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<a class="el" href="dir_000007.html">contrib</a> / <a class="el" href="dir_000008.html">mathsym</a> / <a class="el" href="dir_000012.html">regression</a></div>
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<h1>Scaling.cpp</h1><div class="fragment"><pre class="fragment">00001 <span class="comment">/* </span>
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00002 <span class="comment"> * Copyright (C) 2005 Maarten Keijzer</span>
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00003 <span class="comment"> *</span>
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00004 <span class="comment"> * This program is free software; you can redistribute it and/or modify</span>
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00005 <span class="comment"> * it under the terms of version 2 of the GNU General Public License as </span>
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00006 <span class="comment"> * published by the Free Software Foundation. </span>
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00007 <span class="comment"> *</span>
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00008 <span class="comment"> * This program is distributed in the hope that it will be useful,</span>
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00009 <span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
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00010 <span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
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00011 <span class="comment"> * GNU General Public License for more details.</span>
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00012 <span class="comment"> *</span>
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00013 <span class="comment"> * You should have received a copy of the GNU General Public License</span>
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00014 <span class="comment"> * along with this program; if not, write to the Free Software</span>
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00015 <span class="comment"> * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA</span>
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00016 <span class="comment"> */</span>
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00017
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00018 <span class="preprocessor">#include "Scaling.h"</span>
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00019 <span class="preprocessor">#include "TargetInfo.h"</span>
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00020
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00021 <span class="keyword">using</span> <span class="keyword">namespace </span>std;
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00022
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00023 Scaling slope(<span class="keyword">const</span> std::valarray<double>& x, <span class="keyword">const</span> TargetInfo& targets) {
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00024
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00025 <span class="keywordtype">double</span> xx = 0.0;
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00026 <span class="keywordtype">double</span> xy = 0.0;
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00027
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00028 <span class="keyword">const</span> valarray<double>& y = targets.targets();
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00029
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00030 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < x.size(); ++i) {
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00031 xx += x[i] * x[i];
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00032 xy += x[i] * y[i];
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00033 }
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00034
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00035 <span class="keywordflow">if</span> (xx < 1e-7) <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(0.0,0.0));
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00036
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00037 <span class="keywordtype">double</span> b = xy / xx;
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00038
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00039 <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(0.0, b));
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00040
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00041 }
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00042
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00043 <span class="comment">// Still needs proper testing with non-trivial lambda</span>
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00044 Scaling regularized_least_squares(<span class="keyword">const</span> std::valarray<double>& inputs, <span class="keyword">const</span> TargetInfo& targets, <span class="keywordtype">double</span> lambda) {
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00045
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00046 <span class="keywordtype">double</span> n = inputs.size();
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00047
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00048 valarray<double> x = inputs;
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00049
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00050 <span class="keywordtype">double</span> a,b,d;
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00051 a=b=d=0;
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00052
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00053 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i) {
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00054 a += 1 + lambda;
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00055 b += x[i];
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00056 d += x[i] * x[i] + lambda;
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00057 }
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00058
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00059 <span class="comment">//invert</span>
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00060
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00061 <span class="keywordtype">double</span> ad_bc = a*d - b * b;
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00062 <span class="comment">// if ad_bc equals zero there's a problem</span>
