From 865505673a5f659028762c2ddd2160863075e60f Mon Sep 17 00:00:00 2001 From: Andrew Date: Thu, 24 Oct 2024 20:41:12 +0100 Subject: [PATCH] [CT4100]: Add Week 7 lecture notes --- .../notes/CT4100-Notes.pdf | Bin 378212 -> 576619 bytes .../notes/CT4100-Notes.tex | 255 ++++++++++++++++++ .../notes/images/crossover.png | Bin 0 -> 79961 bytes .../notes/images/mutation.png | Bin 0 -> 37558 bytes .../notes/images/threestages.png | Bin 0 -> 129201 bytes 5 files changed, 255 insertions(+) create mode 100644 year4/semester1/CT4100: Information Retrieval/notes/images/crossover.png create mode 100644 year4/semester1/CT4100: Information Retrieval/notes/images/mutation.png create mode 100644 year4/semester1/CT4100: Information Retrieval/notes/images/threestages.png diff --git a/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.pdf b/year4/semester1/CT4100: Information Retrieval/notes/CT4100-Notes.pdf index 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(population) -- (fitness); + \draw [arrow] (fitness) -- (select); + \draw [arrow] (select) -- (reproduction); + \draw [arrow] (reproduction) -- (population); + \end{tikzpicture} + \caption{Genetic Algorithm Steps} +\end{figure} + +Traditionally, solutions are represented in binary. +A \textbf{phenotype} is the decoding or manifestation of a \textbf{genotype} which is the encoding or representation of a phenotype. +We need an evaluation function which will discriminate between better and worse solutions. +\begin{tcolorbox}[colback=gray!10, colframe=black, title=\textbf{Crossover Examples}] +Example of one-point crossover: +\texttt{11001\underline{011}} and \texttt{11011\underline{111}} gives \texttt{11001\underline{111}} and \texttt{11011\underline{011}}. +\\\\ +Example of $n$-point crossover: \texttt{\underline{110}110\underline{11}0} and \texttt{0001001000} gives \texttt{\underline{110}100\texttt{11}00} and \texttt{000\underline{110}10\underline{01}}. +\end{tcolorbox} + +\textbf{Mutation} occurs in the genetic algorithm at a much lower rate than crossover. +It is important to add some diversity to the population in the hope that new better solutions are discovered and therefore it aids in the evolution of the population. +\begin{tcolorbox}[colback=gray!10, colframe=black, title=\textbf{Mutation Example}] +Example of mutation: \texttt{1\underline{1}001001} $\rightarrow$ \texttt{1\underline{0}001001}. +\end{tcolorbox} + +There are two types of selection: +\begin{itemize} + \item \textbf{Roulette wheel selection:} each sector in the wheel is proportional to an individual's fitness. + Select $n$ individuals by means of $n$ roulette turns. + Each individual is drawn independently. + \item \textbf{Tournament selection:} a number of individuals are selected at random with replacement from the population. + The individual with the best score is selected. + This is repeated $n$ times. +\end{itemize} + +Issues with genetic algorithms include: +\begin{itemize} + \item Choice of representation for encoding individuals. + \item Definition of fitness function. + \item Definition of selection scheme. + \item Definition of suitable genetic operators. + \item Setting of parameters: + \begin{itemize} + \item Size of population. + \item Number of generations. + \item Probability of crossover. + \item Probability of mutation. + \end{itemize} +\end{itemize} + +\begin{tcolorbox}[colback=gray!10, colframe=black, title=\textbf{Case Study 1: Application of Genetic Algorithms to IR}] + The effectiveness of an IR system is dependent on the quality of the weights assigned to terms in documents. + We have seen heuristic-based approaches \& their effectiveness and we've seen axiomatic approaches that could be considered. + \\\\ + Why not learn the weights? + We have a definition of relevant \& non-relevant documents; we can use MAP or precision@$k$ as fitness. + Each genotype can be a set of vectors of length $N$ (the size of the lexicon). + Set all rates randomly initially. + Run the system with a set of queries to obtain fitness; select good chromosomes; crossover; mutate. + Effectively searching the landscape for weights to give a good ranking. +\end{tcolorbox} + + +\subsection{Genetic Programming} +\textbf{Genetic programming} applies the approach of the genetic algorithm to the space of possible computer programs. +``Virtually all problems in artificial intelligence, machine learning, adaptive systems, \& automated learning can be recast as a search for a computer program. +Genetic programming provides a way to successfully conduct the search for a computer program in the space of computer programs.'' -- Koza. +\\\\ +A random population of solutions is created which are modelled in a tree structure with operators as internal nodes and operands as leaf nodes. + + +\begin{figure}[H] + \centering + \usetikzlibrary{trees} + \begin{tikzpicture} + [ + every node/.style = {draw, shape=rectangle, align=center}, + level distance = 1.5cm, + sibling distance = 1.5cm, + edge from parent/.style={draw,-latex} + ] + \node {+} + child { node {1} } + child { node {2} } + child { node {\textsc{if}} + child { node {>} + child { node {\textsc{time}} } + child { node {10} } + } + child { node {3} } + child { node {4} } + }; + \end{tikzpicture} + \caption{\texttt{(+ 1 2 (IF (> TIME 10) 3 4))}} +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{./images/crossover.png} + \caption{Crossover Example} +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[width=0.4\textwidth]{./images/mutation.png} + \caption{Mutation Example} +\end{figure} + +The genetic programming flow is as follows: +\begin{enumerate} + \item Trees are (usually) created at random. + \item Evaluate how each tree performs in its environment (using a fitness function). + \item Selection occurs based on fitness (tournament selection). + \item Crossover of selected solutions to create new individuals. + \item Repeat until population is replaced. + \item Repeat for $N$ generations. +\end{enumerate} + +\subsubsection{Anatomy of a Term-Weighting Scheme} +Typical components of term weighting schemes include: +\begin{itemize} + \item Term frequency aspect. + \item ``Inverse document'' score. + \item Normalisation factor. +\end{itemize} + +The search space should be decomposed accordingly. + +\subsubsection{Why Separate Learning into Stages?} +The search space using primitive measures \& functions is extremely large; +reducing the search space is advantageous as efficiency is increased. +It eases the analysis of the solutions produced at each stage. +Comparisons to existing benchmarks at each of these stages can be used to determine if the GP is finding novel solutions or variations on existing solutions. +It can then be identified from where any improvement in performance is coming. + +\subsubsection{Learning Each of the Three Parts in Turn} +\begin{enumerate} + \item Learn a term-discrimination scheme (i.e., some type of idf) using primitive global measures. + \begin{itemize} + \item 8 terminals \& 8 functions. + \item $T = \{\textit{df}, \textit{cf}, N, V, C, 1, 10, 0.5\}$. + \item $F = \{+, \times, \div, -, \text{square}(), \text{sqrt}(), \text{ln}(), \text{exp}()\}$. + \end{itemize} + + \item Use this global measure and learn a term-frequency aspect. + \begin{itemize} + \item 4 terminals \& 8 functions. + \item $T = \{\textit{tf}, 1, 10, 0.4\}$. + \item $F = \{+, \times, \div, -, \text{square}(), \text{sqrt}(), \text{ln}(), \text{exp}()\}$. + \end{itemize} + + \item Finally, learn a normalisation scheme. + \begin{itemize} + \item 6 terminals \& 8 functions. + \item $T = \{ \text{dl}, \text{dl}_{\text{avg}}, \text{dl}_\text{dev}, 1, 10, 0.5 \}$. + \item $F = \{ +, \times, \div, -, \text{square}(), \text{sqrt}(), \text{ln}(), \text{exp}() \}$. + \end{itemize} +\end{enumerate} + +\begin{figure}[H] + \centering + \includegraphics[width=0.6\textwidth]{./images/threestages.png} + \caption{Learning Each of the Three Stages in Turn} +\end{figure} + +\subsubsection{Details of the Learning Approach} +\begin{itemize} + \item 7 global functions were developed on \~32,000 OHSUMED documents. + \begin{itemize} + \item All validated on a larger unseen collection and the best function taken. + \item Random population of 100 for 50 generations. + \item The fitness function used was MAP. + \end{itemize} + + \item 7 tf functions were developed on \~32,000 LATIMES documents. + \begin{itemize} + \item All validated on a larger unseen collection and the best function taken. + \item Random population of 200 for 25 generations. + \item The fitness function used was MAP. + \end{itemize} + + \item 7 normalisation functions were developed 3 $\times$ \~ 10,000 LATIMES documents. + \begin{itemize} + \item All validated on a larger unseen collection and the best function taken. + \item Random population of 200 for 25 generations. + \item Fitness function used was average MAP over the 3 collections. + \end{itemize} +\end{itemize} + +\subsubsection{Analysis} +The global function $w_3$ always produces a positive number: +\[ + w_3 = \sqrt{\frac{\textit{cf}^3_t \cdot N}{\textit{df}^4_t}} +\] + + +\begin{tcolorbox}[colback=gray!10, colframe=black, title=\textbf{Case Study 1: Application of Genetic Programming to IR}] + Evolutionary computing approaches include: + \begin{itemize} + \item Evolutionary strategies. + \item Genetic algorithms. + \item Genetic programming. + \end{itemize} + + Why genetic programming for IR? + \begin{itemize} + \item Produces a symbolic representation of a solution which is useful for further analysis. + \item Using training data, MAP can be directly optimised (i.e., used as the fitness function). + \item Solutions produced are often generalisable as solution length (size) can be controlled. + \end{itemize} +\end{tcolorbox} \end{document} diff --git a/year4/semester1/CT4100: Information Retrieval/notes/images/crossover.png 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