1 | #ifndef _theplu_statistics_regression_linear_weighted_ |
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2 | #define _theplu_statistics_regression_linear_weighted_ |
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3 | |
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4 | // $Id: LinearWeighted.h 675 2006-10-10 12:08:45Z jari $ |
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5 | |
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6 | /* |
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7 | Copyright (C) The authors contributing to this file. |
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8 | |
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9 | This file is part of the yat library, http://lev.thep.lu.se/trac/yat |
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10 | |
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11 | The yat library is free software; you can redistribute it and/or |
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12 | modify it under the terms of the GNU General Public License as |
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13 | published by the Free Software Foundation; either version 2 of the |
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14 | License, or (at your option) any later version. |
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15 | |
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16 | The yat library is distributed in the hope that it will be useful, |
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17 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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19 | General Public License for more details. |
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20 | |
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21 | You should have received a copy of the GNU General Public License |
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22 | along with this program; if not, write to the Free Software |
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23 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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24 | 02111-1307, USA. |
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25 | */ |
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26 | |
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27 | #include "yat/statistics/OneDimensionalWeighted.h" |
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28 | |
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29 | #include <cmath> |
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30 | |
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31 | namespace theplu { |
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32 | namespace utility { |
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33 | class vector; |
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34 | } |
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35 | namespace statistics { |
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36 | namespace regression { |
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37 | |
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38 | /// |
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39 | /// @brief linear regression. |
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40 | /// |
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41 | /// @todo document |
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42 | /// |
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43 | class LinearWeighted : public OneDimensionalWeighted |
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44 | { |
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45 | |
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46 | public: |
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47 | /// |
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48 | /// Default Constructor. |
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49 | /// |
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50 | inline LinearWeighted(void) |
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51 | : OneDimensionalWeighted(), alpha_(0), alpha_var_(0), beta_(0), |
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52 | beta_var_(0), |
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53 | m_x_(0){} |
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54 | |
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55 | /// |
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56 | /// Destructor |
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57 | /// |
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58 | inline virtual ~LinearWeighted(void) {}; |
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59 | |
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60 | /// |
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61 | /// @return the parameter \f$ \alpha \f$ |
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62 | /// |
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63 | inline double alpha(void) const { return alpha_; } |
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64 | |
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65 | /// |
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66 | /// @return standard deviation of parameter \f$ \alpha \f$ |
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67 | /// |
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68 | inline double alpha_err(void) const { return sqrt(alpha_var_); } |
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69 | |
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70 | /// |
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71 | /// @return the parameter \f$ \beta \f$ |
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72 | /// |
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73 | inline double beta(void) const { return beta_; } |
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74 | |
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75 | /// |
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76 | /// @return standard deviation of parameter \f$ \beta \f$ |
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77 | /// |
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78 | inline double beta_err(void) const { return sqrt(beta_var_); } |
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79 | |
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80 | /** |
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81 | This function computes the best-fit linear regression |
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82 | coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y = |
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83 | \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by |
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84 | minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$, |
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85 | where \f$ m_x \f$ is the weighted average. By construction \f$ |
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86 | \alpha \f$ and \f$ \beta \f$ are independent. |
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87 | **/ |
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88 | void fit(const utility::vector& x, const utility::vector& y, |
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89 | const utility::vector& w); |
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90 | |
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91 | /// |
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92 | /// Function predicting value using the linear model: |
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93 | /// \f$ y =\alpha + \beta (x - m) \f$ |
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94 | /// |
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95 | double predict(const double x) const { return alpha_ + beta_ * (x-m_x_); } |
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96 | |
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97 | /// |
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98 | /// estimated deviation from predicted value for a new data point |
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99 | /// in @a x with weight @a w |
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100 | /// |
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101 | inline double prediction_error(const double x, const double w=1) const |
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102 | { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_)+s2_/w); } |
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103 | |
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104 | /** |
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105 | estimated error \f$ y_{err} = \sqrt{ Var(\alpha) + |
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106 | Var(\beta)*(x-m)} \f$. |
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107 | **/ |
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108 | inline double standard_error(const double x) const |
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109 | { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_) ); } |
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110 | |
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111 | /// |
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112 | /// Function returning the coefficient of determination, |
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113 | /// i.e. fraction of variance explained by the linear model. |
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114 | /// |
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115 | inline double r2(void) const { return r2_; } |
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116 | |
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117 | private: |
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118 | /// |
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119 | /// Copy Constructor. (not implemented) |
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120 | /// |
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121 | LinearWeighted(const LinearWeighted&); |
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122 | |
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123 | double alpha_; |
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124 | double alpha_var_; |
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125 | double beta_; |
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126 | double beta_var_; |
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127 | double m_x_; // average of x values |
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128 | double r2_; // coefficient of determination |
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129 | }; |
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130 | |
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131 | }}} // of namespaces regression, statisitcs and thep |
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132 | |
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133 | #endif |
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