mhjensen
238 lines
14 KiB
HTML
238 lines
14 KiB
HTML
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'sections': [('What is Machine Learning?', 2, None, '___sec0'),
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('Types of Machine Learning', 2, None, '___sec1'),
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('Different algorithms', 2, None, '___sec2'),
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('Software and needed installations', 2, None, '___sec3'),
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('Python installers', 2, None, '___sec4'),
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('Installing R, C++, cython or Julia', 2, None, '___sec5'),
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('Installing R, C++, cython or Julia', 2, None, '___sec6'),
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('Introduction to Jupyter notebook and available tools',
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2,
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None,
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('Representing data, more examples', 2, None, '___sec8'),
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('Predator-Prey model from ecology', 2, None, '___sec9'),
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('Case study from Hudson bay', 2, None, '___sec10'),
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('Hudson bay data', 2, None, '___sec11'),
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('Plotting the data', 2, None, '___sec12'),
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('Hares and lynx in Hudson bay from 1900 to 1920',
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2,
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None,
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'___sec13'),
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('Why now create a computer model for the hare and lynx '
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'populations?',
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2,
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None,
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'___sec14'),
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('The traditional (top-down) approach', 2, None, '___sec15'),
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("The ``new'' discrete bottom-up approach", 2, None, '___sec16'),
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('Basic (computer-friendly) mathematics notation',
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2,
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None,
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'___sec17'),
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('Basic dynamics of the population of hares',
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2,
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None,
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'___sec18'),
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('Basic dynamics of the population of lynx', 2, None, '___sec19'),
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('Evolution equations', 2, None, '___sec20'),
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('Adapt the model to the Hudson Bay case', 2, None, '___sec21'),
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('The program', 2, None, '___sec22'),
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('The plot', 2, None, '___sec23'),
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('Linear regression in Python', 2, None, '___sec24'),
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('Linear Least squares in R', 2, None, '___sec25'),
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('Non-Linear Least squares in R', 2, None, '___sec26')]}
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<a class="navbar-brand" href="How2ReadData-bs.html">Data Analysis and Machine Learning: Introduction and Representing data</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs001.html#___sec0" style="font-size: 80%;">What is Machine Learning?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs002.html#___sec1" style="font-size: 80%;">Types of Machine Learning</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs003.html#___sec2" style="font-size: 80%;">Different algorithms</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs004.html#___sec3" style="font-size: 80%;">Software and needed installations</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs005.html#___sec4" style="font-size: 80%;">Python installers</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs006.html#___sec5" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs007.html#___sec6" style="font-size: 80%;">Installing R, C++, cython or Julia</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs008.html#___sec7" style="font-size: 80%;">Introduction to Jupyter notebook and available tools</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs009.html#___sec8" style="font-size: 80%;">Representing data, more examples</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs010.html#___sec9" style="font-size: 80%;">Predator-Prey model from ecology</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs011.html#___sec10" style="font-size: 80%;">Case study from Hudson bay</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs012.html#___sec11" style="font-size: 80%;">Hudson bay data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs013.html#___sec12" style="font-size: 80%;">Plotting the data</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs014.html#___sec13" style="font-size: 80%;">Hares and lynx in Hudson bay from 1900 to 1920</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs015.html#___sec14" style="font-size: 80%;">Why now create a computer model for the hare and lynx populations?