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### 3.2 Evaluation

The evaluation of IR systems has a long tradition, dating back from before the Cranfield experiments [75164260]. It is an important part of the experimental methodology to determine how well IR systems satisfy users’ information needs and whether some system does this better than another [309325]. There are several publications addressing various aspects of evaluation. Voorhees and Harman [332] detail the history of TREC and the evaluation methods used there. Harman [120] gives an overview of the state of IR evaluation in 1992. More recently, Robertson [260] provided his personal view on the history of evaluation for IR. Sanderson [277] gives an overview of current methods and practices. Tague-Sutcliffe [309] defines six elements that comprise the IR process:

1.
a document set to be searched (the “collection”),
2.
a user need,
3.
a query (usually called “topic”),
4.
a search strategy,
5.
a retrieved list of documents, and
6.
relevance judgments (typically referred to as “qrels”).

Typically when doing IR evaluation, the retrieval system is given a verbalization of the information need (as a query, ranging from a few keywords to a full narrative) which it uses as input to its retrieval algorithm (the “search strategy”, cf. Section 2.1). The output of this algorithm is a ranked list of documents that may then be inspected by the user with the information need. It is common to refer to the combination of the document collection, topics, and accompanying judgments as “test collection.”

Ideally, we would like to verify the effectiveness of every system on real life users. However, as already indicated in the previous section, relevance is not a deterministic notion and varies per user, task, setting, etc. This, as well as the prohibitive costs of such evaluations, have resulted in an established tradition of sampling and pooling methods [121362]. Evaluation campaigns such as FIRE, TREC, CLEF, NTCIR, and INEX provide systematic evaluations on sets of topics and documents, which are subsequently used to rank IR systems according to their performance. In order to make the evaluation tractable, pooling of the results of the participating systems is applied. Here, the top-ranked documents up to a certain rank are taken from each participating system and judged for relevance. Although not all documents in the collection are judged for relevance using this approach, it was found that systems could still be reliably evaluated using this approach [332]. Moreover, even systems not contributing to the pools could still be fairly assessed [362]. Whether these findings still hold for every retrieval metric on very large document collections is a topic of ongoing research [4952]. In the mean time, various alternatives to pooling are investigated [6162], as detailed below. A distinct benefit of such system-based evaluations is the reusability of test collections, since future systems can be reliably evaluated and compared using the same assessments [260277332].

It is common to not evaluate the ranked list itself, but merely the documents that appear in it. Recent work, however, recognizes that the first thing that a user sees and interacts with is the list of retrieved documents [22]. Bailey et al. define a novel evaluation method focusing on this initial interaction and find that it provides a natural complement to traditional, system-based evaluation methods.

With the recent advent of relatively cheap crowdsourcing possibilities such as Amazon’s mechanical turk service, a renewed interest in obtaining relatively cheap, manual relevance assessments for various systems has emerged [57]. Whether such evaluations live up to their premise of cheap, consistent relevance assessments on a substantial scale is as of yet unclear and in the remainder of this thesis we use more traditional, established TREC-style evaluations.

In the following sections, we look at typical IR effectiveness metrics used in this thesis, as well as statistical testing on these measures.

#### 3.2.1 Evaluation Measures

Different search tasks exist, each with a different user model. In all of the cases presented in this thesis, a user wants to find information on a topic (topic-finding or ad hoc retrieval). Other cases include users having a specific web page or document in mind (named-page finding), users looking for an answer to a specific question (question answering), users looking for relevant experts or entities (expert/entity finding), or users having a standing information need, where new documents entering in the collection are to be routed to the users with an interest in the topic of the document (adaptive filtering). Each of these search tasks calls for evaluation measures that fit the task. For example, in the case of named-page finding, there is typically only one relevant document (the one that the user has in mind). A proper evaluation measure for this task should reward systems that place that document at the top of the ranking and penalize systems that do not.