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00063
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00064 <span class="keywordflow">if</span> (ad_bc < 1e-17) <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling);
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00065
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00066 <span class="keywordtype">double</span> ai = d/ad_bc;
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00067 <span class="keywordtype">double</span> bi = -b/ad_bc;
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00068 <span class="keywordtype">double</span> di = a/ad_bc;
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00069 <span class="keywordtype">double</span> ci = bi;
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00070
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00071 <span class="comment">// Now multiply this inverted covariance matrix (C^-1) with x' * t</span>
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00072
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00073 std::valarray<double> ones = x;
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00074
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00075 <span class="comment">// calculate C^-1 * x' )</span>
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00076 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i)
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00077 {
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00078 ones[i] = (ai + bi * x[i]);
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00079 x[i] = (ci + di * x[i]);
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00080 }
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00081
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00082 <span class="comment">// results are in [ones, x], now multiply with y</span>
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00083
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00084 a = 0.0; <span class="comment">// intercept</span>
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00085 b = 0.0; <span class="comment">// slope</span>
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00086
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00087 <span class="keyword">const</span> valarray<double>& t = targets.targets();
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00088
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00089 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i)
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00090 {
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00091 a += ones[i] * t[i];
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00092 b += x[i] * t[i];
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00093 }
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00094
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00095 <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(a,b));
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00096 }
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00097
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00098 Scaling ols(<span class="keyword">const</span> std::valarray<double>& y, <span class="keyword">const</span> std::valarray<double>& t) {
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00099 <span class="keywordtype">double</span> n = y.size();
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00100
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00101 <span class="keywordtype">double</span> y_mean = y.sum() / n;
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00102 <span class="keywordtype">double</span> t_mean = t.sum() / n;
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00103
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00104 std::valarray<double> y_var = (y - y_mean);
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00105 std::valarray<double> t_var = (t - t_mean);
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00106 std::valarray<double> cov = t_var * y_var;
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00107
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00108 y_var *= y_var;
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00109 t_var *= t_var;
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00110
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00111 <span class="keywordtype">double</span> sumvar = y_var.sum();
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00112
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00113 <span class="keywordflow">if</span> (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) <span class="comment">// breakout when numerical problems are likely</span>
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00114 <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(t_mean,0.));
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00115
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00116
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00117 <span class="keywordtype">double</span> b = cov.sum() / sumvar;
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00118 <span class="keywordtype">double</span> a = t_mean - b * y_mean;
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00119
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00120 Scaling s = Scaling(<span class="keyword">new</span> LinearScaling(a,b));
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00121
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00122 <span class="keywordflow">return</span> s;
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00123 }
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00124
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00125 Scaling ols(<span class="keyword">const</span> std::valarray<double>& y, <span class="keyword">const</span> TargetInfo& targets) {
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00126 <span class="keywordtype">double</span> n = y.size();
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00127
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00128 <span class="keywordtype">double</span> y_mean = y.sum() / n;
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00129
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00130 std::valarray<double> y_var = (y - y_mean);
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00131 std::valarray<double> cov = targets.tcov_part() * y_var;
