The optimal weight Parametric and zone indexes
6.1 Parametric and zone indexes
115 Example DocID Query s T s B Judgment Φ 1 37 linux 1 1 Relevant Φ 2 37 penguin 1 Non-relevant Φ 3 238 system 1 Relevant Φ 4 238 penguin Non-relevant Φ 5 1741 kernel 1 1 Relevant Φ 6 2094 driver 1 Relevant Φ 7 3191 driver 1 Non-relevant ◮ Figure 6.5 An illustration of training examples. s T s B Score 1 1 − g 1 g 1 1 1 ◮ Figure 6.6 The four possible combinations of s T and s B . where we have quantized the editorial relevance judgment r d j , q j to 0 or 1. Then, the total error of a set of training examples is given by ∑ j ε g , Φ j . 6.4 The problem of learning the constant g from the given training examples then reduces to picking the value of g that minimizes the total error in 6.4 . Picking the best value of g in 6.4 in the formulation of Section 6.1.3 re- duces to the problem of minimizing a quadratic function of g over the inter- val [ 0, 1 ] . This reduction is detailed in Section 6.1.3 . ✄6.1.3 The optimal weight
g We begin by noting that for any training example Φ j for which s T d j , q j = and s B d j , q j = 1, the score computed by Equation 6.2 is 1 − g . In similar fashion, we may write down the score computed by Equation 6.2 for the three other possible combinations of s T d j , q j and s B d j , q j ; this is summa- rized in Figure 6.6 . Let n 01r respectively, n 01n denote the number of training examples for which s T d j , q j = 0 and s B d j , q j = 1 and the editorial judgment is Relevant respectively, Non-relevant. Then the contribution to the total error in Equa- tion 6.4 from training examples for which s T d j , q j = 0 and s B d j , q j = 1 Preliminary draft c 2008 Cambridge UP 116 6 Scoring, term weighting and the vector space model is [ 1 − 1 − g ] 2 n 01r + [ − 1 − g ] 2 n 01n . By writing in similar fashion the error contributions from training examples of the other three combinations of values for s T d j , q j and s B d j , q j and extending the notation in the obvious manner, the total error corresponding to Equation 6.4 is n 01r + n 10n g 2 + n 10r + n 01n 1 − g 2 + n 00r + n 11n . 6.5 By differentiating Equation 6.5 with respect to g and setting the result to zero, it follows that the optimal value of g is n 10r + n 01n n 10r + n 10n + n 01r + n 01n . 6.6 ? Exercise 6.1 When using weighted zone scoring, is it necessary for all zones to use the same Boo- lean match function? Exercise 6.2 In Example 6.1 above with weights g 1 = 0.2, g 2 = 0.31 and g 3 = 0.49, what are all the distinct score values a document may get? Exercise 6.3 Rewrite the algorithm in Figure 6.4 to the case of more than two query terms. Exercise 6.4 Write pseudocode for the function WeightedZone for the case of two postings lists in Figure 6.4 . Exercise 6.5 Apply Equation 6.6 to the sample training set in Figure 6.5 to estimate the best value of g for this sample. Exercise 6.6 For the value of g estimated in Exercise 6.5 , compute the weighted zone score for each query, document example. How do these scores relate to the relevance judgments in Figure 6.5 quantized to 01? Exercise 6.7 Why does the expression for g in 6.6 not involve training examples in which s T d t , q t and s B d t , q t have the same value? Preliminary draft c 2008 Cambridge UP6.2 Term frequency and weighting
Parts
» cambridge introductiontoinformationretrieval2008 readingversion
» An example information retrieval problem
» A first take at building an inverted index
» Processing Boolean queries cambridge introductiontoinformationretrieval2008 readingversion
» The extended Boolean model versus ranked retrieval
» References and further reading
» Obtaining the character sequence in a document
» Tokenization Determining the vocabulary of terms
» Dropping common terms: stop words
» Normalization equivalence classing of terms
» Stemming and lemmatization Determining the vocabulary of terms
» Faster postings list intersection via skip pointers
» Biword indexes Positional postings and phrase queries
» Positional indexes Positional postings and phrase queries
» Combination schemes Positional postings and phrase queries
» Search structures for dictionaries
» General wildcard queries Wildcard queries
» k-gram indexes for wildcard queries
» Implementing spelling correction Spelling correction
» Forms of spelling correction Edit distance
» k-gram indexes for spelling correction
» Context sensitive spelling correction
» Phonetic correction cambridge introductiontoinformationretrieval2008 readingversion
» Hardware basics Blocked sort-based indexing
» Single-pass in-memory indexing cambridge introductiontoinformationretrieval2008 readingversion
» Distributed indexing cambridge introductiontoinformationretrieval2008 readingversion
» Dynamic indexing cambridge introductiontoinformationretrieval2008 readingversion
» References and further reading Exercises
» Heaps’ law: Estimating the number of terms Zipf’s law: Modeling the distribution of terms
» Blocked storage Dictionary compression
