1 | #ifndef _theplu_yat_regression_onedimensioanlweighted_ |
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2 | #define _theplu_yat_regression_onedimensioanlweighted_ |
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3 | |
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4 | // $Id: OneDimensionalWeighted.h 1020 2008-02-01 17:17:26Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2005 Peter Johansson |
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8 | Copyright (C) 2006 Jari Häkkinen, Peter Johansson |
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9 | Copyright (C) 2007 Peter Johansson |
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10 | |
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11 | This file is part of the yat library, http://trac.thep.lu.se/yat |
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12 | |
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13 | The yat library is free software; you can redistribute it and/or |
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14 | modify it under the terms of the GNU General Public License as |
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15 | published by the Free Software Foundation; either version 2 of the |
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16 | License, or (at your option) any later version. |
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17 | |
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18 | The yat library is distributed in the hope that it will be useful, |
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19 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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20 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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21 | General Public License for more details. |
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22 | |
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23 | You should have received a copy of the GNU General Public License |
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24 | along with this program; if not, write to the Free Software |
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25 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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26 | 02111-1307, USA. |
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27 | */ |
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28 | |
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29 | #include "yat/statistics/AveragerPairWeighted.h" |
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30 | |
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31 | #include <ostream> |
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32 | |
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33 | namespace theplu { |
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34 | namespace yat { |
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35 | namespace utility { |
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36 | class VectorBase; |
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37 | } |
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38 | namespace regression { |
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39 | |
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40 | /// |
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41 | /// @brief Interface Class for One Dimensional fitting in a weighted |
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42 | /// fashion. |
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43 | /// |
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44 | class OneDimensionalWeighted |
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45 | { |
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46 | |
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47 | public: |
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48 | /// |
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49 | /// Default Constructor. |
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50 | /// |
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51 | OneDimensionalWeighted(void); |
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52 | |
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53 | /// |
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54 | /// Destructor |
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55 | /// |
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56 | virtual ~OneDimensionalWeighted(void); |
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57 | |
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58 | /** |
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59 | This function computes the best-fit given a model (see |
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60 | specific class for details) by minimizing \f$ |
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61 | \sum{w_i(\hat{y_i}-y_i)^2} \f$, where \f$ \hat{y} \f$ is the |
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62 | fitted value. The weight \f$ w_i \f$ should be proportional |
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63 | to the inverse of the variance for \f$ y_i \f$ |
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64 | */ |
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65 | virtual void fit(const utility::VectorBase& x, const utility::VectorBase& y, |
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66 | const utility::VectorBase& w)=0; |
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67 | |
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68 | /// |
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69 | /// @return expected value in @a x according to the fitted model |
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70 | /// |
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71 | virtual double predict(const double x) const=0; |
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72 | |
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73 | /** |
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74 | The prediction error is defined as expected squared deviation a |
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75 | new data point (with weight @a w) will be from the model |
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76 | value \f$ E((Y|x - \hat{y}(x))^2|w) \f$ and is typically |
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77 | divided into the conditional variance ( see s2() ) |
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78 | given \f$ x \f$ and the squared standard error ( see |
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79 | standard_error2() ) of the model estimation in \f$ x \f$. |
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80 | |
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81 | \f$ E((Y|x - E(Y|x))^2|w) + E((E(Y|x) - \hat{y}(x))^2) \f$ |
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82 | |
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83 | @return expected prediction error for a new data point in @a x |
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84 | with weight @a w. |
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85 | */ |
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86 | double prediction_error2(const double x, const double w=1.0) const; |
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87 | |
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88 | /** |
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89 | r2 is defined as \f$ \frac{\sum |
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90 | w_i(y_i-\hat{y}_i)^2}{\sum w_i(y_i-m_y)^2} \f$ or the fraction |
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91 | of the variance explained by the regression model. |
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92 | */ |
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93 | double r2(void) const; |
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94 | |
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95 | /** |
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96 | \f$ s^2 \f$ is the estimation of variance of residuals or |
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97 | equivalently the conditional variance of Y. |
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98 | |
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99 | @return Conditional variance of Y |
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100 | */ |
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101 | virtual double s2(double w=1) const=0; |
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102 | |
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103 | /** |
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104 | The standard error is defined as \f$ E((Y|x,w - |
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105 | \hat{y}(x))^2) \f$ |
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106 | |
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107 | @return error of model value in @a x |
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108 | */ |
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109 | virtual double standard_error2(const double x) const=0; |
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110 | |
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111 | protected: |
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112 | /// |
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113 | /// Averager for pair of x and y |
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114 | /// |
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115 | statistics::AveragerPairWeighted ap_; |
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116 | |
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117 | /** |
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118 | @brief Chi-squared |
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119 | |
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120 | Chi-squared is defined as the \f$ |
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121 | \sum{w_i(\hat{y_i}-y_i)^2} \f$ |
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122 | */ |
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123 | double chisq_; |
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124 | |
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125 | private: |
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126 | }; |
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127 | |
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128 | }}} // of namespaces regression, yat, and theplu |
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129 | |
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130 | #endif |
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