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00132
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00133 y_var *= y_var;
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00134
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00135 <span class="keywordtype">double</span> sumvar = y_var.sum();
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00136
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00137 <span class="keywordflow">if</span> (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) <span class="comment">// breakout when numerical problems are likely</span>
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00138 <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(targets.tmean(),0.));
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00139
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00140
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00141 <span class="keywordtype">double</span> b = cov.sum() / sumvar;
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00142 <span class="keywordtype">double</span> a = targets.tmean() - b * y_mean;
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00143
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00144 <span class="keywordflow">if</span> (!finite(b)) {
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00145
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00146 cout << a << <span class="charliteral">' '</span> << b << endl;
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00147 cout << sumvar << endl;
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00148 cout << y_mean << endl;
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00149 cout << cov.sum() << endl;
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00150 exit(1);
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00151 }
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00152
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00153 Scaling s = Scaling(<span class="keyword">new</span> LinearScaling(a,b));
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00154
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00155 <span class="keywordflow">return</span> s;
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00156 }
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00157
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00158
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00159 Scaling wls(<span class="keyword">const</span> std::valarray<double>& inputs, <span class="keyword">const</span> TargetInfo& targets) {
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00160
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00161 std::valarray<double> x = inputs;
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00162 <span class="keyword">const</span> std::valarray<double>& w = targets.weights();
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00163
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00164 <span class="keywordtype">unsigned</span> n = x.size();
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00165 <span class="comment">// First calculate x'*W (as W is a diagonal matrix it's simply elementwise multiplication</span>
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00166 std::valarray<double> wx = targets.weights() * x;
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00167
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00168 <span class="comment">// Now x'*W is contained in [w,wx], calculate x' * W * x (the covariance)</span>
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00169 <span class="keywordtype">double</span> a,b,d;
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00170 a=b=d=0.0;
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00171
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00172 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i)
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00173 {
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00174 a += w[i];
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00175 b += wx[i];
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00176 d += x[i] * wx[i];
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00177 }
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00178
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00179 <span class="comment">//invert</span>
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00180
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00181 <span class="keywordtype">double</span> ad_bc = a*d - b * b;
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00182 <span class="comment">// if ad_bc equals zero there's a problem</span>
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00183
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00184 <span class="keywordflow">if</span> (ad_bc < 1e-17) <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling);
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00185
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00186 <span class="keywordtype">double</span> ai = d/ad_bc;
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00187 <span class="keywordtype">double</span> bi = -b/ad_bc;
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00188 <span class="keywordtype">double</span> di = a/ad_bc;
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00189 <span class="keywordtype">double</span> ci = bi;
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00190
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00191 <span class="comment">// Now multiply this inverted covariance matrix (C^-1) with x' * W * y</span>
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00192
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00193 <span class="comment">// create alias to reuse the wx we do not need anymore</span>
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00194 std::valarray<double>& ones = wx;
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00195
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00196 <span class="comment">// calculate C^-1 * x' * W (using the fact that W is diagonal)</span>
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00197 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i)
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00198 {
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00199 ones[i] = w[i]*(ai + bi * x[i]);
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00200 x[i] = w[i]*(ci + di * x[i]);
