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Added variance & rowwise variance (for matricies) and vector variance #3249
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/* | ||
* Copyright (c) The Shogun Machine Learning Toolbox | ||
* Written (w) 2016 Chris Goldsworthy | ||
* All rights reserved. | ||
* | ||
* Redistribution and use in source and binary forms, with or without | ||
* modification, are permitted provided that the following conditions are met: | ||
* | ||
* 1. Redistributions of source code must retain the above copyright notice, this | ||
* list of conditions and the following disclaimer. | ||
* 2. Redistributions in binary form must reproduce the above copyright notice, | ||
* this list of conditions and the following disclaimer in the documentation | ||
* and/or other materials provided with the distribution. | ||
* | ||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND | ||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED | ||
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE | ||
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR | ||
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES | ||
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | ||
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND | ||
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | ||
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | ||
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
* | ||
* The views and conclusions contained in the software and documentation are those | ||
* of the authors and should not be interpreted as representing official policies, | ||
* either expressed or implied, of the Shogun Development Team. | ||
*/ | ||
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#ifndef SRC_SHOGUN_MATHEMATICS_LINALG_INTERNAL_IMPLEMENTATION_VARIANCE_H_ | ||
#define SRC_SHOGUN_MATHEMATICS_LINALG_INTERNAL_IMPLEMENTATION_VARIANCE_H_ | ||
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#include <shogun/lib/config.h> | ||
#include <shogun/lib/SGVector.h> | ||
#include <shogun/lib/SGMatrix.h> | ||
#include <shogun/mathematics/linalg/internal/implementation/MeanEigen3.h> | ||
#include <shogun/mathematics/eigen3.h> | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. we never want eigen3 includes in header files, messes up things quite a bit |
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#include <iostream> | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. also, no stdlib includes in header files. There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. What do you mean by that? What will be set for all of Shogun? Just curious. There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. the std namespace will be active everywhere you include this file (which is for example happening in the class list, so everywhere) |
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using namespace std; | ||
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namespace shogun | ||
{ | ||
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namespace linalg | ||
{ | ||
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namespace implementation | ||
{ | ||
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/** | ||
* @brief Generic class variance which provides a static compute method. This class | ||
* can work with generic matricies. | ||
*/ | ||
template <enum Backend, class Matrix> | ||
struct variance | ||
{ | ||
/** Scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Calculates unbiased empirical variance estimate given the entries from a matrix. Given a matrix | ||
* \f$x\f$ with entries \f$\{x_{11}, ..., x_{mn}\}\f$, this is | ||
* \f$\frac{1}{m*n-1}\sum_{i=1}^m\sum_{j=1}^n (x_{ij}-\bar{x})^2\f$ where | ||
* \f$\bar x=\frac{1}{mn}\sum_{i=1}^m\sum_{j=1}^n x_{ij}\f$ | ||
* | ||
* @param x matrix of values | ||
* @return variance of given values | ||
*/ | ||
static T compute(Matrix x); | ||
}; | ||
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/** | ||
* @brief Specialization of element-wise variance which works with SGMatrix | ||
* and uses Eigen3 as backend for computing variance. | ||
*/ | ||
template <class Matrix> | ||
struct variance<Backend::EIGEN3, Matrix> | ||
{ | ||
/** Scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Eigen matrix type */ | ||
typedef Eigen::Matrix<T,Eigen::Dynamic, Eigen::Dynamic> MatrixXt; | ||
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/** Calculates unbiased empirical variance estimate given the entries from a matrix. Given a matrix | ||
* \f$x\f$ with entries \f$\{x_{11}, ..., x_{mn}\}\f$, this is | ||
* \f$\frac{1}{m*n-1}\sum_{i=1}^m\sum_{j=1}^n (x_{ij}-\bar{x})^2\f$ where | ||
* \f$\bar x=\frac{1}{mn}\sum_{i=1}^m\sum_{j=1}^n x_{ij}\f$ | ||
* | ||
* @param x matrix of values | ||
* @return variance of given values | ||
*/ | ||
static T compute(SGMatrix<T> x) | ||
{ | ||
