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that contain term $t_i$. \end{itemize} +\section{Evaluation of IR Systems} +When evaluating an IR system, we need to consider: +\begin{itemize} + \item The \textbf{functional requirements}: whether or not the system works as intended. + This is done with standard testing techniques. + \item The \textbf{performance:} + \begin{itemize} + \item Response time. + \item Space requirements. + \item Measure by empirical analysis, efficiency of algorithms \& data structures for compression, + indexing, etc. + \end{itemize} + \item The \textbf{retrieval performance:} how useful is the system? + IR is a highly empirical discipline and there is a long history of the evaluation of retrieval performance. + This is less of an issue in data retrieval systems wherein perfect matching is possible as there exists + a correct answer. +\end{itemize} +\subsection{Test Collections} +Evaluation of IR systems is usually based on a reference \textbf{test collection} involving human evaluations. +The test collection usually comprises: +\begin{itemize} + \item A collection of documents $D$. + \item A set of information needs that can be represented as queries. + \item A list of relevance judgements for each query-document pair. +\end{itemize} +Issues with using test collections include: +\begin{itemize} + \item It can be very costly to obtain relevance judgements. + \item Crowd sourcing. + \item Pooling approaches. + \item Relevance judgements don't have to be binary. + \item Agreement among judges. +\end{itemize} +\textbf{TREC (Text REtrieval Conference)} provides a means to empirically test the performance of systems in +different domains by providing \textit{tracks} consisting of a data set \& test problems. +These tracks include: +\begin{itemize} + \item \textbf{Ad-hoc retrieval:} different tracks have been proposed to test ad-hoc retrieval including the + Web track (retrieval on web corpora) and the Million Query track (large number of queries). + \item \textbf{Interactive Track}: users interact with the system for relevance feedback. + \item \textbf{Contextual Search:} multiple queries over time. + \item \textbf{Entity Retrieval:} the task is to retrieve entities (people, places, organisations). + \item \textbf{Spam Filtering:} identifying \& filtering out non-relevant or harmful content such as email + spam. + \item \textbf{Question Answering (QA):} the goal is to retrieve precise answers to user questions rather than + returning entire documents. + \item \textbf{Cross-Language Retrieval:} the goal is to retrieve relevant documents in a different language + from the query. + Requires machine translation. + \item \textbf{Conversational IR:} retrieving information in conversational IR systems. + \item \textbf{Sentiment Retrieval:} emphasis on identifying opinions \& sentiments. + \item \textbf{Fact Checking:} misinformation track. + \item \textbf{Domain-Specific Retrieval:} e.g., genomic data. + \item Summarisation Tasks. +\end{itemize} +Relevance is assessed for the information need and not the query. +Because tuning \& optimisation can occur for many IR systems, it is considered good practice to tune on one +collection and then test on another. +\\\\ +Interaction with an IR system may be a one-off query or an interactive session. +For the former, \textit{quality} of the returned set is the important metric, while for interactive systems other +issues have to be considered: duration of the session, user effort required, etc. +These issues make evaluation of interactive sessions more difficult. +\subsection{Precision \& Recall} +The most commonly used metrics are \textbf{precision} \& \textbf{recall}. +\subsubsection{Unranked Sets} +Given a set $D$ and a query $Q$, let $R$ be the set of documents relevant to $Q$. +Let $A$ be the set actually returned by the system. +\begin{itemize} + \item \textbf{Precision} is defined as $\frac{|R \cap A|}{|A|} = \frac{\text{relevant retrieved documents}}{\text{all retrieved documents}}$, i.e. what fraction of the retrieved documents are relevant. + \item \textbf{Recall} is defined as $\frac{|R \cap A|}{|R|} = \frac{\text{relevant retrieved documents}}{\text{all relevant documents}}$, i.e. what fraction of the relevant documents were returned. +\end{itemize} + +Having two separate measures is useful as different IR systems may have different user requirements. +For example, in web search precision is of the greatest importance, but in the legal domain recall is of the greatest +importance. +\\\\ +There is a trade-off between the two measures; for example, by returning every document in the set, recall is +maximised (because all relevant documents will be returned) but precision will be poor (because many irrelevant documents will be returned). +Recall is non-decreasing as the number of documents returned increases, while precision usually decreases as the +number of documents returned increases. + +\begin{table}[h!] + \centering + \begin{tabular}{|p{0.3\textwidth}|p{0.3\textwidth}|p{0.3\textwidth}|} + \hline + & \textbf{Relevant} & \textbf{Non-Relevant} \\ + \hline + \textbf{Relevant} & True Positive (TP) & False Negative (FN) \\ + \hline + \textbf{Non-Relevant} & False Positive (FP) & True Negative (TN) \\ + \hline + \end{tabular} + \caption{Confusion Matrix of True/False Positives \& Negatives} +\end{table} + +$$ +\text{Precision } P = \frac{tp}{tp + fp} = \frac{\text{true positives}}{\text{true positives + false positives}} +$$ +$$ +\text{Recall } R = \frac{tp}{tp + fn} = \frac{\text{true positives}}{\text{true positives + false negatives}} +$$ + +The \textbf{accuracy} of a system is the fraction of these classifications that are correct: +$$ +\text{Accuracy} = \frac{tp + tn}{tp +fp + fn + tn} +$$ + +Accuracy is a commonly used evaluation measure in machine learning classification work, but is not a very useful +measure in IR; for example, when searching for relevant documents in a very large set, the number of irrelevant +documents is usually much higher than the number of relevant documents, meaning that a high accuracy score is +attainable by getting true negatives by discarding most documents, even if there aren't many true positives. +\\\\ +There are also many single-value measures that combine precision \& recall into one value: +\begin{itemize} + \item F-measure. + \item Balanced F-measure. +\end{itemize} + +\subsubsection{Evaluation of Ranked Results} +In IR, returned documents are usually ranked. +One way of evaluating ranked results is to use \textbf{Precision-Recall plots}, wherein precision is typically +plotted against recall. +In an ideal system, we would have a precision value of 1 for a recall value of 1, i.e., all relevant documents +have been returned and no irrelevant documents have been returned. + +\begin{tcolorbox}[colback=gray!10, colframe=black, title=Example] + Given $|D| = 20$ \& $|R| = 10$ and a ranked list of length 10, let the returned ranked list be: + $$ + \mathbf{d_1}, \mathbf{d_2}, d_3, \mathbf{d_4}, d_5, d_6, \mathbf{d_7}, d_8, d_9, d_{10} + $$ + + where those in items in bold are those that are relevant. + \begin{itemize} + \item Considering the list as far as the first document: Precision = 1, Recall = 0.1. + \item As far as the first two documents: Precision = 1, Recall = 0.2. + \item As far as the first three documents: Precision = 0.67, Recall = 0.2. + \end{itemize} + + We usually plot for recall values = 10\% ... 90\%. +\end{tcolorbox} + +We typically calculate precision for these recall values over a set of queries to get a truer measure of a system's +performance: +$$ +P(r) = \frac{1}{N} \sum^N_{i=1}P_i(r) +$$ + +Advantages of Precision-Recall include: +\begin{itemize} + \item Widespread use. + \item It gives a definable measure. + \item It summarises the behaviour of an IR system. +\end{itemize} + +Disadvantages of Precision-Recall include: +\begin{itemize} + \item It's not always possible to calculate the recall measure effective of queries in batch mode. + \item Precision \& recall graphs can only be generated when we have ranking. + \item They're not necessarily of interest to the user. +\end{itemize} + +Single-value measures for evaluating ranked results include: +\begin{itemize} + \item Evaluating precision when every new document is retrieved and averaging precision values. + \item Evaluating precision when the first relevant document is retrieved. + \item $R$-precision: calculate precision when the final document has been retrieved. + \item Precision at $k$ (P@k). + \item Mean Average Precision (MAP). +\end{itemize} + +Precision histograms are used to compare two algorithms over a set of queries. +We calculate the $R$-precision (or possibly another single summary statistic) of two systems over all queries. +The difference between the two are plotted for each of the queries. + +\subsection{User-Oriented Measures} +Let $D$ be the document set, $R$ be the set of relevant documents, $A$ be the answer set returned to the users, +and $U$ be the set of relevant documents previously known to the user. +Let $AU$ be the set of returned documents previously known to the user. +$$ +\text{Coverage} = \frac{|AU|}{|U|} +$$ +Let \textit{New} refer to the set of relevant documents returned to the user that were previously unknown to the user. +We can define \textbf{novelty} as: +$$ +\text{Novelty} = \frac{|\text{New}|}{|\text{New}| + |AU|} +$$ + +The issues surrounding interactive sessions are much more difficult to assess. +Much of the work in measuring user satisfaction comes from the field of HCI. +The usability of these systems is usually measured by monitoring user behaviour or via surveys of the user's +experience. +Another closely related area is that of information visualisation: ow best to represent the retrieved data for a +user etc.