</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs016.html#___sec15" style="font-size: 80%;">The traditional (top-down) approach</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs017.html#___sec16" style="font-size: 80%;">The ``new'' discrete bottom-up approach</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs018.html#___sec17" style="font-size: 80%;">Basic (computer-friendly) mathematics notation</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs019.html#___sec18" style="font-size: 80%;">Basic dynamics of the population of hares</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs020.html#___sec19" style="font-size: 80%;">Basic dynamics of the population of lynx</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs021.html#___sec20" style="font-size: 80%;">Evolution equations</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs022.html#___sec21" style="font-size: 80%;">Adapt the model to the Hudson Bay case</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs023.html#___sec22" style="font-size: 80%;">The program</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs024.html#___sec23" style="font-size: 80%;">The plot</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs025.html#___sec24" style="font-size: 80%;">Linear regression in Python</a></li>
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<!-- navigation toc: --> <li><a href="._How2ReadData-bs026.html#___sec25" style="font-size: 80%;">Linear Least squares in R</a></li>
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<!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Non-Linear Least squares in R</a></li>
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<!-- !split -->
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<h2 id="___sec26" class="anchor">Non-Linear Least squares in R </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000">set</span><span style="color: #666666">.</span>seed(<span style="color: #666666">1485</span>)
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<span style="color: #008000">len</span> <span style="color: #666666">=</span> <span style="color: #666666">24</span>
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x <span style="color: #666666">=</span> runif(<span style="color: #008000">len</span>)
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y <span style="color: #666666">=</span> x<span style="color: #666666">^3+</span>rnorm(<span style="color: #008000">len</span>, <span style="color: #666666">0</span>,<span style="color: #666666">0.06</span>)
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ds <span style="color: #666666">=</span> data<span style="color: #666666">.</span>frame(x <span style="color: #666666">=</span> x, y <span style="color: #666666">=</span> y)
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<span style="color: #008000">str</span>(ds)
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plot( y <span style="color: #666666">~</span> x, main <span style="color: #666666">=</span><span style="color: #BA2121">"Known cubic with noise"</span>)
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s <span style="color: #666666">=</span> seq(<span style="color: #666666">0</span>,<span style="color: #666666">1</span>,length <span style="color: #666666">=100</span>)
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lines(s, s<span style="color: #666666">^3</span>, lty <span style="color: #666666">=2</span>, col <span style="color: #666666">=</span><span style="color: #BA2121">"green"</span>)
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m <span style="color: #666666">=</span> nls(y <span style="color: #666666">~</span> I(x<span style="color: #666666">^</span>power), data <span style="color: #666666">=</span> ds, start <span style="color: #666666">=</span> <span style="color: #008000">list</span>(power<span style="color: #666666">=1</span>), trace <span style="color: #666666">=</span> T)
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class(m)
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summary(m)
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power <span style="color: #666666">=</span> <span style="color: #008000">round</span>(summary(m)$coefficients[<span style="color: #666666">1</span>], <span style="color: #666666">3</span>)
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power<span style="color: #666666">.</span>se <span style="color: #666666">=</span> <span style="color: #008000">round</span>(summary(m)$coefficients[<span style="color: #666666">2</span>], <span style="color: #666666">3</span>)
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plot(y <span style="color: #666666">~</span> x, main <span style="color: #666666">=</span> <span style="color: #BA2121">"Fitted power model"</span>, sub <span style="color: #666666">=</span> <span style="color: #BA2121">"Blue: fit; green: known"</span>)
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s <span style="color: #666666">=</span> seq(<span style="color: #666666">0</span>, <span style="color: #666666">1</span>, length <span style="color: #666666">=</span> <span style="color: #666666">100</span>)
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lines(s, s<span style="color: #666666">^3</span>, lty <span style="color: #666666">=</span> <span style="color: #666666">2</span>, col <span style="color: #666666">=</span> <span style="color: #BA2121">"green"</span>)
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lines(s, predict(m, <span style="color: #008000">list</span>(x <span style="color: #666666">=</span> s)), lty <span style="color: #666666">=</span> <span style="color: #666666">1</span>, col <span style="color: #666666">=</span> <span style="color: #BA2121">"blue"</span>)
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text(<span style="color: #666666">0</span>, <span style="color: #666666">0.5</span>, paste(<span style="color: #BA2121">"y =x^ ("</span>, power, <span style="color: #BA2121">" +/- "</span>, power<span style="color: #666666">.</span>se, <span style="color: #BA2121">")"</span>, sep <span style="color: #666666">=</span> <span style="color: #BA2121">""</span>), pos <span style="color: #666666">=</span> <span style="color: #666666">4</span>)
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</pre></div>
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<p>
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