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00201 }
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00202
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00203 <span class="comment">// results are in [ones, x], now multiply with y</span>
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00204
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00205 a = 0.0; <span class="comment">// intercept</span>
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00206 b = 0.0; <span class="comment">// slope</span>
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00207
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00208 <span class="keyword">const</span> valarray<double>& t = targets.targets();
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00209
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00210 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < n; ++i)
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00211 {
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00212 a += ones[i] * t[i];
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00213 b += x[i] * t[i];
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00214 }
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00215
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00216 <span class="keywordflow">return</span> Scaling(<span class="keyword">new</span> LinearScaling(a,b));
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00217 }
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00218
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00219
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00220 <span class="comment">//Scaling med(const std::valarray<double>& inputs, const TargetInfo& targets);</span>
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00221
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00222 <span class="keywordtype">double</span> mse(<span class="keyword">const</span> std::valarray<double>& y, <span class="keyword">const</span> TargetInfo& t) {
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00223
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00224 valarray<double> residuals = t.targets()-y;
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00225 residuals *= residuals;
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00226 <span class="keywordtype">double</span> sz = residuals.size();
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00227 <span class="keywordflow">if</span> (t.has_weights()) {
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00228 residuals *= t.weights();
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00229 sz = 1.0;
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00230 }
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00231
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00232 <span class="keywordflow">return</span> residuals.sum() / sz;
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00233 }
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00234
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00235 <span class="keywordtype">double</span> rms(<span class="keyword">const</span> std::valarray<double>& y, <span class="keyword">const</span> TargetInfo& t) {
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00236 <span class="keywordflow">return</span> sqrt(mse(y,t));
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00237 }
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00238
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00239 <span class="keywordtype">double</span> mae(<span class="keyword">const</span> std::valarray<double>& y, <span class="keyword">const</span> TargetInfo& t) {
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00240 valarray<double> residuals = abs(t.targets()-y);
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00241 <span class="keywordflow">if</span> (t.has_weights()) residuals *= t.weights();
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00242 <span class="keywordflow">return</span> residuals.sum() / residuals.size();
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00243 }
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00244
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00245
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00246 <span class="comment">/*</span>
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00247 <span class="comment"> double standard_error(const std::valarray<double>& y, const std::pair<double,double>& scaling) {</span>
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00248 <span class="comment"> double a = scaling.first;</span>
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00249 <span class="comment"> double b = scaling.second;</span>
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00250 <span class="comment"> double n = y.size();</span>
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00251 <span class="comment"> double se = sqrt( pow(a+b*y-current_set->targets,2.0).sum() / (n-2));</span>
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00252 <span class="comment"> </span>
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00253 <span class="comment"> double mean_y = y.sum() / n;</span>
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00254 <span class="comment"> double sxx = pow( y - mean_y, 2.0).sum();</span>
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00255 <span class="comment"></span>
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00256 <span class="comment"> return se / sqrt(sxx);</span>
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00257 <span class="comment"> }</span>
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00258 <span class="comment"> </span>
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00259 <span class="comment"> double scaled_mse(const std::valarray<double>& y){</span>
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00260 <span class="comment"> std::pair<double,double> scaling;</span>
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00261 <span class="comment"> return scaled_mse(y,scaling);</span>
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00262 <span class="comment"> }</span>
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00263 <span class="comment"> </span>
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00264 <span class="comment"> double scaled_mse(const std::valarray<double>& y, std::pair<double, double>& scaling)</span>
