TA release homework3.
This commit is contained in:
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132
hw3/report/dtx-style.sty
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132
hw3/report/dtx-style.sty
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%%
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%% This is file `dtx-style.sty',
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%% generated with the docstrip utility.
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%%
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%% The original source files were:
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%%
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%% thucoursework.dtx (with options: `dtx-style')
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%%
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%% This is a generated file.
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%%
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%% Copyright (C) 2021 by zhaofeng-shu33 <616545598@qq.com>
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%%
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%% This work may be distributed and/or modified under the
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%% conditions of the LaTeX Project Public License, either version 1.3
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%% of this license or (at your option) any later version.
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%% The latest version of this license is in
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%% http://www.latex-project.org/lppl.txt
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%% and version 1.3 or later is part of all distributions of LaTeX
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%% version 2005/12/01 or later.
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%%
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%% To produce the documentation run the original source files ending with `.dtx'
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%% through LaTeX.
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%%
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\ProvidesPackage{dtx-style}
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\RequirePackage{hypdoc}
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\RequirePackage[UTF8,scheme=chinese]{ctex}
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\RequirePackage{newpxtext}
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\RequirePackage{newpxmath}
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\RequirePackage[
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top=2.5cm, bottom=2.5cm,
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left=4cm, right=2cm,
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headsep=3mm]{geometry}
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\RequirePackage{array,longtable,booktabs}
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\RequirePackage{listings}
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\RequirePackage{fancyhdr}
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\RequirePackage{xcolor}
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\RequirePackage{enumitem}
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\RequirePackage{etoolbox}
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\RequirePackage{metalogo}
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\colorlet{thu@macro}{blue!60!black}
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\colorlet{thu@env}{blue!70!black}
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\colorlet{thu@option}{purple}
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\patchcmd{\PrintDescribeMacro}{\MacroFont}{\MacroFont\bfseries\color{thu@macro}}{}{}
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\patchcmd{\PrintDescribeEnv}{\MacroFont}{\MacroFont\bfseries\color{thu@env}}{}{}
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\patchcmd{\PrintEnvName}{\MacroFont}{\MacroFont\bfseries\color{thu@env}}{}{}
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\def\DescribeOption{%
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\leavevmode\@bsphack\begingroup\MakePrivateLetters%
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\Describe@Option}
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\def\Describe@Option#1{\endgroup
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\marginpar{\raggedleft\PrintDescribeOption{#1}}%
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\thu@special@index{option}{#1}\@esphack\ignorespaces}
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\def\PrintDescribeOption#1{\strut \MacroFont\bfseries\sffamily\color{thu@option} #1\ }
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\def\thu@special@index#1#2{\@bsphack
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\begingroup
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\HD@target
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\let\HDorg@encapchar\encapchar
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\edef\encapchar usage{%
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\HDorg@encapchar hdclindex{\the\c@HD@hypercount}{usage}%
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(#1)\encapchar usage}%
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\index{#1:\levelchar#2\actualchar
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{\string\ttfamily\space#2}\encapchar usage}%
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\endgroup
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\@esphack}
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\lstdefinestyle{lstStyleBase}{%
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basicstyle=\small\ttfamily,
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aboveskip=\medskipamount,
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belowskip=\medskipamount,
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lineskip=0pt,
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boxpos=c,
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gobble=2,
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framesep=3pt,
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rulesep=1pt,
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framerule=1pt,
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backgroundcolor=\color{gray!5},
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stringstyle=\color{green!40!black!100},
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keywordstyle=\bfseries\color{blue!50!black},
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commentstyle=\slshape\color{black!60}}
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\lstdefinestyle{lstStyleShell}{%
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style=lstStyleBase,
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frame=l,
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rulecolor=\color{purple},
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language=bash}
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\lstdefinestyle{lstStyleLaTeX}{%
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style=lstStyleBase,
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frame=l,
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rulecolor=\color{violet},
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language=[LaTeX]TeX}
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\lstnewenvironment{latex}{\lstset{style=lstStyleLaTeX}}{}
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\lstnewenvironment{shell}{\lstset{style=lstStyleShell}}{}
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\setlist{nosep}
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\DeclareDocumentCommand{\option}{m}{\textsf{#1}}
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\DeclareDocumentCommand{\env}{m}{\texttt{#1}}
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\DeclareDocumentCommand{\pkg}{s m}{%
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\texttt{#2}\IfBooleanF#1{\thu@special@index{package}{#2}}}
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\DeclareDocumentCommand{\file}{s m}{%
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\texttt{#2}\IfBooleanF#1{\thu@special@index{file}{#2}}}
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\newcommand{\myentry}[1]{%
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\marginpar{\raggedleft\color{purple}\bfseries\strut #1}}
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\newcommand{\note}[2][Note]{{%
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\color{magenta}{\bfseries #1}\emph{#2}}}
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\def\thucoursework{\textsc{Thu}\-\textsc{Coursework}}
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153
hw3/report/iidef.sty
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153
hw3/report/iidef.sty
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%%
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%% This is file `iidef.sty',
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%% generated with the docstrip utility.
