From 7ac6ed701f7972beae25221c07867529f70d3592 Mon Sep 17 00:00:00 2001 From: Andrew Date: Wed, 25 Sep 2024 16:23:09 +0100 Subject: [PATCH] [CT4101]: Add Week 3 lecture notes + slides --- .../notes/CT4101-Notes.pdf | Bin 102143 -> 627514 bytes .../notes/CT4101-Notes.tex | 274 +++++++++++++++++- .../images/classification_data_example.png | Bin 0 -> 187158 bytes .../images/decision_tree_college_athletes.png | Bin 0 -> 79120 bytes .../images/example_binary_classification.png | Bin 0 -> 76681 bytes .../feature_space_lot_college_athlete.png | Bin 0 -> 43736 bytes ..._lot_college_athlete_decision_boundary.png | Bin 0 -> 62435 bytes .../gaussian_process_college_athletes.png | Bin 0 -> 71853 bytes .../logistic_regression_college_athletes.png | Bin 0 -> 69193 bytes .../images/supervised_learning_overview.png | Bin 0 -> 44252 bytes .../slides/CT4101 - 03 - Classification-1.pdf | Bin 0 -> 4802654 bytes 11 files changed, 273 insertions(+), 1 deletion(-) create mode 100644 year4/semester1/CT4101: 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zXv!{P#Vax~+xH0X#tAb=mQLV=l+m9kOGlu5``zE6dW4~7l{-YRL%uW1xLYLf+tF1)q+0W8Oa{fzR z_O)5ipIPxrE7pF$px-9e#s@rIF{b&7t|6-?)vnTdsZa1J3D+IJcb}=Pz||qWA1?*) z+Aie|H%jqUcnJ-rJD>4a_VyhN>;QK!Dat_d&%>f7VwBLoTTHaZKi;UC zE?j+Z#n?)J0+;Y$5n)q7TF13qF`QoeFr3^BIEYiy#*nfYZaF$FW3No+|SVU5on3EHt Hr%L=^7(l$r diff --git a/year4/semester1/CT4101: Machine Learning/notes/CT4101-Notes.tex b/year4/semester1/CT4101: Machine Learning/notes/CT4101-Notes.tex index e6412da0..863ec5f2 100644 --- a/year4/semester1/CT4101: Machine Learning/notes/CT4101-Notes.tex +++ b/year4/semester1/CT4101: Machine Learning/notes/CT4101-Notes.tex @@ -2,6 +2,7 @@ \documentclass[a4paper,11pt]{article} % packages \usepackage{censor} +\usepackage{multicol} \StopCensoring \usepackage{fontspec} \setmainfont{EB Garamond} @@ -374,12 +375,283 @@ According to PEP 8, different naming conventions are used for different identifi ``Class names should normally use the CapWords convention''. This helps programmers to quickly \& easily distinguish which category an identifier name represents. +\subsubsection{Whitespace in Python} +A key difference between Python and other languages such as C is that whitespace has meaning in Python. +The PEP 8 style guidelines say to ``Use 4 spaces per indentation level'', not 2 spaces, and not a tab character. +This applies to all indented code blocks. + \subsection{Dynamic Typing} In Python, variable names can point to objects of any type. Built-in data types in python include \mintinline{python}{str}, \mintinline{python}{int}, \mintinline{python}{float}, etc. Each type can hold a different type of data. -As we saw, \mintinline{python}{str} can hold any combination of characters. +Because variables in Python are simply pointers to objects, the variable names themselves do not have any attached +type information. +Types are linked not to the variable names but to the objects themselves. + +\begin{code} +\begin{minted}[linenos, breaklines, frame=single]{python} +x = 4 +print(type(x)) # prints "" to the console +x = "Hello World!" +print(type(x)) # prints "" to the console +x = 3.14159 +print(type(x)) # prints "" to the console +\end{minted} +\caption{Dynamic Typing Example} +\end{code} + +Note that \mintinline{python}{type()} is a built-in function that returns the type of any object that is passed to +it as an argument. +It returns a \textbf{type object}. +\\\\ +Because the type of object referred to by a variable is not known until runtime, we say that Python is a +\textbf{dynamically typed language}. +In \textbf{statically typed languages}, we must declare the type of a variable before it is used: the type of +every variable is known before runtime. +\\\\ +Another important difference between Python and statically typed languages is that we do not need to declare +variables before we use them. +Assigning a value to a previously undeclared variable name is fine in Python. + +\subsection{Modules, Packages, \& Virtual Environments} +\subsubsection{Modules} +A \textbf{module} is an object that serves as an organisational unit of Python code. +Modules have a \textit{namespace} containing arbitrary Python objects and are loaded into Python by the process +of \textit{importing}. +A module is essentially a file containing Python definitions \& statements. +\\\\ +Modules can be run either as standalone scripts or they can be \textbf{imported} into other modules so that their +built-in variables, functions, classes, etc. can be used. +Typically, modules group together statements, functions, classes, etc. with related functionality. +When developing larger programs, it is convenient to split the source