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00265 <span class="comment"> {</span>
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00266 <span class="comment"> scaling = scale(y);</span>
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00267 <span class="comment"> </span>
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00268 <span class="comment"> double a = scaling.first;</span>
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00269 <span class="comment"> double b = scaling.second;</span>
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00270 <span class="comment"> </span>
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00271 <span class="comment"> std::valarray<double> tmp = current_set->targets - a - b * y;</span>
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00272 <span class="comment"> tmp *= tmp;</span>
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00273 <span class="comment"> </span>
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00274 <span class="comment"> if (weights.size())</span>
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00275 <span class="comment"> return (weights * tmp).sum();</span>
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00276 <span class="comment"></span>
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00277 <span class="comment"> return tmp.sum() / tmp.size();</span>
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00278 <span class="comment"> }</span>
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00279 <span class="comment"> </span>
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00280 <span class="comment"> double robust_mse(const std::valarray<double>& ny, std::pair<double, double>& scaling) {</span>
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00281 <span class="comment"> </span>
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00282 <span class="comment"> double smse = scaled_mse(ny,scaling);</span>
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00283 <span class="comment"></span>
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00284 <span class="comment"> std::valarray<double> y = ny;</span>
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00285 <span class="comment"> // find maximum covariance case </span>
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00286 <span class="comment"> double n = y.size();</span>
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00287 <span class="comment"></span>
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00288 <span class="comment"> int largest = 0;</span>
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00289 <span class="comment"> </span>
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00290 <span class="comment"> {</span>
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00291 <span class="comment"> double y_mean = y.sum() / n;</span>
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00292 <span class="comment"> </span>
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00293 <span class="comment"> std::valarray<double> y_var = (y - y_mean);</span>
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00294 <span class="comment"> std::valarray<double> cov = tcov * y_var;</span>
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00295 <span class="comment"> </span>
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00296 <span class="comment"> std::valarray<bool> maxcov = cov == cov.max();</span>
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00297 <span class="comment"> </span>
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00298 <span class="comment"> for (unsigned i = 0; i < maxcov.size(); ++i) {</span>
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00299 <span class="comment"> if (maxcov[i]) {</span>
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00300 <span class="comment"> largest = i;</span>
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00301 <span class="comment"> break;</span>
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00302 <span class="comment"> }</span>
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00303 <span class="comment"> }</span>
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00304 <span class="comment"> }</span>
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00305 <span class="comment"> </span>
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00306 <span class="comment"> double y_mean = (y.sum() - y[largest]) / (n-1);</span>
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00307 <span class="comment"> y[largest] = y_mean; // dissappears from covariance calculation</span>
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00308 <span class="comment"> </span>
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00309 <span class="comment"> std::valarray<double> y_var = (y - y_mean);</span>
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00310 <span class="comment"> std::valarray<double> cov = tcov * y_var;</span>
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00311 <span class="comment"> y_var *= y_var;</span>
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00312 <span class="comment"></span>
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00313 <span class="comment"> double sumvar = y_var.sum();</span>
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00314 <span class="comment"> </span>
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00315 <span class="comment"> if (sumvar == 0. || sumvar/n < 1e-7 || sumvar/n > 1e+7) // breakout when numerical problems are likely</span>
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00316 <span class="comment"> return worst_performance();</span>
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00317 <span class="comment"> </span>
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00318 <span class="comment"> double b = cov.sum() / sumvar;</span>
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00319 <span class="comment"> double a = tmean - b * y_mean;</span>
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00320 <span class="comment"> </span>
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00321 <span class="comment"> std::valarray<double> tmp = current_set->targets - a - b * y;</span>
|
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00322 <span class="comment"> tmp[largest] = 0.0;</span>
|
|
00323 <span class="comment"> tmp *= tmp;</span>
|
|
00324 <span class="comment"> </span>
|
|
00325 <span class="comment"> double smse2 = tmp.sum() / (tmp.size()-1);</span>