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%%
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%% The original source files were:
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%%
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%% thucoursework.dtx (with options: `sty')
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%%
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%% This is a generated file.
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%%
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%% Copyright (C) 2021 by zhaofeng-shu33 <616545598@qq.com>
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%%
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%% This work may be distributed and/or modified under the
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%% conditions of the LaTeX Project Public License, either version 1.3
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%% of this license or (at your option) any later version.
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%% The latest version of this license is in
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%% http://www.latex-project.org/lppl.txt
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%% and version 1.3 or later is part of all distributions of LaTeX
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%% version 2005/12/01 or later.
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%%
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%% To produce the documentation run the original source files ending with `.dtx'
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%% through LaTeX.
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%%
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\NeedsTeXFormat{LaTeX2e}[1999/12/01]
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\ProvidesClass{iidef}
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[2020/09/09 2.6 Tsinghua University Coursework Template]
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%% configuration of nested enumerate env
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\RequirePackage{enumitem}
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%% set hwcount key-value option
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\RequirePackage{kvoptions}
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%% required by macro DeclareMathOperator
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\RequirePackage{amsmath}
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%% Set up page headers using with fancyhdr
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\@ifundefined{lhead}{\RequirePackage{fancyhdr}}
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{\def\@thulhead{thulhead}}
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\RequirePackage{amsthm}
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%% semester
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\def\@term{term}
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\newcommand{\theterm}[1]{\renewcommand\@term{#1}}
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%% institute
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\newcommand{\@courseinstitute}[1]{institute}
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\newcommand{\thecourseinstitute}[1]{\renewcommand\@courseinstitute{#1}}
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%% coursename
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\newcommand{\@coursename}[1]{coursename}
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\newcommand{\thecoursename}[1]{\renewcommand\@coursename{\textsc{#1}}}
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%% user can rewrite homework name
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\def\@hwname{Homework}
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\def\hwname#1{\renewcommand\@hwname{#1}}
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%% \iidef@thehwcnt = 1
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\DeclareStringOption[1]{thehwcnt}
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\ProcessKeyvalOptions*
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\def\thehwcnt{\iidef@thehwcnt}
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%% page header setup, distinguish between first page(plain style)
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%% and second page on (runningpage style)
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%%***************************************************************************
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\newcommand{\courseheader}{
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\thispagestyle{plain}%first page use native plain style to suppress header
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\vspace*{-1in}
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\begin{center}
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\@courseinstitute\\
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\@coursename\\
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\@term
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\vspace*{0.1in}
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\hrule
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\end{center}
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\begin{center}
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\underline{\bf \@hwname\;\thehwcnt} \\
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\end{center}
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}
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\@ifundefined{@thulhead}{
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\fancypagestyle{runningpage}
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{
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\fancyhead[L]{\small\@coursename}
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\fancyhead[R]{\small\@courseinstitute}
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}
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%% use runningpage style from second page on
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\pagestyle{runningpage}
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}{}