code up into separate modules. +As well as creating our own modules to break up our source code into smaller units, we can also import built-in +modules that come with Python, as well as modules developed by third parties. +\\\\ +Python provides a comprehensive set of built-in modules for commonly used functionality, e.g. mathematical +functions, date \& tie, error handling, random number generation, handling command-line arguments, parallel +processing, networking, sending email messages, etc. +Examples of modules that are built-in to Python include \mintinline{python}{math}, \mintinline{python}{string}, +\mintinline{python}{argparse}, \mintinline{python}{calendar}, etc. +The \mintinline{python}{math} module is one of the most commonly used modules in Python, although the functions +in the \mintinline{python}{math} module do not support complex numbers; if you require complex number support, +you can use the \mintinline{python}{cmath} module. +A full list of built-in modules is available at \url{https://docs.python.org/3/py-modindex.html}. + +\subsubsection{Packages} +\textbf{Packages} are a way of structuring Python's module namespace by using ``dotted module names'': +for example, the module name \mintinline{python}{A.B} designates a submodule named \mintinline{python}{B} in a +package \mintinline{python}{A}. +Just like the use of modules saves the authors of different modules from having to worry about each other's global +variable names, the use of dotted module names saves the authors of multi-module packages like +\mintinline{python}{NumPy} or \mintinline{python}{Pillow} from having to worry about each other's module names. +Individual modules can be imported from a package: \mintinline{python}{import sound.effects.echo}. +\\\\ +PEP 8 states that ``Modules should have short, all-lowercase names. +Underscores can be used in the module name if it improves readability. +Python packages should also have short, all-lowercase names, although the use of underscores is discouraged.'' + +\subsubsection{Managing Packages with \mintinline{shell}{pip}} +\textbf{\mintinline{shell}{pip}} can be used to install, upgrade, \& remove packages and is supplied by default with +your Python installation. +By default, \mintinline{shell}{pip} will install packages from the Python Package Index (PyPI) \url{https://pypi.org}. +You can browse the Python Package Index by visiting it in your web browser. +To install packages from PyPI: +\begin{minted}[linenos, breaklines, frame=single]{shell} +python -m pip install projectname +\end{minted} + +To upgrade a package to the latest version: +\begin{minted}[linenos, breaklines, frame=single]{shell} +python -m pip install --upgrade projectname +\end{minted} + + + +\subsubsection{Virtual Environments} +Python applications will often use packages \& modules that don't come as part of the standard library. +Applications will sometimes need a specific version of a library, because the application may require that a +particular bug has been fixed or the application may have been written using an obsolete version of the library's +interface. +This means that it may not be possible for one Python installation to meet the requirements of every application. +If application $A$ needs version 1.0 of a particular module but application $B$ needs version 2.0, then the +requirements are in conflict and installing either version 1.0 or 2.0 will leave one application unable to run. +The solution for this problem is to create a \textbf{virtual environment}, a self-contained directory tree that +contains a Python installation for a particular version of Python plus a number of additional packages. +Different applications can then use different virtual environments. +\\\\ +By default, most IDEs will create a new virtual environment for each new project created. +It is also possible to set up a project to run on a specific pre-configured virtual environment. +The built-in module \mintinline{python}{venv} can also be used to create \& manage virtual environments through +the console. +\\\\ +To use the \mintinline{python}{venv} module, first decide where you want the virtual environment to be created, +then open a command line at that location use the command \mintinline{bash}{python -m venv environmentname} to +create a virtual environment with the specified name. +You should then see the directory containing the virtual environment appear on the file system, which can then be +activated using the command \mintinline{shell}{source environmentname/bin/activate}. +\\\\ +To install a package to a virtual environment, first activate the virtual environment that you plan to install it to +and