INFO 4300 / CS4300 Information Retrieval. slides adapted from Hinrich Schütze s, linked from

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1 INFO 4300 / CS4300 Information Retrieval slides adapted from Hinrich Schütze s, linked from IR 8: Evaluation & SVD Paul Ginsparg Cornell University, Ithaca, NY 23 Sep / 50

2 Administrativa Ass t 2 to be posted tomorrow 24 Sep, due Sat 9 Oct, 1pm (late submission permitted until Sun 10 Oct at 11 p.m.) No class Tue 12 Oct (midterm break) The Midterm Examination is on Thu Oct 14 from 11:40 to 12:55, in Olin 165. It will be open book. Topics examined include assignments, lectures and discussion class readings before the midterm break. According to the registrar ( ), final exam is Fri 17 Dec 2:00-4:30 pm (location TBD). Early opportunity to take exam will be Mon 13 Dec, 2:00pm 2/ 50

3 Overview 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 3/ 50

4 Outline 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 4/ 50

5 How do we compute the top k in ranking? In many applications, we don t need a complete ranking. We just need the top k for a small k (e.g., k = 100). If we don t need a complete ranking, is there an efficient way of computing just the top k? Naive: Compute scores for all N documents Sort Return the top k What s bad about this? Alternative? 5/ 50

6 Cluster pruning Cluster docs in preprocessing step Pick N leaders For non-leaders, find nearest leader (expect N / leader) For query q, find closest leader L ( N computations) Rank L and followers or generalize: b 1 closest leaders, and then b 2 leaders closest to query 6/ 50

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8 Non-docID ordering of postings lists So far: postings lists have been ordered according to docid. Alternative: a query-independent measure of goodness of a page. Example: PageRank g(d) of page d, a measure of how many good pages hyperlink to d Order documents in postings lists according to PageRank: g(d 1 ) > g(d 2 ) > g(d 3 ) >... Define composite score of a document: net-score(q,d) = g(d) + cos(q,d) This scheme supports early termination: We do not have to process postings lists in their entirety to find top k. 8/ 50

9 Precision and recall Precision (P) is the fraction of retrieved documents that are relevant Precision = #(relevant items retrieved) #(retrieved items) = P(relevant retrieved) Recall (R) is the fraction of relevant documents that are retrieved Recall = #(relevant items retrieved) #(relevant items) = P(retrieved relevant) 9/ 50

10 A precision-recall curve Precision Recall Each point corresponds to a result for the top k ranked hits (k = 1,2,3,4,...). Interpolation (in red): Take maximum of all future points Rationale for interpolation: The user is willing to look at more stuff if both precision and recall get better. Questions? 10/ 50

11 Averaged 11-point precision/recall graph Precision Recall Compute interpolated precision at recall levels 0.0, 0.1, 0.2,... Do this for each of the queries in the evaluation benchmark Average over queries This measure measures performance at all recall levels. The curve is typical of performance levels at TREC. Note that performance is not very good! 11/ 50

12 Outline 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 12/ 50

13 Precision/recall tradeoff You can increase recall by returning more docs. Recall is a non-decreasing function of the number of docs retrieved. A system that returns all docs has 100% recall! The converse is also true (usually): It s easy to get high precision for very low recall. Suppose the document with the largest score is relevant. How can we maximize precision? 13/ 50

14 A combined measure: F F allows us to trade off precision against recall. 1 F = α 1 P + (1 α) 1 R = (β2 + 1)PR β 2 P + R where β 2 = 1 α α α [0,1] and thus β 2 [0, ] Most frequently used: balanced F with β = 1 or α = 0.5 This is the harmonic mean of P and R: 1 F = 1 2 ( 1 P + 1 R ) What value range of β weights recall higher than precision? 14/ 50

15 F: Example relevant not relevant retrieved not retrieved 60 1,000,000 1,000, ,000,040 1,000,120 P = 20/( ) = 1/3 R = 20/( ) = 1/4 F 1 = = 2/ / 50

16 Accuracy Why do we use complex measures like precision, recall, and F? Why not something simple like accuracy? Accuracy is the fraction of decisions (relevant/nonrelevant) that are correct. In terms of the contingency table above, accuracy = (TP + TN)/(TP + FP + FN + TN). Why is accuracy not a useful measure for web information retrieval? 16/ 50