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%% *********************************************************************************************
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%%name command macro
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%%*************************
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\newcommand{\name}[1]{
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\begin{flushleft}
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#1\hfill
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\today
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\end{flushleft}
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\hrule
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\vspace{2em}
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\flushleft
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}
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%%*************************
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%% enumitem related configuration
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\setlist[enumerate,1]{label=\thehwcnt.\arabic*.}
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\setlist[enumerate,2]{label=(\alph*)}
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\setlist[enumerate,3]{label=\roman*.}
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\setlist[enumerate,4]{label=\greek*}
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%%******************************
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\def\@slname{Solution}
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\def\slname#1{\renewcommand\@slname{#1}}
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\@ifundefined{solution}{
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\newenvironment{solution}
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{
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\proof[\@slname]
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}
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{
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%% no qed symbol in solution env
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\renewcommand{\qedsymbol}{}
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\endproof
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}
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}{}
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%%******************************
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%%common math symbols go here
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%%*************************************************
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\def\v#1{\underline{#1}}
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\newcommand{\uc}{\underline{c}} % c, vec
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\newcommand{\uv}{\underline{v}} % x, vec
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\newcommand{\uw}{\underline{w}} % w, vec
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\newcommand{\ux}{\underline{x}} % x, vec
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\newcommand{\uy}{\underline{y}} % y, vec
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\newcommand{\uz}{\underline{z}} % z, vec
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\newcommand{\um}{\underline{m}} % m, vec
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\newcommand{\rvx}{\mathsf{x}} % x, r.v.
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\newcommand{\rvy}{\mathsf{y}} % y, r.v.
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\newcommand{\rvz}{\mathsf{z}} % z, r.v.
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\newcommand{\rvw}{\mathsf{w}} % w, r.v.
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\newcommand{\rvH}{\mathsf{H}} % H, r.v.
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\newcommand{\urvx}{\underline{\mathsf{x}}} % x, r.v. vec
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\newcommand{\urvy}{\underline{\mathsf{y}}} % y, r.v. vec
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\newcommand{\urvz}{\underline{\mathsf{z}}} % z, r.v. vec
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\newcommand{\urvw}{\underline{\mathsf{w}}} % w, r.v. vec
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\newcommand{\defas}{\triangleq} %\coloneqq
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\newcommand{\reals}{\mathbb{R}}
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\newcommand{\TT}{\mathrm{T}} % transpose
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\DeclareMathOperator*{\argmax}{arg\,max}
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\DeclareMathOperator*{\argmin}{arg\,min}
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\DeclareMathOperator*{\argsup}{arg\,sup}
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\DeclareMathOperator*{\arginf}{arg\,inf}
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\DeclareMathOperator{\diag}{diag}
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\DeclareMathOperator{\Var}{Var}
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\DeclareMathOperator{\Cov}{Cov}
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\DeclareMathOperator{\MSE}{MSE}
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\DeclareMathOperator{\1}{\mathds{1}}
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\DeclareMathOperator{\In}{\mathbb{I}}
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\DeclareMathOperator{\E}{\mathbb{E}}
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\DeclareMathOperator{\Prob}{\mathbb{P}}
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\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}}
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\def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}
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%%************************************************************************************
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101
hw3/report/main.tex
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hw3/report/main.tex
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% Homework Template
