix object capable of representing column
vectors
INITIAL VALUE
- in_vector_size() == 0
- out_vector_size() == 0
- means().size() == 0
- std_devs().size() == 0
- pca_matrix().size() == 0
WHAT THIS OBJECT REPRESENTS
This object represents something that can learn to normalize a set
of column vectors. In particular, normalized column vectors should
have zero mean and a variance of one.
Also, this object uses principal component analysis for the purposes
of reducing the number of elements in a vector.
THREAD SAFETY
Note that this object contains a cached matrix object it uses
to store intermediate results for normalization. This avoids
needing to reallocate it every time this object performs normalization
but also makes it non-thread safe. So make sure you don't share
instances of this object between threads.
!*/
public:
typedef typename matrix_type::mem_manager_type mem_manager_type;
typedef typename matrix_type::type scalar_type;
typedef matrix<scalar_type,0,1,mem_manager_type> result_type;
template <typename vector_type>
void train (
const vector_type& samples,
const double eps = 0.99
);
/*!
requires
- 0 < eps <= 1
- samples.size() > 0
- samples == a column matrix or something convertible to a column
matrix via mat(). Also, x should contain
matrix_type objects that represent nonempty column vectors.
- samples does not contain any infinite or NaN values
ensures
- This object has learned how to normalize vectors that look like
vectors in the given set of samples.
- Principal component analysis is performed to find a transform
that might reduce the number of output features.
- #in_vector_size() == samples(0).nr()
- 0 < #out_vector_size() <= samples(0).nr()
- eps is a number that controls how "lossy" the pca transform will be.
Large values of eps result in #out_vector_size() being larger and
smaller values of eps result in #out_vector_size() being smaller.
- #means() == mean(samples)
- #std_devs() == reciprocal(sqrt(variance(samples)));
- #pca_matrix() == the PCA transform matrix that is out_vector_size()
rows by in_vector_size() columns.
!*/
long in_vector_size (
) const;
/*!
ensures
- returns the number of rows that input vectors are
required to contain if they are to be normalized by
this object.
!*/
long out_vector_size (
) const;
/*!
ensures
- returns the number of rows in the normalized vectors
that come out of this object.
!*/
const matrix<scalar_type,0,1,mem_manager_type>& means (
) const;
/*!
ensures
- returns a matrix M such that:
- M.nc() == 1
- M.nr() == in_vector_size()
- M(i) == the mean of the ith input feature shown to train()
!*/
const matrix<scalar_type,0,1,mem_manager_type>& std_devs (
) const;
/*!
ensures
- returns a matrix SD such that:
- SD.nc() == 1
- SD.nr() == in_vector_size()
- SD(i) == the reciprocal of the standard deviation of the ith
input feature shown to train()
!*/
const matrix<scalar_type,0,0,mem_manager_type>& pca_matrix (
) const;
/*!
ensures
- returns a matrix PCA such that:
- PCA.nr() == out_vector_size()
- PCA.nc() == in_vector_size()
- PCA == the principal component analysis transformation
matrix
!*/
const result_type& operator() (
const matrix_type& x
) const;
/*!
requires
- x.nr() == in_vector_size()
- x.nc() == 1
ensures
- returns a normalized version of x, call it Z, that has the
following properties:
- Z.nr() == out_vector_size()
- Z.nc() == 1
- the mean of each element of Z is 0
- the variance of each element of Z is 1
- Z == pca_matrix()*pointwise_multiply(x-means(), std_devs());
!*/
void swap (
vector_normalizer_pca& item
);
/*!
ensures
- swaps *this and item
!*/
};
template <
typename matrix_type
>
inline void swap (
vector_normalizer_pca<matrix_type>& a,
vector_normalizer_pca<matrix_type>& b
) { a.swap(b); }
/*!
provides a global swap function
!*/
template <
typename matrix_type,
>
void deserialize (
vector_normalizer_pca<matrix_type>& item,
std::istream& in
);
/*!
provides deserialization support
!*/
template <
typename matrix_type,
>
void serialize (
const vector_normalizer_pca<matrix_type>& item,
std::ostream& out
);
/*!
provides serialization support
!*/
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_STATISTICs_ABSTRACT_
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