» Variable byte codes γ Postings file compression
» Exercises cambridge introductiontoinformationretrieval2008 readingversion
» Weighted zone scoring Parametric and zone indexes
» Learning weights Parametric and zone indexes
» The optimal weight Parametric and zone indexes
» Inverse document frequency Term frequency and weighting
» Tf-idf weighting Term frequency and weighting
» Dot products The vector space model for scoring
» Queries as vectors Computing vector scores
» Sublinear tf scaling Maximum tf normalization
» Document and query weighting schemes Pivoted normalized document length
» Inexact top Efficient scoring and ranking
» Index elimination Champion lists
» Static quality scores and ordering
» Impact ordering Efficient scoring and ranking
» Cluster pruning Efficient scoring and ranking
» Tiered indexes Query-term proximity
» Designing parsing and scoring functions
» Vector space scoring and query operator interaction
» Information retrieval system evaluation
» Standard test collections cambridge introductiontoinformationretrieval2008 readingversion
» Evaluation of unranked retrieval sets
» Evaluation of ranked retrieval results
» Critiques and justifications of the concept of relevance
» Results snippets cambridge introductiontoinformationretrieval2008 readingversion
» The Rocchio algorithm for relevance feedback
» Probabilistic relevance feedback When does relevance feedback work?
» Relevance feedback on the web
» Evaluation of relevance feedback strategies
» Pseudo relevance feedback Indirect relevance feedback
» Vocabulary tools for query reformulation Query expansion
» Basic XML concepts cambridge introductiontoinformationretrieval2008 readingversion
» A vector space model for XML retrieval
» Text-centric vs. data-centric XML retrieval
» Review of basic probability theory
» The 10 loss case The Probability Ranking Principle
» Deriving a ranking function for query terms
» Probability estimates in theory
» Probability estimates in practice
» Probabilistic approaches to relevance feedback
» An appraisal of probabilistic models
» Tree-structured dependencies between terms Okapi BM25: a non-binary model
» Finite automata and language models
» Multinomial distributions over words
» Using query likelihood language models in IR
» Estimating the query generation probability
» Ponte and Croft’s Experiments
» Language modeling versus other approaches in IR
» Extended language modeling approaches
» The text classification problem
» The Bernoulli model cambridge introductiontoinformationretrieval2008 readingversion
» Mutual information Feature selection
» Frequency-based feature selection Feature selection for multiple classifiers
» Evaluation of text classification
» Document representations and measures of relatedness in vec-
» Rocchio classification cambridge introductiontoinformationretrieval2008 readingversion
» Time complexity and optimality of kNN
» Linear versus nonlinear classifiers
» Classification with more than two classes
» The bias-variance tradeoff cambridge introductiontoinformationretrieval2008 readingversion
» Support vector machines: The linearly separable case
» Soft margin classification Extensions to the SVM model
» Multiclass SVMs Nonlinear SVMs
» Experimental results Extensions to the SVM model
» Choosing what kind of classifier to use
» Improving classifier performance Issues in the classification of text documents
» A simple example of machine-learned scoring
» Result ranking by machine learning
» Clustering in information retrieval
» Evaluation of clustering cambridge introductiontoinformationretrieval2008 readingversion
» Cluster cardinality in K-means
» Model-based clustering cambridge introductiontoinformationretrieval2008 readingversion
» Centroid clustering cambridge introductiontoinformationretrieval2008 readingversion
» Optimality of HAC cambridge introductiontoinformationretrieval2008 readingversion
» Divisive clustering cambridge introductiontoinformationretrieval2008 readingversion
» Cluster labeling cambridge introductiontoinformationretrieval2008 readingversion
» Implementation notes cambridge introductiontoinformationretrieval2008 readingversion
» Term-document matrices and singular value decompositions
» Low-rank approximations cambridge introductiontoinformationretrieval2008 readingversion
» Latent semantic indexing cambridge introductiontoinformationretrieval2008 readingversion
» Background and history cambridge introductiontoinformationretrieval2008 readingversion
» The web graph Web characteristics
» Advertising as the economic model
» Near-duplicates and shingling cambridge introductiontoinformationretrieval2008 readingversion
» Features a crawler Features a crawler
» Distributing indexes cambridge introductiontoinformationretrieval2008 readingversion
» Connectivity servers cambridge introductiontoinformationretrieval2008 readingversion
» Anchor text and the web graph
» The PageRank computation PageRank
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