Chapter 8 Evaluating Search Engine
Evaluation Evaluation is key to building effective and efficient search engines Measurement usually carried out in controlled laboratory experiments Online testing can also be done Effectiveness, efficiency, and cost are related e.g., if we want a particular level of effectiveness and efficiency, this will determine the cost of the system configuration Efficiency and cost targets may impact effectiveness & vice versa 2
Evaluation Corpus Test collections consisting of documents, queries, and relevance judgments, e.g., 3
Test Collections Bibliographic Records Full-text Documents Policy Descriptions Based on TREC topics 4
TREC Topic Example Short Query Long Query Criteria for Relevance 5
Relevance Judgments TREC judgments Depend on task being evaluated, e.g., topical relevance Generally binary, i.e., relevant vs. non-relevant Agreement good because of narrative Emphasize on high recall Obtaining relevance judgments is an expensive, timeconsuming process that requires manual effort Who does it? What are the instructions? What is the level of agreement? 6
Effectiveness Measures A is set of relevant documents; B is set of retrieved documents Relevant Non-Relevant Retrieved A B A B Not Retrieved A B A B Collection Recall = A B A B Precision = A B (true positive rate) (positive predictive value) Relevant Set, A A B A B Retrieved Set, B Retrieved Relevant, A B 7
Classification Errors Precision is used when probability that a positive result is correct is important False Positive (Type I Error) Non-relevant documents retrieved: A B False positive/false alarm rate: False Negative (Type II Error) Relevant documents not retrieved: A B FN Ratio: 1 - Recall 8
F Measure Harmonic mean of recall & precision, a single measure Harmonic mean emphasizes the importance of small values, whereas the arithmetic mean is affected more by outliers that are unusually large More general form β is a parameter that determines relative importance of recall and precision What if β = 1? 9
Ranking Effectiveness (1/6 1/6 2/6 3/6 4/6 5/6 5/6 5/6 5/6 6/6) (1/1 1/2 2/3 3/4 4/5 5/6 5/7 5/8 5/9 6/10) (0/6 1/6 1/6 1/6 2/6 3/6 4/6 4/6 5/6 6/6) (0/1 1/2 1/3 1/4 2/5 3/6 4/7 4/8 5/9 6/10) 10
Summarizing a Ranking Calculating recall and precision at fixed rank positions Calculating precision at standard recall levels, from 0.0 to 1.0 Requires interpolation Averaging the precision values from the rank positions where a relevant document was retrieved 11
Average Precision Mean Average Precision: (0.78 + 0.52) / 2 = 0.65 12
Averaging Mean Average Precision (MAP) Summarize rankings from multiple queries by averaging average precision Most commonly used measure in research papers Assumes user is interested in finding many relevant documents for each query Requires many relevance judgments in text collection Recall-precision graphs are also useful summaries 13
MAP 14
Recall-Precision Graph Too much information could be lost using MAP Recall-precision graphs provide more detail on the effectiveness of the ranking at different recall levels Example. The recall-precision graphs for the two previous queries Ranking of Query 1 Ranking of Query 2 15
Precision and Recall Precision versus Recall Curve A visual display of the evaluation measure of a retrieval strategy such that documents are ranked accordingly Example. Let q be a query in the text reference collection Let R q = { d 3, d 5, d 9, d 25, d 39, d 44, d 56, d 71, d 89, d 123 } be the set of 10 relevant documents for q Assume the following ranking of retreived documents in the answer set of q: 1. d 123 6. d 9 11. d 38 2. d 84 7. d 511 12. d 48 3. d 56 8. d 129 13. d 250 4. d 6 9. d 187 14. d 113 5. d 8 10. d 25 15. d 3 16
Precision Example. Precision Versus Recall Curve R q = 10, total number of relevant documents for q Given ranking of retrieved documents in the answer set of q: 1. d 123 6. d 9 11. d 38 2. d 84 7. d 511 12. d 48 3. d 56 8. d 129 13. d 250 4. d 6 9. d 187 14. d 113 5. d 8 10. d 25 15. d 3 100 100% An Interpolated Value 80 60 66% 50% 40 40% 33% 20 0 10 20 30 40 50 60 80 100 Recall 17
Precision and Recall To evaluate the performance of a retrieval strategy over all test queries, compute the average of precision at each recall level: P(r) = N q i=1 P i (r) N q where = 1 N q N q i=1 P(r) = average precision at the r th recall level P i (r) = precision at the r th recall level for the i th query N q = number of queries used P i (r) 18
Precision Example. Precision Versus Recall Curve R q = {d 3, d 56, d 129 } & R q = 3, number of relevant docs for q Given ranking of retreived documents in the answer set of q: 1. d 123 6. d 9 11. d 38 2. d 84 7. d 511 12. d 48 3. d 56 8. d 129 13. d 250 4. d 6 9. d 187 14. d 113 5. d 8 10. d 25 15. d 3 100 80 60 Interpolated precision at the 11 recall levels 40 20 33% 25% 20% 0 10 30 50 70 90 20 40 60 80 100 Recall 19
Precision Interpolation of Precision at Various Recall Levels 100 80 60 Interpolated precision at the 11 recall levels 40 20 0 10 30 50 70 90 20 40 60 80 100 Recall Let r i (0 i < 10) be a reference to the i th recall level P(r i ) = max r i r r i+1 P(r) Interpolation of previous levels by using the next known level 20
Precision Precision Versus Recall Curve 120 100 80 60 40 20 0 20 40 60 80 100 Average precision at each recall level for two distinct retrieval strategies Recall Compare the retrieval performance of distinct retrieval strategies using precision versus recall figures Average precision versus recall figures become a standard evaluation strategy for IR systems Simple and intuitive Qualify the overall answer set 21