REQUIRE(x.num_rows > 0, "Please ensure that m has more than 0 rows.\n") | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Should always state what was given by the user, see our wiki on error messages |
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REQUIRE(x.num_cols > 0, "Please ensure that m has more than %d columns.\n") | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. this might segfault as there is nothing passed to %d |
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Eigen::Map<MatrixXt> eigX = x; | ||
MatrixXt eigSquaredResult(x.num_rows, x.num_cols); | ||
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T meanVal = mean<Backend::EIGEN3, SGMatrix<T>>::compute(x); | ||
eigSquaredResult.fill(meanVal); | ||
eigSquaredResult = (eigX - eigSquaredResult).array().square(); | ||
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return ((T) 1 / (x.num_rows*x.num_cols - 1)) * eigSquaredResult.sum(); | ||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I think there should be a flag degrees of freedom that can be used to change normalisation to 1/n, 1/(n-1) , etc |
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} | ||
}; | ||
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/** | ||
* @brief Generic class variance which provides a static compute method. This class | ||
* can work with generic vectors. | ||
*/ | ||
template <enum Backend, class Vector> | ||
struct vector_variance | ||
{ | ||
/** Scalar type */ | ||
typedef typename Vector::Scalar T; | ||
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/** Calculates unbiased empirical variance estimate of given values. Given | ||
* \f$\{x_1, ..., x_m\}\f$, this is | ||
* \f$\frac{1}{m-1}\sum_{i=1}^m (x_i-\bar{x})^2\f$ where | ||
* \f$\bar x=\frac{1}{m}\sum_{i=1}^m x_i\f$ | ||
* | ||
* @param x vector of values | ||
* @return variance of given values | ||
*/ | ||
static T compute(Vector x); | ||
}; | ||
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/** | ||
* @brief Specialization of generic variance which works with SGVector | ||
* and uses Eigen3 as backend for computing variance. | ||
*/ | ||
template <class Vector> | ||
struct vector_variance<Backend::EIGEN3, Vector> | ||
{ | ||
/** Scalar type */ | ||
typedef typename Vector::Scalar T; | ||
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/** Eigen vector type */ | ||
typedef Eigen::Matrix<T,Eigen::Dynamic,1> VectorXt; | ||
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/** Calculates unbiased empirical variance estimate of given values. Given | ||
* \f$\{x_1, ..., x_m\}\f$, this is | ||
* \f$\frac{1}{m-1}\sum_{i=1}^m (x_i-\bar{x})^2\f$ where | ||
* \f$\bar x=\frac{1}{m}\sum_{i=1}^m x_i\f$ | ||
* | ||
* @param x vector of values | ||
* @return variance of given values | ||
*/ | ||
static T compute(SGVector<T> x) | ||
{ | ||
REQUIRE(x.vlen>1, "Please ensure that vector length is greater than 1.\n") | ||
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Eigen::Map<VectorXt> eigX = x; | ||
VectorXt eigSquaredResult(x.vlen); | ||
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T meanVal = mean<Backend::EIGEN3, SGVector<T>>::compute(x); | ||
eigSquaredResult.fill(meanVal); | ||
eigSquaredResult = (eigX - eigSquaredResult).array().square(); | ||
return ((T) 1 / (x.vlen - 1)) * eigSquaredResult.sum(); | ||
} | ||
}; | ||
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/** | ||
* @Brief A generic class that computes the variance of a matrix column-wise. | ||
*/ | ||
template<enum Backend, typename Matrix> | ||
struct colwise_variance | ||
{ | ||
/** Generic scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Vector return type */ | ||
typedef SGVector<T> ReturnType; | ||
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/** Calculates unbiased empirical variance estimate of given values for each column of | ||
* an input matrix. Given a single column \f$k\f$ with entries \f$\{x_{1k}, ..., x_{mk}\}\f$ | ||
* from matrix \f$x\f$, this is \f$\frac{1}{m-1}\sum_{i=1}^m (k_i-\bar{k})^2\f$ where | ||
* \f$\bar k=\frac{1}{m}\sum_{i=1}^m k_i\f$. This is computed for each column \f$k\f$. | ||
* | ||
* Computes the variance for each column of a matrix | ||
* | ||
* @param x matrix of values | ||
* @return the column-wise variance of a matrix | ||
*/ | ||
static ReturnType compute(Matrix x); | ||
}; | ||
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/** | ||
* @Brief A specialization of colwise_variance that uses SGMatrix and SGVector as its types | ||
* and uses Eigen3 as its backend component | ||
*/ | ||
template<typename Matrix> | ||
struct colwise_variance<Backend::EIGEN3, Matrix> | ||
{ | ||
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/** Generic scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Vector return type */ | ||
typedef SGVector<T> ReturnType; | ||
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/** Eigen vector type */ | ||