17 Exercise Compute precision, recall and F 1 for this result set: relevant not relevant retrieved 18 2 not retrieved 82 1,000,000,000 The snoogle search engine below always returns 0 results ( 0 matching results found ), regardless of the query. 17/ 50

18 Why accuracy is not a useful measure in IR Simple trick to maximize accuracy in IR: always say no and return nothing You then get 99.99% accuracy on most queries. Searchers on the web (and in IR in general) want to find something and have a certain tolerance for junk. It s better to return some bad hits as long as you return something. We use precision, recall, and F for evaluation, not accuracy. 18/ 50

19 F: Why harmonic mean? Why don t we use a different mean of P and R as a measure? e.g., the arithmetic mean The simple (arithmetic) mean is 50% for return-everything search engine, which is too high. Desideratum: Punish really bad performance on either precision or recall. Taking the minimum achieves this. But minimum is not smooth and hard to weight. F (harmonic mean) is a kind of smooth minimum. 19/ 50

20 Difficulties in using precision, recall and F We need relevance judgments for information-need-document pairs but they are expensive to produce. There are some alternatives to using precision/recall and having to produce relevance judgments 20/ 50

21 Variance of measures like precision/recall For a test collection, it is usual that a system does badly on some information needs (e.g., P = 0.2 at R = 0.1) and really well on others (e.g., P = 0.95 at R = 0.8). Indeed, it is usually the case that the variance of the same system across queries is much greater than the variance of different systems on the same query. That is, there are easy information needs and hard ones. 21/ 50

22 Outline 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 22/ 50

23 What we need for a benchmark A collection of documents Documents must be representative of the documents we expect to see in reality. A collection of information needs... incorrectly but necessarily called queries Information needs must be representative of the information needs we expect to see in reality. Human relevance assessments We need to hire/pay judges or assessors to do this. Expensive, time-consuming Judges must be representative of the users we expect to see in reality. 23/ 50

24 Standard relevance benchmark: Cranfield Pioneering: first testbed allowing precise quantitative measures of information retrieval effectiveness Late 1950s, UK 1398 abstracts of aerodynamics journal articles, a set of 225 queries, exhaustive relevance judgments of all query-document-pairs Too small, too untypical for serious IR evaluation today 24/ 50

25 Standard relevance benchmark: TREC TREC = Text Retrieval Conference (TREC) Organized by the U.S. National Institute of Standards and Technology (NIST) TREC is actually a set of several different relevance benchmarks. Best known: TREC Ad Hoc, used for first 8 TREC evaluations between 1992 and million documents, mainly newswire articles, 450 information needs No exhaustive relevance judgments too expensive Rather, NIST assessors relevance judgments are available only for the documents that were among the top k returned for some system which was entered in the TREC evaluation for which the information need was developed. 25/ 50

26 Standard relevance benchmarks: Others GOV2 Another TREC/NIST collection 25 million web pages Used to be largest collection that is easily available But still 3 orders of magnitude smaller than what Google/Yahoo/MSN index NTCIR East Asian language and cross-language information retrieval Cross Language Evaluation Forum (CLEF) This evaluation series has concentrated on European languages and cross-language information retrieval. Many others 26/ 50

27 Validity of relevance assessments Relevance assessments are only usable if they are consistent. If they are not consistent, then there is no truth and experiments are not repeatable. How can we measure this consistency or agreement among judges? Kappa measure 27/ 50

28 Kappa measure Kappa is measure of how much judges agree or disagree. Designed for categorical judgments Corrects for chance agreement P(A) = proportion of time judges agree P(E) = what agreement would we get by chance κ = P(A) P(E) 1 P(E) κ =? for (i) chance agreement (ii) total agreement 28/ 50

29 Kappa measure (2) Values of κ in the interval [2/3,1.0] are seen as acceptable. With smaller values: need to redesign relevance assessment methodology used etc. 29/ 50

30 Calculating the kappa statistic Judge 2 Relevance Yes No Total Judge 1 Yes Relevance No Total Observed proportion of the times the judges agreed P(A) = ( )/400 = 370/400 = Pooled marginals P(nonrelevant) = ( )/( ) = 170/800 = P(relevant) = ( )/( ) = 630/800 = Probability that the two judges agreed by chance P(E) = P(nonrelevant) 2 + P(relevant) 2 = = Kappa statistic κ = (P(A) P(E))/(1 P(E)) = ( )/( ) = (still in acceptable range) 30/ 50

