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author | Karl Berry <karl@freefriends.org> | 2018-04-01 22:28:35 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2018-04-01 22:28:35 +0000 |
commit | a90952824018c8cc8372c913f1778fc7a7ed2e37 (patch) | |
tree | a3c582e4ce7450b449e3b39424e9d92ff395f6e6 /Master/texmf-dist/doc/latex/thucoursework/iihw.tex | |
parent | 7d7e6b60a7a00f27ba7119097bc7484ef28fb826 (diff) |
thucoursework (2apr18)
git-svn-id: svn://tug.org/texlive/trunk@47227 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/thucoursework/iihw.tex b/Master/texmf-dist/doc/latex/thucoursework/iihw.tex new file mode 100644 index 00000000000..b444b3d01b0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thucoursework/iihw.tex @@ -0,0 +1,162 @@ +% Sample tex file for usage of iidef.sty +% Homework template for Inference and Information +% UPDATE: October 12, 2017 by Xiangxiang +% UPDATE: 22/03/2018 by zhaofeng-shu33 +\documentclass[a4paper]{article} +\usepackage[T1]{fontenc} +\usepackage{amsmath, amssymb, amsthm} +% amsmath: equation*, amssymb: mathbb, amsthm: proof +\usepackage{moreenum} +\usepackage{mathtools} +\usepackage{url} +\usepackage[outdir=./]{epstopdf} +\usepackage{graphicx} +\usepackage{subcaption} +\usepackage{booktabs} % toprule +\usepackage[mathcal]{eucal} +\usepackage{dsfont} + +\usepackage[numbered,framed]{matlab-prettifier} +\lstset{ + style = Matlab-editor, + captionpos =b, + basicstyle = \mlttfamily, + escapechar = ", + mlshowsectionrules = true, +} + +\usepackage[thehwcnt = 6]{iidef} +\thecourseinstitute{Tsinghua-Berkeley Shenzhen Institute} +\thecoursename{Information Inference} +\theterm{Fall 2017} +\hwname{Coursework} +\begin{document} +\courseheader +\name{YOUR NAME} +\rule{\textwidth}{1pt} +\begin{itemize} +\item {\bf Acknowledgments: \/} + This template takes some materials from course CSE 547/Stat 548 of Washington University: \small{\url{https://courses.cs.washington.edu/courses/cse547/17sp/index.html}}. + + If you refer to other materials in your homework, please list here. +\item {\bf Collaborators: \/} + I finish this template by myself. If you finish your homework all by yourself, make a similar statement. If you get help from others in finishing your homework, state like this: + \begin{itemize} + \item 1.2 (b) was solved with the help from \underline{\hspace{3em}}. + \item Discussion with \underline{\hspace{3em}} helped me finishing 1.3. + \end{itemize} +\end{itemize} +\rule{\textwidth}{1pt} + +\vspace{2em} + +You may use \texttt{enumerate} to generate answers for each question: + +\begin{enumerate} + \setlength{\itemsep}{3\parskip} + + \item Type of commonly used notations. Use another \texttt{enumerate} to start generate answers for sub-questions: + \begin{enumerate} + \item Use \verb|$ $| to get an inline equation: $\Prob(A) = \E[\1_A(\omega)]$. + \item Use \texttt{equation} to have equation in display math mode: + \begin{equation} + \frac{a + b}{2} \geq \sqrt{ab} + \label{eq:1} + \end{equation} + + \item Use \verb|\eqref| to get reference for equations: \eqref{eq:1} holds when $a\geq 0, b\geq 0$. + + \item Now we would introduce some commonly used notations: + \begin{enumerate} + \item Use \verb|\mathbb{P}, \mathbb{R}, \mathbb{E}| to type $\mathbb{P}, \mathbb{R}, \mathbb{E}$. + \item Use \verb|\mathcal{A}, \mathcal{X}, \mathcal{Y}, \mathcal{N}| to type $\mathcal{A}, \mathcal{X}, \mathcal{Y}, \mathcal{N}$. + \item Use \verb|\underline{x}, \underline{y}| to type vectors $\underline{x}, \underline{y}$. + \item Use \verb|\mathsf{x}, \mathsf{y}, \mathsf{z}| to type random variables $\rvx, \rvy, \rvz$. For simplicity, I have defined several macros so you could simply type \verb|\rvx, \rvy, \rvz|. Don't forget \verb|$ $|! + \item Thanks to these macros, we could have $\reals, \E[\rvx], \Var(\rvy), \Prob(A), \independent, \1$ by typing \verb|\reals, \E[\rvx], \Var(\rvy), \Prob(A),\independent,| \verb|\1|. + \item Now you can use \verb|\ux, \uy, \uz| to type vectors $\ux, \uy, \uz$, and use \verb|\urvx, \urvy, \urvz| to type random vectors $\urvx, \urvy, \urvz$. + \item Remember that $P_{\rvx|\rvy}(x|y) \defas \Prob(\rvx = x|\rvy = y)$. + \begin{enumerate} + \item Writing $\Prob(x)$ is wrong. $\Prob$ should only operate on events. + \item $\rvx$ is a random variable, while $x$ is a real number. + \end{enumerate} + + \end{enumerate} + \item You may find \url{https://en.wikibooks.org/wiki/LaTeX} useful. + \item Writing \LaTeX\ online may be easier for beginners: + \begin{enumerate} + \item ShareLaTeX: \url{https://www.sharelatex.com/}. + \item Overleaf: \url{https://www.overleaf.com/}. + \end{enumerate} + \end{enumerate} + \item You may need aligned equations for your homework, here are several examples: + + Total propability rule: + \begin{equation*} + \begin{aligned} + \Prob(\rvx = x) + &= \sum_{y \in \mathcal{Y}} \Prob(\rvx = x, \rvy = y)\\ + &= \sum_{y \in \mathcal{Y}} \Prob(\rvx = x| \rvy = y) \Prob(\rvy = y),\\ + \end{aligned} + \end{equation*} + or + \begin{equation*} + \begin{aligned} + &\quad~ P_{\rvx}(x)\\ + &= \sum_{y \in \mathcal{Y}} P_{\rvx\rvy}(x,y)\\ + &= \sum_{y \in \mathcal{Y}} P_{\rvx|\rvy}(x|y)P_{\rvy}(y).\\ + \end{aligned} + \end{equation*} + Indicator function: + \begin{equation*} + \1_A(\omega)= + \left\{ + \begin{aligned} + 1, &\quad\text{if}~ \omega \in A,\\ + 0, &\quad\text{if}~ \omega \notin A. + \end{aligned} + \right. + \end{equation*} + + \item You may need to add figure and source codes in your homework. Figure \ref{fig:1} is an example that compares the empirical distribution (histogram) and probability density function of the Gaussian random variable. + \begin{figure}[htbp] + \centering + \includegraphics[width = 0.8\textwidth]{pdf_normal.eps} + \caption{Gaussian PDF and histogram of samples} + \label{fig:1} + \end{figure} + + The source code to plot Figure \ref{fig:1} could be found in Appendix \ref{sec:a:code}. Here are the core codes: + \lstinputlisting[firstline=4,lastline=4, firstnumber=4]{matlabscript.m} + \lstinputlisting[firstline=6,lastline=7, firstnumber=6]{matlabscript.m} + To understand line 6, note that if we have $n$ samples of $\rvx$ denoted by $x^{(i)}, i = 1, 2, \cdots, n$, then the probability density function $p_{\rvx}$ could be estimated as + \begin{equation*} + \begin{aligned} + p_{\rvx}(x_0) &= \left.\frac{\mathrm{d}}{\mathrm{d}x} \Prob(\rvx \leq x) \right|_{x = x_0} \\ + &\approx \frac{\Prob(x_0 - \Delta x < \rvx \leq x_0)}{\Delta x}\\ + &\approx \frac{1}{n\Delta x} \sum_{i = 1}^n \1_{x^{(i)} \in (x_0 - \Delta x, x_0]}. + \end{aligned} + \end{equation*} + +\item An example of hypothesis testing: + \begin{equation*} + \log \frac{\Prob(\rvH = H_1|\rvy = y)}{\Prob(\rvH = H_0|\rvy = y)} + \mathop{\gtreqless}_{\hat{\rvH} = H_0}^{\hat{\rvH} = H_1} \gamma + \end{equation*} + + \end{enumerate} + + + \newpage + + \appendix + \section{Source code} + \label{sec:a:code} + % \lstlistoflistings + Source code for plotting Figure \ref{fig:1} is shown as follows. + \lstinputlisting[caption=FigurePlot]{matlabscript.m} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: |