Researchers have been considering how to evaluate results originating from a retrieval system for a number of decades now and the choice of measures and their analysis remains an active theme of research. Kent et al. [164] were the first to introduce the notion of recall and precision. These intuitive measures consider the documents retrieved in response to a user’s query as a set and indicate the fraction of retrieved documents that are relevant (precision) or the fraction of relevant documents retrieved (recall) [202]. These measures are best explained through the use of a contingency (or confusion) table, cf. Table 3.1. In this table, the documents are split by whether they are retrieved by a system and whether they are relevant.

 Relevant Non-relevant Retrieved True positives (tp) False positives (fp) Not retrieved False negatives (fn) True negatives (tn)

Table 3.1: Contingency table.

Precision, then, is defined as: $\begin{array}{rcll}\text{Precision}=\frac{\text{tp}}{\text{tp}+\text{fp}},& & & \text{(3.1)}\text{}\text{}\end{array}$

whereas recall is defined as: $\begin{array}{rcll}\text{Recall}=\frac{\text{tp}}{\text{tp}+\text{fn}}.& & & \text{(3.2)}\text{}\text{}\end{array}$

Although precision and recall are set-based measures, they are commonly applied to ranked lists by truncating the lists at a certain rank. A common visualization of these measures is to plot precision values at different levels of recall. The resulting graph is called a precision-recall graph; an example may be found in Figure 5.3 (see page 259).

Given that precision is the ratio of retrieved relevant documents to all documents retrieved at a given rank, the average precision (AP) is defined as the average of precisions at the ranks of relevant documents. More formally, for a set of relevant documents, $R$: $\begin{array}{rcll}\text{AP}=\frac{1}{|R|}\sum _{d\in R}prec@rank\left(d\right),& & & \text{(3.3)}\text{}\text{}\end{array}$

where $|R|$ equals the size of the set of known relevant documents for this query. Buckley and Voorhees [49] show that AP is stable; that is, it is able to reliably identify a difference between two systems when one exists. In later chapters, our main evaluation measure is AP averaged over a number of queries, called mean average precision (MAP). These and other measures are obtained using the trec_eval1 program.

In later chapters we use the following abbreviations for the evaluation measures:

PX
– Precision at rank X. In the case of P1 this indicates the proportion of queries for which a relevant occurred at rank 1.
R-prec
– Precision at rank $|R|$. If this value equals 1, all relevant documents are placed at the top of the ranking.
MAP
– Mean average precision.
SRX
– Success rate at rank X; a binary measure that indicates whether at least one correct document has been returned in the top-X (when there is no rank indicated we assume X=5). When averaged over a number of queries it indicates the proportion of queries for which a relevant document occurred in the top-X.
MRR
– The mean of the reciprocal of the rank of the first relevant document.
RelRet
– The number of relevant documents retrieved (measured at rank 1000, unless indicated otherwise). When this value is expressed as a fraction of the total number of relevant documents, it is called “recall”, cf. Eq. 3.2.

Of these, MRR, PX, and SRX correspond directly to common user experience since they measure the presence and/or amount of relevant documents at the top of the document ranking [262286]. Other users, however, may be more interested in retrieving as many relevant documents as possible and, for them, RelRet might be more appropriate. As indicated above, MAP has both a precision and a recall aspect. We will therefore use this measure as our main evaluation metric.

As indicated above, for relatively small document collections it is feasible to collect relevance assessments on all the documents given a query. For larger collections, it is assumed that the top-ranked documents collected from a variety of systems form a reliable basis for evaluation. This in turn enables the comparisons of systems on the basis of recall, which requires the count of all relevant documents for a query. As document collections grow, however, these assumptions may no longer hold [4952]. Therefore, several new measures (typically based on a form of sampling or bootstrapping) are being developed for such collections [1146271]. For the largest document collection that we employ later in the thesis (ClueWeb09; introduced in Section 3.3.4), we report these measures instead of the traditional ones. Specifically, for ClueWeb09, Category B we report statMAP and statP10 [14], whereas for ClueWeb09, Category A we also report expected MAP (eMAP), expected R-precision (eR-prec), and expected precision at rank 10 (eP10) [6162]. Systems participating in TREC tracks that use ClueWeb09 were pooled up until a relatively shallow depth and these measures are intended to yield the same ranking as traditional measures would have if the runs had been fully judged.

