65 lines
2.1 KiB
TeX
65 lines
2.1 KiB
TeX
\documentclass[12pt]{book}
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\input{../../header}
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\renewcommand{\exercisesolutions}{here} % 0: here, 1: chapter, 2: end
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\lstset{inputpath=../code}
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\graphicspath{{figures/}}
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\typein[\pagenumber]{Number of first page}
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\typein[\chapternumber]{Chapter number}
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\setcounter{page}{\pagenumber}
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\setcounter{chapter}{\chapternumber}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\include{regression}
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\subsection{Notes}
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\begin{itemize}
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\item Fig 8.2 right: this should be a chi-squared distribution with one degree of freedom!
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\end{itemize}
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\subsection{Start with one-dimensional problem!}
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\begin{itemize}
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\item Let's fit a cubic function $y=cx^3$ (weight versus length of a tiger)\\
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\includegraphics[width=0.8\textwidth]{cubicfunc}
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\item Introduce the problem, $c$ is density and form factor
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\item How to generate an artificial data set (refer to simulation chapter)
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\item How to plot a function (do not use the data x values!)
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\item Just the mean square error as a function of the factor c\\
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\includegraphics[width=0.8\textwidth]{cubicerrors}
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\item Also mention the cost function for a straight line
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\item 1-d gradient, NO quiver plot (it is a nightmare to get this right)\\
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\includegraphics[width=0.8\textwidth]{cubicmse}
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\item 1-d gradient descend
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\item Describe in words the n-d problem.
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\item Homework is to do the 2d problem with the straight line!
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\end{itemize}
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\subsection{Linear fits}
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\begin{itemize}
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\item Polyfit is easy: unique solution! $c x^2$ is also a linear fit.
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\item Example for overfitting with polyfit of a high order (=number of data points)
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\end{itemize}
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\section{Fitting in practice}
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Fit with matlab functions lsqcurvefit, polyfit
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\subsection{Non-linear fits}
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\begin{itemize}
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\item Example that illustrates the Nebenminima Problem (with error surface)
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\item You need got initial values for the parameter!
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\item Example that fitting gets harder the more parameter yuo have.
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\item Try to fix as many parameter before doing the fit.
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\item How to test the quality of a fit? Residuals. $\chi^2$ test. Run-test.
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\end{itemize}
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\end{document}
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