then enter the command \mintinline{shell}{python -m pip install packagename}. +\\\\ +If you have installed packages to a virtual environment, you will need to make that virtual environment available +to Jupyter Lab so that your \verb|.ipynb| files can be executed on the correct environment. +You can use the package \verb|ipykrenel| to do this. + +\section{Classification} +\subsection{Supervised Learning Principles} +Recall from before that there are several main types of machine learning techniques, including \textbf{supervised +learning}, unsupervised learning, semi-supervised learning, \& reinforcement learning. +Supervised learning tasks include both \textbf{classification} \& regression. +\\\\ +The task definition of supervised learning is to, given examples, return a function $h$ (hypothesis) that +approximates some ``true'' function $f$ that (hypothetically) generated the labels for the examples. +We need to have a set of examples called the \textbf{training data}, each having a \textbf{label} \& a set of +\textbf{attributes} that have known \textbf{values}. +\\\\ +We consider the labels (classes) to be the outputs of some function $f$: the observed attributes are its inputs. +We denote the attribute value inputs $x$ and labels are their corresponding outputs $f(x)$. +An example is a pair $(x, f(x))$. +The function $f$ is unknown, and we want to discover an approximation of it $h$. +We can then use $h$ to predict labels of new data (generalisation). +This is also known as \textbf{pure inductive learning}. + +\begin{figure}[H] + \centering + \includegraphics[width=\textwidth]{./images/classification_data_example.png} + \caption{Training Data Example for a Classification Task} +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[width=0.6\textwidth]{./images/supervised_learning_overview.png} + \caption{Overview of the Supervised Learning Process} +\end{figure} + +\subsection{Introduction to Classification} +The simplest type of classification task is where instances are assigned to one of two categories: this is referred +to as a \textbf{binary classification task} or two-class classification task. +Many popular machine learning problems fall into this category: +\begin{itemize} + \item Is cancer present in a scan? (Yes / No). + \item Should this loan be approved? (Yes / No). + \item Sentiment analysis in text reviews of products (Positive / Negative). + \item Face detection in images (Present / Not Present). +\end{itemize} + +The more general form of classification task is the \textbf{mutli-class classification} where the number of classes +is $\geq 3$. + +\subsubsection{Example Binary Classification Task} +Objective: build a binary classifier to predict whether a new previously unknown athlete who did not feature in the +dataset should be drafted. + +\begin{minipage}{0.5\textwidth} + There are 20 examples in the dataset, see \verb|college_athletes.csv| on Canvas. + \\\\ + The college athlete's dataset contains two attributes: + \begin{itemize} + \item Speed (continuous variable). + \item Agility (continuous variable). + \end{itemize} + + The target data: whether or not each athlete was drafted to a professional team (yes / no). +\end{minipage} +\hfill +\begin{minipage}{0.5\textwidth} + \begin{figure}[H] + \centering + \includegraphics[width=0.6\textwidth]{./images/example_binary_classification.png} + \caption{Example Dataset for a Binary Classification Task} + \end{figure} +\end{minipage} + +\begin{figure}[H] + \centering + \includegraphics[width=0.6\textwidth]{./images/feature_space_lot_college_athlete.png} + \caption{Feature Space Plot for the College Athlete's Dataset} +\end{figure} + +We want to decide on a reasonable \textbf{decision boundary} to categorise new unseen examples, such as the one +denoted by the purple question mark below. +We need algorithms that will generate a hypothesis / model consistent with the training data. +Is the decision boundary shown below in thin black lines a good one? +It is consistent with all of the training data, but it was drawn manually; in general, it won't be possible to +manually draw such decision boundaries when dealing with higher dimensional data (e.g., more than 3 features). + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{./images/feature_space_lot_college_athlete_decision_boundary.png} + \caption{Feature Space Plot for the College Athlete's Dataset} +\end{figure} + +\subsubsection{Example Classification Algorithms} +There are many machine learning algorithms available to learn a classification hypothesis / model. +Some examples (with corresponding scikit-learn classes) are: +\begin{itemize} + \item $k$-nearest neighbours: scikit-learn \verb|KNeighboursClassifier|. + \item Decision trees: scikit-learn \verb|DecisionTreeClassifier|. + \item Gaussian Processes: scikit-learn \verb|GaussianProcessClassifier|. + \item Neural networks: scikit-learn \verb|MLPClassifier|. + \item Logistic regression: scikit-learn \verb|LogisticRegression|. + Note that despite its name, logistic regression is a linear model for classification rather than regression. +\end{itemize} + +\subsubsection{Logistic Regression on the College Athletes Dataset} +Below is an example of a very simple hypothesis generated using an ML model -- a linear classifier created using the +scikit-learn \verb|LogisticRegression| with the default settings. + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{./images/logistic_regression_college_athletes.png} + \caption{Logistic Regression on the College Athletes Dataset} +\end{figure} + +Is this a good decision boundary? +$\frac{19}{21}$ training examples correct = $90.4\%$ accuracy. +Note how the decision boundary is a straight line (in 2D). +Note also that using logistic regression makes a strong underlying assumption that the data is +\textbf{linearly separable}. + +\subsubsection{Decision Tree on the College Athletes Dataset} +Below is an example of a more complex hypothesis, generated using the scikit-learn \verb|DecisionTreeClassifier| +with the default settings. + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{./images/decision_tree_college_athletes.png} + \caption{Decision Tree on the College Athletes Dataset} +\end{figure} + +Note the two linear decision boundaries: this is a very different form of hypothesis compared to logistic +regression. +Is this a good decision boundary? +$\frac{21}{21}$ training examples correct = $100\%$ accuracy. + +\subsubsection{Gaussian Process on the College Athletes Dataset} +Below is an example of a much more complex hypothesis generated using the scikit-learn +\verb|GaussianProcessClassifier| with the default settings. + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{./images/gaussian_process_college_athletes.png} + \caption{Gaussian Process on the College Athletes Dataset} +\end{figure} + +Note the smoothness of the decision boundary compared to the other methods. +Is this a good decision boundary? +$\frac{21}{21}$ training examples correct = $100\%$ accuracy. +\\\\ +Which of the three models explored should we choose? +It's complicated; we need to consider factors such as accuracy of the training data \& independent test data, +complexity of the hypothesis, per-class accuracy etc. + +\subsubsection{Use of Independent Test Data} +Use of separate training \& test datasets is very important when developing an ML model. +If you use all of your data for training, your model could potentially have good performance on the training data +but poor performance on new independent test data. + + diff --git a/year4/semester1/CT4101: Machine Learning/notes/images/classification_data_example.png b/year4/semester1/CT4101: Machine Learning/notes/images/classification_data_example.png new file mode 100644 index 0000000000000000000000000000000000000000..244a56e3c4e1525dfcef49c5e8b6da408d306eb5 GIT binary patch literal 187158 zcmce-hd-PD*FR3FQmbg~(VDd>wMU0ptE$xAqxPy*g4SM9d()z{_KYod5Tj-g#NK+uK@$(7eQuXCQ~`8+4=t*SiXed_xd7#M_#3Nr67FmS>#Fz!s@ z;sCGUFkzlyU_8c9lzI8yGkt5u!{?#fHEbWzx5N4*iaC(hak&j+!pRBYV%I>_j`x@FURrzs<5lr`t*<43opY|uR zM);i!Fi}(E`5+`MpoZifQ*%vIF8a^pF?i5r?QQ6RGr za>w}J?*^7jVFJX;hv?!vu&j0a*R~ z|MNbmZ|xUNqvfqJewRcF4q)-`N&eR%%bi?*UN6}xx=ezwH!z5-;lg-flZ0(bn$rex zt|Oc}QJyO04-ciq{jcFERJvYrUx{8PUXvgsg-)2X`eq1PL-G5|ch@MuK zV?Fqf(E-0>x_MT!c zaXKL^mC3N1Q~sZ42^hJ@idwM>GK}y3akPJTKKIKTe2%lDFGd)lU^JicD=RTV1(vgK zB8?W9iTRGE`;lW9mm;==O)z)kiAPQC;KTFyAWg+=dZuAYXE%mev5s<((%r)5zLka~ z0rmlQ$G3LCj!Eppq6=bWuvB;ZWO>2U5#!=zR_38)M{wuz_@`q=(v(@E|JgQ1!lf{0SMN&p_0$+AD-^MiqA@&qi4?*Bb}ySb zCUjKM5%+(LC+4b!Y?1Y+h6ILt%a6uCG!;@pqV*fAMUF1NCw7pFu9J}V!?@L0QR#dB zOoMA}%Z`!iz~XP@4!hot?B0)Mc+z3th?=^gy5d?@9gg!pp1#NS*wNNxWlVP5%3276 z?_8bLO_YUrpxSa{oMQfKap#$8#JAMc&lovKsO6w<78>Qp057Rq_8!1!?+_%!p%?Wp zEN%WQoxX^697q>!6x~$W@|Rsh*Af!6w|uIrU0R5s6f;*~lEtl@{Ty+mCf!+4q$~B> z-(fjAOkk$LL;CG}SZKH5$DwBh8>{}jM>k~Eb`(m8R(qYpZSn&|{NCI*wCDv2 zHe}|h8!#|0!nZhRbO`s}^f!)Ot3V_$lg6B@|Bd6150Q>gAjn)ap7g@w<3DI^9tnmi zDP)_4oTU26KBPzwnk3|Wmu$1;0nC>_oj`28bz8|OR{o}Mo! z871#;aC&07Z_{0RcVLgaejlG!G5n4t{Nzu?GTaNaqU@7kcxPazN11Ho6B!*@=bj0S zZck>YK(kQ0&V>cMxVJ*%$afJiiGBGcRr)nXu;M!xPO&OS`O?g$(1_^8wU+@33JM}` zO(H@Suq}cN6G8PcQPLD|%Sr-!N&Pex>!u^KbtOJhKhlGH;SR5br9gNijUCB3v^iRRL)8TllX>BYJjofx=h57+dN;MDEyhMSfFzbB&8vq$?sM zi-a8b)u4!i)959=_fKd_hiV*AS9B$zp)zxv#Crqw5!!s*Omj3T|p1hzCzz$3M-kA4f4tE7rjpD? 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