Focusing on Top Documents Users tend to look at only the top part of the ranked result list to find relevant documents Some search tasks have only one relevant doc (P@1) in mind the top-ranked doc is expected to be relevant e.g., in question-answering system, navigation search, etc. Precision at R (5, 10, or 20): ratio of top ranked relevant docs Easy to compute, average, understand Not sensitive to rank positions less than R, higher or lower Recall not an appropriate measure in this case Instead need to measure how well the search engine does at retrieving relevant documents at very high ranks 22
Focusing on Top Documents Reciprocal Rank Reciprocal of the rank at which the 1 st relevant doc retrieved Very sensitive to rank position, e.g., d n, d r, d n, d n, d n (RR = ½), whereas d n, d n, d n, d n, d r (RR = 1/5) Mean Reciprocal Rank (MRR) is the average of the reciprocal ranks over a set of queries, i.e., Number of Queries 1 MRR = Qs Qs i=1 1 rank i Normalization factor Ranking position of the first relevant document 23
Discounted Cumulative Gain Popular measure for evaluating web search and related tasks Two assumptions: Highly relevant documents are more useful than marginally relevant document The lower the ranked position of a relevant document, the less useful it is for the user, since it is less likely to be examined 24
Discounted Cumulative Gain Uses graded relevance (i.e., a value) as a measure of the usefulness, or gain, from examining a document Gain is accumulated starting at the top of the ranking and may be reduced, or discounted, at lower ranks Typical discount is 1 / log 2 (rank) With base 2, the discount at rank 4 is, and at rank 8 it is 25
Discounted Cumulative Gain DCG is the total gain accumulated at a particular rank p: where rel i is the graded relevance of the document at rank i, e.g., ranging from Bad to Perfect is 0 rel i 5, or 0 or 1 log 2 i is the discount/reduction factor applied to the gain Alternative formulation: Used by some web search companies Emphasis on retrieving highly relevant documents 26
DCG Example Assume that there are 10 ranked documents judged on a 0-3 ( not relevant to highly relevant ) relevance scale: 3, 2, 3, 0, 0, 1, 2, 2, 3, 0 which represent the gain at each rank The discounted gain is 3, 2/1, 3/1.59, 0, 0, 1/2.59, 2/2.81, 2/3, 3/3.17, 0 = 3, 2, 1.89, 0, 0, 0.39, 0.71, 0.67, 0.95, 0 DCG at each rank is formed by accumulating the numbers 3, 5, 6.89, 6.89, 6.89, 7.28, 7.99, 8.66, 9.61, 9.61 (5) (10) 27
Normalized DCG DCG numbers are averaged across a set of queries at specific rank values, similar to precision@p e.g., DCG at rank 5 is 6.89 and at rank 10 is 9.61 DCG values are often normalized by comparing the DCG at each rank with the DCG value for the perfect ranking NDCG p = DCG p / IDCG p Makes averaging easier for queries with different numbers of relevant documents 28
NDCG Example Perfect ranking for which each relevance level is on the scale 0-3: Ideal DCG values: 3, 3, 3, 2, 2, 2, 1, 0, 0, 0 (5) (10) 3, 6, 7.89, 8.89, 9.75, 10.52, 10.88, 10.88, 10.88, 10.88 (5) Given the DCG values are 3, 5, 6.89, 6.89, 6.89, 7.28, 7.99, 8.66, 9.61, 9.61, the NDCG values: (10) 1, 0.83, 0.87, 0.77, 0.71, 0.69, 0.73, 0.8, 0.88, 0.88 (5) (10) NDCG 1 at any rank position 29
Significance Tests Given the results from a number of queries, how can we conclude that (a new) ranking algorithm B is better than (the baseline) algorithm A? A significance test, which allows us to quantify, enables us to reject the null hypothesis (no difference) in favor of the alternative hypothesis (there is a difference) The power of a test is the probability that the test will reject the null hypothesis correctly Increasing the number of queries in the experiment also increases power (confidence in any judgment) of test Type 1 Error: the null hypothesis is rejected when it is true Type 2 Error: the null hypothesis is accepted when it is false 30
Significance Tests Standard Procedure for comparing two retrieval systems: 0.01, 31
Significance Test P = 0.05 Test Statistic Value Probability distribution for test statistic values assuming the null hypothesis. The shaded area is the region of rejection for a one-sided test. x 32
t-test Assumption is that the difference between the effectiveness data values is a sample from a normal distribution Null hypothesis is that the mean of the distribution of differences is zero Test statistic for the paired t-test is Mean of the differences Example. Given that N = 10 such that Standard derivation A = < 25, 43, 39, 75, 43, 15, 20, 52, 49, 50 > and B = < 35, 84, 15, 75, 68, 85, 80, 50, 58, 75 > One-tailed P Value QuickCalcs (http://www.graphpad.com/quickcalcs/ttest2.cfm) 33
Example: t-test 34
Wilcoxon Signed-Ranks Test Nonparametric test based on differences between effectiveness scores Test statistic To compute the signed-ranks, the differences are ordered by their absolute values (increasing), and then assigned rank values Rank values are given the sign of the original difference Sample website (http://scistatcalc.blogspot.com/2013/10/wilcoxon-signedrank-test-calculator.html) 35
Wilcoxon Test Example 9 non-zero differences are (in order of absolute value): Signed-ranks: 2, 9, 10, 24, 25, 25, 41, 60, 70-1, +2, +3, -4, +5.5, +5.5, +7, +8, +9 w (sum of the signed-ranks) = 35, p-value = 0.038 Two-tailed P Value Null hypothesis holds if of + ranks = of the - ranks 36