31 Interjudge agreement at TREC information number of disagreements need docs judged fair range (.67.8 ) 31/ 50

32 Impact of interjudge disagreement Judges disagree a lot. Does that mean that the results of information retrieval experiments are meaningless? No. Large impact on absolute performance numbers Virtually no impact on ranking of systems Supposes we want to know if algorithm A is better than algorithm B An information retrieval experiment will give us a reliable answer to this question......even if there is a lot of disagreement between judges. 32/ 50

33 Evaluation at large search engines Recall is difficult to measure on the web Search engines often use precision at top k, e.g., k = or use measures that reward you more for getting rank 1 right than for getting rank 10 right. Search engines also use non-relevance-based measures. Example 1: clickthrough on first result Not very reliable if you look at a single clickthrough (you may realize after clicking that the summary was misleading and the document is nonrelevant) but pretty reliable in the aggregate. Example 2: Ongoing studies of user behavior in the lab recall last lecture Example 3: A/B testing 33/ 50

34 A/B testing Purpose: Test a single innovation Prerequisite: You have a large search engine up and running. Have most users use old system Divert a small proportion of traffic (e.g., 1%) to the new system that includes the innovation Evaluate with an automatic measure like clickthrough on first result Now we can directly see if the innovation does improve user happiness. Probably the evaluation methodology that large search engines trust most 34/ 50

35 Critique of pure relevance We ve defined relevance for an isolated query-document pair. Alternative definition: marginal relevance The marginal relevance of a document at position k in the result list is the additional information it contributes over and above the information that was contained in documents d 1...d k 1. Exercise Why is marginal relevance a more realistic measure of user happiness? Give an example where a non-marginal measure like precision or recall is a misleading measure of user happiness, but marginal relevance is a good measure. In a practical application, what is the difficulty of using marginal measures instead of non-marginal measures? 35/ 50

36 Outline 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 36/ 50

37 Discussion 2 K. Sparck Jones, A statistical interpretation of term specificity and its application in retrieval. Journal of Documentation 28, 11-21, Letter by Stephen Robertson and reply by Karen Sparck Jones, Journal of Documentation 28, , / 50

38 Exhaustivity and specificity What are the semantic and statistical interpretations of specificity? Semantic: tea, coffee, cocoa (more specific, smaller # docs) beverage (less specific, larger # docs) Statistical: specificity a function of term usage, frequently used implies non-specific (even if has specific meaning). Exhaustivity of a document description is determined by the number of controlled vocabulary terms assigned. Reject frequently occurring terms? via conjunction (but according to item C table I, average number of matched terms smaller than request, so would reduce recall) remove them entirely (again hurts recall, needed for many relevant documents) What is graphed in figure 1 and what does it illustrate? (Why aren t axes labelled?) 38/ 50

39 idf weight Spärck Jones defines f (n) = m such that 2 m 1 < n <= 2 m (In other words f (n) = log 2 (n), where x denotes the smallest integer not less than x, equivalent to one plus the greatest integer less than x) and suggests weight = f (N) f (n) + 1 e.g. for N = 200 documents, f (N) = 8 (2 8 = 256) n = 90, f (n) = 7 (2 7 = 128), hence weight = = 2 n = 3, f (n) = 2 (2 2 = 4), hence weight = = 7 overall weight for query is then = 9 +1 so that terms occurring in more than roughly half the documents in the corpus not given zero weight (for N = 200, anything in more than 128 documents) 39/ 50

40 idf weight, modified Robertson: Spärck Jones weight f (N) f (n) + 1 log 2 (N/n) + 1 Note that n/n is the probability an item chosen (at random) will contain the term. Suppose an item contains a,b,c in common with query, and probabilities are p a, p b, p c. Then weight assigned to the document is log(1/p a ) + log(1/p b ) + log(1/p c ) = log(1/p a p b p c ) (probability that doc will randomly contain all three terms a,b,c under what assumption?) quantifies statement: less likely that given combination of terms occurs, more likely relevant to query (theoretical justification for logarithmic idf weights) 40/ 50