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\documentclass[a4paper]{article}
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\usepackage{ctex}
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\usepackage{amsmath, amssymb, amsthm}
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\usepackage{moreenum}
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\usepackage{mathtools}
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\usepackage{url}
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\usepackage{bm}
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\usepackage{enumitem}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{booktabs} % toprule
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\usepackage[mathcal]{eucal}
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\usepackage[thehwcnt = 3]{iidef}
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\thecourseinstitute{清华大学电子工程系}
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\thecoursename{\textbf{媒体与认知}}
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\theterm{2023-2024学年春季学期}
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\hwname{作业}
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\begin{document}
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\courseheader
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% 请在YOUR NAME处填写自己的姓名
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\name{YOUR NAME}
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\vspace{3mm}
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\centerline{\textbf{\Large{理论部分}}}
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\section{单选题（15分）}
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% 请在？处填写答案
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\subsection{\underline{?}}
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\subsection{\underline{?}}
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\subsection{\underline{?}}
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\subsection{\underline{?}}
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\subsection{\underline{?}}
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\section{计算题（15 分）}
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\subsection{给定两个类别的样本分别为:
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\begin{align*}
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&\omega_1:\{(3,1),(2,2),(4,3),(3,2)\} \\
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&\omega_2:\{(1,3),(1,2),(-1,1),(-1,2)\}
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\end{align*}
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试利用LDA，将样本特征维数压缩为一维。
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}
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\vspace{3mm}
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\subsection{模型训练通常需要大量的数据，假设某采集的数据集包含80\%的有效数据和20\%的无效数据。采用一种算法判断数据是否有效，其中无效数据被成功判别为无效数据的概率为90\%，而有效数据被误判为无效数据的概率为5\%。如果某条数据经过该算法被判别为无效数据，则根据贝叶斯定理，这条数据是无效数据的概率是多少？(提示：全概率公式$P(Y)=\sum^{N}_{i=1}P(Y|X_i)P(X_i)$)\\}
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\vspace{3mm}
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\subsection{设有两类正态分布的样本集，第一类均值为$\mu_1=[2,-1]^T$，第二类均值为$\mu_2=[1,1]^T$。两类样本集的协方差矩阵和出现的先验概率都相等：$\Sigma_1=\Sigma_2=\Sigma=\left[ \begin{array}{cc}
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4 & 2 \\
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2 & \frac{4}{3}
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\end{array} \right]$，$p(\omega_1)=p(\omega_2)$。试计算分类界面，并对特征向量$x=[6,2]^T$分类。}
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\vspace{3mm}
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\subsection{给定异或的样本集$D=\left\{\left((0,0)^T,-1\right),\left((0,1)^T,1\right),\left((1,0)^T,1\right),\left((1,1)^T,-1\right)\right\}$该样本集是线性不可分的，可采用如下所示的多项式函数$\phi(\mathbf{x})$将样本$D=\left\{(\mathbf{x}_n,y_n)\right\}$映射为$D_\phi=\left\{(\phi(\mathbf{x}_n),y_n)\right\}$，其中$\phi(\mathbf{x})$满足
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\begin{equation*}
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\begin{aligned}
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\phi_1(\mathbf{x})&=2(x_1-0.5) \\
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\phi_2(\mathbf{x})&=4(x_1-0.5)(x_2-0.5)
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\end{aligned}
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\end{equation*}
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\\
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\qquad(1) 给出映射后的样本集；\\
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\qquad(2) 在映射后的样本集中，设计一个线性SVM分类器，给出支持向量及分类界面。
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}
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\vspace{3mm}
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\subsection{使用KMeans算法对2维空间中的6个点$(0,2)$,$(2,0)$,$(2,3)$,$(3,2)$,$(4,0)$,$(5,4)$进行聚类，距离函数选择欧氏距离$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$。\\
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\qquad (1)起始聚类中心选择(0,0)和(4,3)，计算聚类中心；\\
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\qquad (2)起始聚类中心选择(1,4)和(3,1)，计算聚类中心。\\
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}
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\vspace{3mm}
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\centerline{\textbf{\Large{编程部分}}}
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\vspace{3mm}
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% 请根据是否选择自选课题的情况选择“编程作业报告”或“自选课题进度汇报”中的一项完成
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\section{编程作业报告}
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% 请在此处完成编程作业报告
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\section{自选课题进度汇报}
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% 请在此处介绍自选课题
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\end{document}
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%%% Local Variables:
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%%% mode: late\rvx
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%%% TeX-master: t
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%%% End:
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