typedef Eigen::Matrix<T,Eigen::Dynamic,1> VectorXt; | ||
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/** Calculates unbiased empirical variance estimate of given values for each column of | ||
* an input matrix. Given a single column \f$k\f$ with entries \f$\{x_{1k}, ..., x_{mk}\}\f$ | ||
* from matrix \f$x\f$, this is \f$\frac{1}{m-1}\sum_{i=1}^m (k_i-\bar{k})^2\f$ where | ||
* \f$\bar k=\frac{1}{m}\sum_{i=1}^m k_i\f$. This is computed for each column \f$k\f$. | ||
* | ||
* Computes the variance for each column of a matrix | ||
* | ||
* @param m matrix of values | ||
* @return the column-wise variance of a matrix | ||
*/ | ||
static ReturnType compute(SGMatrix<T> m) | ||
{ | ||
REQUIRE(m.num_rows > 0, "Please ensure that m has more than 0 rows.\n") | ||
REQUIRE(m.num_cols > 0, "Please ensure that m has more than %d columns.\n") | ||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Impl? There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I had mentioned this above, but there currently is no implementation for a columnwise mean, so I'm leaving this unimplemented for now. |
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} | ||
}; | ||
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/** | ||
* @Brief A generic class that computes the variance of a matrix row-wise. | ||
*/ | ||
template<enum Backend, typename Matrix> | ||
struct rowwise_variance | ||
{ | ||
/** Generic scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Vector return type */ | ||
typedef SGVector<T> ReturnType; | ||
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/** Calculates unbiased empirical variance estimate of the given values from each row of | ||
* an input matrix. Given a single row \f$k\f$ with entries \f$\{x_{k1}, ..., x_{kn}\}\f$ | ||
* from matrix \f$x\f$, this is \f$\frac{1}{n-1}\sum_{i=1}^n (k_i-\bar{k})^2\f$ where | ||
* \f$\bar k=\frac{1}{n}\sum_{i=1}^n k_i\f$. This is computed for each row \f$n\f$. | ||
* | ||
* Computes the variance for each row of a matrix | ||
* | ||
* @param x matrix of values | ||
* @return the row-wise variance of a matrix | ||
*/ | ||
static ReturnType compute(Matrix x); | ||
}; | ||
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/** | ||
* @Brief A specialization of colwise_variance that uses SGMatrix and SGVector as its types | ||
* and uses Eigen3 as its backend component | ||
*/ | ||
template<typename Matrix> | ||
struct rowwise_variance<Backend::EIGEN3, Matrix> | ||
{ | ||
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/** Generic scalar type */ | ||
typedef typename Matrix::Scalar T; | ||
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/** Vector return type */ | ||
typedef SGVector<T> ReturnType; | ||
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/** Eigen vector type */ | ||
typedef Eigen::Matrix<T,Eigen::Dynamic,1> VectorXt; | ||
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/** Eigen matrix type */ | ||
typedef Eigen::Matrix<T,Eigen::Dynamic, Eigen::Dynamic> MatrixXt; | ||
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/** Calculates unbiased empirical variance estimate of the given values from each row of | ||
* an input matrix. Given a single row \f$k\f$ with entries \f$\{x_{k1}, ..., x_{kn}\}\f$ | ||
* from matrix \f$x\f$, this is \f$\frac{1}{n-1}\sum_{i=1}^n (k_i-\bar{k})^2\f$ where | ||
* \f$\bar k=\frac{1}{n}\sum_{i=1}^n k_i\f$. This is computed for each row \f$n\f$. | ||
* | ||
* Computes the variance for each row of a matrix | ||
* | ||
* @param m matrix of values | ||
* @return the column-wise variance of a matrix | ||
*/ | ||
static ReturnType compute(SGMatrix<T> x) | ||
{ | ||
REQUIRE(x.num_rows > 0, "Please ensure that x has more than 0 rows.\n") | ||
REQUIRE(x.num_cols > 0, "Please ensure that x has more than 0 columns.\n") | ||
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SGVector<T> tempVec; //used to store multiple results | ||
Eigen::Map<MatrixXt> eigX = x; | ||
MatrixXt eigSquaredResult(x.num_rows, x.num_cols); | ||
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tempVec = rowwise_mean<Backend::EIGEN3, SGVector<T>>::compute(x, false); | ||
Eigen::Map<VectorXt> eigTempVec = tempVec; | ||
for(int i = 0; i < x.num_cols; ++i) | ||
{ | ||
eigSquaredResult.col(i) = eigTempVec; | ||
} | ||
eigSquaredResult = (eigX - eigSquaredResult).array().square(); | ||
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eigTempVec = eigSquaredResult.rowwise().sum(); | ||
eigTempVec *= ((T) 1 / (x.num_cols -1)); | ||
return tempVec; | ||
} | ||
}; | ||
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} | ||
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} | ||
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} | ||
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#endif /* SRC_SHOGUN_MATHEMATICS_LINALG_INTERNAL_IMPLEMENTATION_VARIANCE_H_ */ |
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ehm.....this might be a bit long, no? :)