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- <meta name="description" content="Local Regression and Likelihood, Figure 8.2.">
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- <h1>fig8_2
- </h1>
- <h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
- <div class="box"><strong>Local Regression and Likelihood, Figure 8.2.</strong></div>
- <h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
- <div class="box"><strong>This is a script file. </strong></div>
- <h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
- <div class="fragment"><pre class="comment"> Local Regression and Likelihood, Figure 8.2.
- Discrimination/Classification, simple example using
- density estimation.
- First, compute density estimates fit0, fit1 ('family','rate'
- - output is in events per unit area) for each class in the
- training sample. The ratio fit1/(fit1+fit0) estimates the
- posterior probability that an observation comes from population 1.
- plotting the classification boundary is slightly tricky - it depends
- on both fits, so lfplot() can't be used. Instead, both fits must be
- evaluated on the same grid of values, which is then used to make a
- contour plot.
- Author: Catherine Loader</pre></div>
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- <h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
- This function calls:
- <ul style="list-style-image:url(../../../matlabicon.gif)">
- <li><a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a> Smoothing noisy data using Local Regression and Likelihood.</li><li><a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a> Interpolate a fit produced by locfit().</li></ul>
- This function is called by:
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- <li><a href="runbook.html" class="code" title="">runbook</a> </li></ul>
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- <h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../../up.png"></a></h2>
- <div class="fragment"><pre>0001 <span class="comment">% Local Regression and Likelihood, Figure 8.2.</span>
- 0002 <span class="comment">%</span>
- 0003 <span class="comment">% Discrimination/Classification, simple example using</span>
- 0004 <span class="comment">% density estimation.</span>
- 0005 <span class="comment">%</span>
- 0006 <span class="comment">% First, compute density estimates fit0, fit1 ('family','rate'</span>
- 0007 <span class="comment">% - output is in events per unit area) for each class in the</span>
- 0008 <span class="comment">% training sample. The ratio fit1/(fit1+fit0) estimates the</span>
- 0009 <span class="comment">% posterior probability that an observation comes from population 1.</span>
- 0010 <span class="comment">%</span>
- 0011 <span class="comment">% plotting the classification boundary is slightly tricky - it depends</span>
- 0012 <span class="comment">% on both fits, so lfplot() can't be used. Instead, both fits must be</span>
- 0013 <span class="comment">% evaluated on the same grid of values, which is then used to make a</span>
- 0014 <span class="comment">% contour plot.</span>
- 0015 <span class="comment">%</span>
- 0016 <span class="comment">% Author: Catherine Loader</span>
- 0017
- 0018 load cltrain;
- 0019 u0 = find(y==0);
- 0020 u1 = find(y==1);
- 0021 fit0 = <a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a>([x1(u0) x2(u0)],y(u0),<span class="string">'family'</span>,<span class="string">'rate'</span>,<span class="string">'scale'</span>,0);
- 0022 fit1 = <a href="../../../chronux_2_10/locfit/m/locfit.html" class="code" title="function fit=locfit(varargin)">locfit</a>([x1(u1) x2(u1)],y(u1),<span class="string">'family'</span>,<span class="string">'rate'</span>,<span class="string">'scale'</span>,0);
- 0023
- 0024 v0 = -3+6*(0:50)'/50;
- 0025 v1 = -2.2+4.2*(0:49)'/49;
- 0026 <span class="comment">% predict returns log(rate)</span>
- 0027 z = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,{v0 v1})-<a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,{v0 v1});
- 0028 z = reshape(z,51,50);
- 0029 figure(<span class="string">'Name'</span>,<span class="string">'fig8_2: classification'</span>);
- 0030 contour(v0,v1,z',[0 0]);
- 0031 hold on;
- 0032 plot(x1(u0),x2(u0),<span class="string">'.'</span>);
- 0033 plot(x1(u1),x2(u1),<span class="string">'.'</span>,<span class="string">'color'</span>,<span class="string">'red'</span>);
- 0034 hold off;
- 0035
- 0036 p0 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,[x1 x2]);
- 0037 p1 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,[x1 x2]);
- 0038 py = (p1 > p0);
- 0039 disp(<span class="string">'Classification table for training data'</span>);
- 0040 tabulate(10*y+py);
- 0041
- 0042 load cltest;
- 0043 p0 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit0,[x1 x2]);
- 0044 p1 = <a href="../../../chronux_2_10/locfit/m/predict.html" class="code" title="function [y, se] = predict(varargin)">predict</a>(fit1,[x1 x2]);
- 0045 py = (p1 > p0);
- 0046 disp(<span class="string">'Classification table for test data'</span>);
- 0047 tabulate(10*y+py);
- 0048</pre></div>
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