|
|
00326 <span class="comment"> </span>
|
|
00327 <span class="comment"> static std::ofstream os("smse.txt");</span>
|
|
00328 <span class="comment"> os << smse << ' ' << smse2 << '\n';</span>
|
|
00329 <span class="comment"> </span>
|
|
00330 <span class="comment"> if (smse2 > smse) {</span>
|
|
00331 <span class="comment"> return worst_performance();</span>
|
|
00332 <span class="comment"> //std::cerr << "overfit? " << smse << ' ' << smse2 << '\n';</span>
|
|
00333 <span class="comment"> }</span>
|
|
00334 <span class="comment"> </span>
|
|
00335 <span class="comment"> scaling.first = a;</span>
|
|
00336 <span class="comment"> scaling.second = b;</span>
|
|
00337 <span class="comment"> </span>
|
|
00338 <span class="comment"> return smse2;</span>
|
|
00339 <span class="comment"> }</span>
|
|
00340 <span class="comment"> </span>
|
|
00341 <span class="comment"> class Sorter {</span>
|
|
00342 <span class="comment"> const std::valarray<double>& scores;</span>
|
|
00343 <span class="comment"> public:</span>
|
|
00344 <span class="comment"> Sorter(const std::valarray<double>& _scores) : scores(_scores) {}</span>
|
|
00345 <span class="comment"> </span>
|
|
00346 <span class="comment"> bool operator()(unsigned i, unsigned j) const {</span>
|
|
00347 <span class="comment"> return scores[i] < scores[j];</span>
|
|
00348 <span class="comment"> }</span>
|
|
00349 <span class="comment"> };</span>
|
|
00350 <span class="comment"> </span>
|
|
00351 <span class="comment"> double coc(const std::valarray<double>& y) {</span>
|
|
00352 <span class="comment"> std::vector<unsigned> indices(y.size());</span>
|
|
00353 <span class="comment"> for (unsigned i = 0; i < y.size(); ++i) indices[i] = i;</span>
|
|
00354 <span class="comment"> std::sort(indices.begin(), indices.end(), Sorter(y));</span>
|
|
00355 <span class="comment"> </span>
|
|
00356 <span class="comment"> const std::valarray<double>& targets = current_set->targets;</span>
|
|
00357 <span class="comment"> </span>
|
|
00358 <span class="comment"> double neg = 1.0 - targets[indices[0]];</span>
|
|
00359 <span class="comment"> double pos = targets[indices[0]];</span>
|
|
00360 <span class="comment"> </span>
|
|
00361 <span class="comment"> double cumpos = 0;</span>
|
|
00362 <span class="comment"> double cumneg = 0;</span>
|
|
00363 <span class="comment"> double sum=0;</span>
|
|
00364 <span class="comment"> </span>
|
|
00365 <span class="comment"> double last_score = y[indices[0]];</span>
|
|
00366 <span class="comment"> </span>
|
|
00367 <span class="comment"> for(unsigned i = 1; i < targets.size(); ++i) {</span>
|
|
00368 <span class="comment"> </span>
|
|
00369 <span class="comment"> if (fabs(y[indices[i]] - last_score) < 1e-9) { // we call it tied</span>
|
|
00370 <span class="comment"> pos += targets[indices[i]];</span>
|
|
00371 <span class="comment"> neg += 1.0 - targets[indices[i]];</span>
|
|
00372 <span class="comment"> </span>
|
|
00373 <span class="comment"> if (i < targets.size()-1)</span>
|
|
00374 <span class="comment"> continue;</span>
|
|
00375 <span class="comment"> }</span>
|
|
00376 <span class="comment"> sum += pos * cumneg + (pos * neg) * 0.5;</span>
|
|
00377 <span class="comment"> cumneg += neg;</span>
|
|
00378 <span class="comment"> cumpos += pos;</span>
|
|
00379 <span class="comment"> pos = targets[indices[i]];</span>
|
|
00380 <span class="comment"> neg = 1.0 - targets[indices[i]];</span>
|
|
00381 <span class="comment"> last_score = y[indices[i]];</span>
|
|
00382 <span class="comment"> }</span>
|
|
00383 <span class="comment"> </span>
|
|
00384 <span class="comment"> return sum / (cumneg * cumpos);</span>
|
|
00385 <span class="comment"> }</span>
|
|
00386 <span class="comment"> </span>
|
|
00387 <span class="comment"> // iterative re-weighted least squares (for parameters.classification)</span>
|
|
00388 <span class="comment"> double irls(const std::valarray<double>& scores, std::pair<double,double>& scaling) {</span>
|
|
00389 <span class="comment"> const std::valarray<double>& t = current_set->targets;</span>
|
|
00390 <span class="comment"> </span>
|
|
00391 <span class="comment"> std::valarray<double> e(scores.size());</span>
|
|
00392 <span class="comment"> std::valarray<double> u(scores.size()); </span>
|
|
00393 <span class="comment"> std::valarray<double> w(scores.size());</span>
|
|
00394 <span class="comment"> std::valarray<double> z(scores.size());</span>
|
|
00395 <span class="comment"> </span>
|
|
00396 <span class="comment"> parameters.use_irls = false; parameters.classification=false;</span>
|
|
00397 <span class="comment"> scaling = scale(scores);</span>
|
|
00398 <span class="comment"> parameters.use_irls=true;parameters.classification=true;</span>
|
|
00399 <span class="comment"> </span>
|
|
00400 <span class="comment"> if (scaling.second == 0.0) return worst_performance(); </span>
|
|
00401 <span class="comment"> </span>
|
|
00402 <span class="comment"> for (unsigned i = 0; i < 10; ++i) {</span>
|
|
00403 <span class="comment"> e = exp(scaling.first + scaling.second*scores);</span>
|
|
00404 <span class="comment"> u = e / (e + exp(-(scaling.first + scaling.second * scores)));</span>
|
|
00405 <span class="comment"> w = u*(1.-u);</span>
|
|
00406 <span class="comment"> z = (t-u)/w;</span>
|
|
00407 <span class="comment"> scaling = wls(scores, u, w);</span>
|
|
00408 <span class="comment"> //double ll = (log(u)*t + (1.-log(u))*(1.-t)).sum();</span>
|
|
00409 <span class="comment"> //std::cout << "Scale " << i << ' ' << scaling.first << " " << scaling.second << " LL " << 2*ll << std::endl;</span>
|
|
00410 <span class="comment"> }</span>
|
|
00411 <span class="comment"></span>
|
|
00412 <span class="comment"> // log-likelihood</span>
|
|
00413 <span class="comment"> u = exp(scaling.first + scaling.second*scores) / (1 + exp(scaling.first + scaling.second*scores));</span>
|
|
00414 <span class="comment"> double ll = (log(u)*t + (1.-log(u))*(1.-t)).sum();</span>
|
|
00415 <span class="comment"> return 2*ll;</span>
|
|
00416 <span class="comment"> }</span>
|
|
00417 <span class="comment">*/</span>
|
|
</pre></div><hr size="1"><address style="align: right;"><small>Generated on Thu Oct 19 05:06:42 2006 for EO by
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<a href="http://www.doxygen.org/index.html">
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<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.3.9.1 </small></address>
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