source: trunk/yat/regression/OneDimensionalWeighted.h @ 1486

Last change on this file since 1486 was 1486, checked in by Jari Häkkinen, 13 years ago

Addresses #436.

  • Property svn:eol-style set to native
  • Property svn:keywords set to Id
File size: 3.4 KB
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1#ifndef _theplu_yat_regression_onedimensioanlweighted_
2#define _theplu_yat_regression_onedimensioanlweighted_
3
4// $Id: OneDimensionalWeighted.h 1486 2008-09-09 21:17:19Z jari $
5
6/*
7  Copyright (C) 2005 Peter Johansson
8  Copyright (C) 2006, 2007 Jari Häkkinen, Peter Johansson
9  Copyright (C) 2008 Peter Johansson
10
11  This file is part of the yat library, http://dev.thep.lu.se/yat
12
13  The yat library is free software; you can redistribute it and/or
14  modify it under the terms of the GNU General Public License as
15  published by the Free Software Foundation; either version 3 of the
16  License, or (at your option) any later version.
17
18  The yat library is distributed in the hope that it will be useful,
19  but WITHOUT ANY WARRANTY; without even the implied warranty of
20  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
21  General Public License for more details.
22
23  You should have received a copy of the GNU General Public License
24  along with this program; if not, write to the Free Software
25  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
26  02111-1307, USA.
27*/
28
29#include "yat/statistics/AveragerPairWeighted.h"
30
31#include <ostream>
32
33namespace theplu {
34namespace yat {
35namespace utility {
36  class VectorBase;
37}
38namespace regression {
39 
40  ///
41  /// @brief Interface Class for One Dimensional fitting in a weighted
42  /// fashion.
43  ///
44  class OneDimensionalWeighted
45  {
46 
47  public:
48    ///
49    /// Default Constructor.
50    ///
51    OneDimensionalWeighted(void);
52
53    ///
54    /// Destructor
55    ///
56    virtual ~OneDimensionalWeighted(void);
57         
58    /**
59       This function computes the best-fit given a model (see
60       specific class for details) by minimizing \f$
61       \sum{w_i(\hat{y_i}-y_i)^2} \f$, where \f$ \hat{y} \f$ is the
62       fitted value. The weight \f$ w_i \f$ should be proportional
63       to the inverse of the variance for \f$ y_i \f$
64    */
65    virtual void fit(const utility::VectorBase& x, const utility::VectorBase& y, 
66                     const utility::VectorBase& w)=0;
67
68    ///
69    /// @return expected value in @a x according to the fitted model
70    ///
71    virtual double predict(const double x) const=0;
72
73    /**
74       The prediction error is defined as expected squared deviation a
75       new data point (with weight @a w) will be from the model
76       value \f$ E((Y|x - \hat{y}(x))^2|w) \f$ and is typically
77       divided into the conditional variance ( see s2() )
78       given \f$ x \f$ and the squared standard error ( see
79       standard_error2() ) of the model estimation in \f$ x \f$.
80
81       \f$ E((Y|x - E(Y|x))^2|w) + E((E(Y|x) - \hat{y}(x))^2) \f$
82
83       @return expected prediction error for a new data point in @a x
84       with weight @a w.
85    */
86    double prediction_error2(const double x, const double w=1.0) const; 
87
88    /**
89       r2 is defined as \f$ \frac{\sum
90       w_i(y_i-\hat{y}_i)^2}{\sum w_i(y_i-m_y)^2} \f$ or the fraction
91       of the variance explained by the regression model.
92    */
93    double r2(void) const; 
94
95    /**
96       \f$ s^2 \f$ is the estimation of variance of residuals or
97       equivalently the conditional variance of Y.
98
99       @return Conditional variance of Y
100    */
101    virtual double s2(double w=1) const=0;
102
103    /**
104       The standard error is defined as \f$ E((Y|x,w -
105       \hat{y}(x))^2) \f$
106
107       @return error of model value in @a x
108    */
109    virtual double standard_error2(const double x) const=0;
110
111  protected:
112    ///
113    /// Averager for pair of x and y
114    ///
115    statistics::AveragerPairWeighted ap_;
116
117    /**
118       @brief Chi-squared
119       
120       Chi-squared is defined as the \f$
121       \sum{w_i(\hat{y_i}-y_i)^2} \f$
122    */
123    double chisq_;
124
125  private:
126  };
127
128}}} // of namespaces regression, yat, and theplu
129
130#endif
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