TREC Web 2009 (a test collection that makes use of the ClueWeb09 document collection—see below) featured a novel sub-track, aiming to improve diversity in the result list. The diversity task is similar to the ad hoc retrieval task, but differs in its judging process and evaluation measures. The goal of this task is to return documents that together provide complete coverage for a query, while avoiding excessive redundancy in the result list; the probability of relevance of a document is conditioned on the documents that appear before it in the result list. Each topic is therefore structured as a representative set of subtopics (and unknown to the system). Each subtopic, in turn, is related to a different user need and documents are judged with respect to the subtopics. The evaluation measures associated with diversity that we report upon in the thesis are: $\alpha$-nDCG [71] and intent aware precision@10 (IA-P@10) [1]. The former is based on normalized discounted cumulative gain [146] and rewards novelty and diversity in the retrieved documents. The parameter $\alpha$ indicates the probability that a user is still interested in a document, given that subtopic of the current document has already been covered by the preceding documents. We use the default setting of $\alpha =0.5$. The second measure is similar to precision@10, but incorporates information from a taxonomy (the ODP taxonomy in particular) to determine diversity.

#### 3.2.2 Statistical Significance Testing

As indicated earlier in this chapter, relevance assessments are not deterministic and there is inherent noise in an evaluation. Early work on a small document collection indicated that a large variance in relevance assessments does not have a significant influence on average recall and precision [186]. As test collections grew, however, questions were asked with respect to the validity of this conclusion on larger and more variable test collections [141].

So, given two systems that produce a ranking of documents for a topic, how can we determine which one is better than the other? Our method should be robust and promote the system that is truly better, rather than promoting the one that performed better by chance. Statistical significance testing plays an important role in making this assertion. A significance tests consists of the following three ingredients [287]:

1.
A test statistic or criterion by which to judge the two systems. Typically, the mean of a retrieval metric introduced in Section 3.2.1 is used.
2.
A distribution of the test statistic given the null hypothesis. The typical null hypothesis (and the one we use in this thesis) is that there is no difference between the systems.
3.
A significance level that is computed by taking the value of the test statistic for the systems and determining how likely a large or larger value could have occurred under the null hypothesis. This probability of the experimental criterion score given the distribution created by the null hypothesis is also known as the p-value.

Statistical testing methods that are commonly used for IR include the sign test, paired Wilcoxon signed rank test, Friedman test, and Student’s t-test [141278]. In later chapters (except Chapter 6), we use the paired Wilcoxon signed rank test [343], although recent work has indicated some potential issues with this particular test [287]. The null hypothesis of this test is that the results produced by both systems are sampled from the same distribution; in particular that the median difference between pairs of observations is zero. It proceeds as follows. First, it transforms each instance (a pair of observations, i.e., the scores on a retrieval metric for two systems on a particular topic) into absolute values. Then, zero differences are removed and the remaining differences are ranked from lowest to highest. After the signs (that were removed in the first step) are reattributed to the ranks (hence the name signed rank test), the test statistic is calculated. For sample sizes greater than 25, a normal approximation to this statistic exists. Related to this number is the minimum number of topics one needs to assess to account for the variance in evaluation measures over different topics; 50 topics has been found to be a suitable minimum by Buckley and Voorhees [49], whereas Sanderson and Zobel [278] indicate significant improvements on 25 or less topics does not guarantee that this result will be repeatable on other sets of topics. All of the topic sets we use later in the thesis consist of at least 25 topics, as we describe in the next section.

In the thesis, we look for improvements at the $p<0.05$ level, indicated with a ‘*’. All reported p-values are for two-sided tests. In Chapter 6 we compare multiple methods. There, we use a one-way analysis of variance (ANOVA) test which is a common test when there are more than two systems or methods to be compared. It simultaneously tests for differences in the average score of each method, correcting for the effects of the individual queries. We subsequently use the Tukey-Kramer test to determine which of the individual pairs are significantly different. We use a bold-faced font in the result tables to indicate the best performing model in our result tables.

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