41 Outline 1 Recap 2 More on Unranked evaluation 3 Evaluation benchmarks 4 Discussion 2, cont d 5 SVD Intuition 41/ 50

42 Netflix challenge, Next 9 slides adapted from ( Simon Funk = Brandyn Webb) simon/journal/ html See also popular article: Netflix provided 100M ratings (from 1 to 5) of 17K movies by 500K users. i.e., 100 million (User,Movie,Rating) s of the form (105932,14002,3) Predict (User,Movie,?) not in the database (how would the given User rate the given Movie?) $50k incentive to the best each year, and $1M to the first to beat a set target (10% better than Netflix) 42/ 50

43 User-Movie Rating Matrix R um Visualize as large sparse 500k 17k user-movie matrix R um, with (u,m) th matrix element containing rating (1 5) by user u for movie m. About 8.5B entries total, so data in only 1 of 85 = 1.2%. Certain specified? elements constitute a quiz: make best guess P um at missing ratings. Use mean squared error (mse) as measure of accuracy: guess 1.5 and actual is 2, penalty = (2 1.5) 2 = Then sum over penalties for all guesses (including optional sqrt): rmse E = (R um P um ) 2 u,m 43/ 50

44 Linear Dependencies If one had the full 8.5 billion ratings (and many weary users ), they would contains many regularities, i.e., not consist of 8.5B independent and unrelated ratings. Describe each movie in terms of some basic attributes such as overall quality action or comedy actors... Describe user preferences in terms of complementary attributes or preferences they rate high or low prefer action or comedy preferred actors... 44/ 50

45 Model the data Explain 8.5 billion ratings by far less than 8.5 billion numbers (e.g., a single number specifying movie s action content can explain the attraction to a few million action-buffs) Define model (for data with smaller number of parameters, infer parameters from the data, SVD ( = singular value decomposition) reduces in this case to the assumption that user s overall rating is composed of a sum of preferences over movie features 45/ 50

46 Example: Just one Feature Suppose only 1 feature, overall quality, and 1 corresponding user tendency to rate high/low. Three users: U u = (1,2,3) Five movies: V m = (1,1,3,2,1) Predicted rating matrix: P um = U u V m = Explain 15 data points with only 7 parameters (only one overall scale) 46/ 50

47 More Features Now suppose 40 features: Each movie described by 40 values, specifying for each feature degree to which contained in movie; Each user described by 40 values, specifying degree to which each feature preferred by user. To calculate rating, sum products of each user preference multiplied by the corresponding movie feature. E.g., movie Terminator might be (action=1.2, chickflick=-1,...), and user Joe might be (action=3, chickflick=-1,...). Combine to find Joe likes Terminator with rating ( 1) ( 1) +... = (Negative numbers OK: Terminator is anti-chickflick, Joe has aversion to chickflicks, so Terminator actively scores positive points with Joe for being decidedly un-chickflicky. ) 47/ 50

48 Concise Model Model requires roughly 40 (500K+17K) values, or about 20M: less than the original 8.5B by a factor of 400. Predicted ratings: P um = r Uu f Vm f f =1 Uu f is the preference of user u for feature f, V m f is the degree to which movie m contains feature f (up to r = 40). Original matrix has been decomposed into product of two rectangular matrices: the 500, user preference matrix U f u, and the 40 17,000 movie feature matrix V f m. (Matrix multiplication just performs the products and sums described above, resulting in an approximation to the original 500,000 17,000 rating matrix.) 48/ 50

49 ( ) }{{} P um = U u V m = 2 = }{{}}{{} P um = r f =1 Uf u Vm f = }{{} r m = }{{} } {{ 4 4 } n r n m 49/ 50

50 How to calculate model parameters Singular value decomposition (SVD) is the mathematical method for finding the two smaller matrices which minimize the resulting approximation error (rmse) to original matrix. The rank-40 SVD of the 8.5B matrix gives the best approximation within framework of 40 feature user-movie-rating model. Difficult to calculate SVD of large matrix. Moreover don t have all 8.5B entries (instead have 100M entries and 8.4B empty cells) But can train parameters by following derivative of the approximation error (steepest descent). (also means the unknown error on the 8.4B empty matrix elements can be ignored for a fully known matrix, end result coincides exactly with the SVD) 50/ 50