Probability estimates in practice
11.3 The Binary Independence Model
227 α = 1 2 . This is a form of maximum a posteriori MAP estimation, where we MAXIMUM A POSTERIORI MAP choose the most likely point value for probabilities based on the prior and the observed evidence, following Equation 11.4 . We will further discuss methods of smoothing estimated counts to give probability models in Sec- tion 12.2.2 page 243 ; the simple method of adding 1 2 to each observed count will do for now.11.3.3 Probability estimates in practice
Under the assumption that relevant documents are a very small percentage of the collection, it is plausible to approximate statistics for nonrelevant doc- uments by statistics from the whole collection. Under this assumption, u t the probability of term occurrence in nonrelevant documents for a query is df t N and log [ 1 − u t u t ] = log [ N − df t df t ] ≈ log Ndf t 11.22 In other words, we can provide a theoretical justification for the most fre- quently used form of idf weighting, which we saw in Section 6.2.1 . The approximation technique in Equation 11.22 cannot easily be extended to relevant documents. The quantity p t can be estimated in various ways: 1. We can use the frequency of term occurrence in known relevant docu- ments if we know some. This is the basis of probabilistic approaches to relevance feedback weighting in a feedback loop, discussed in the next subsection. 2. Croft and Harper 1979 proposed using a constant in their combination match model. For instance, we might assume that p t is constant over all terms x t in the query and that p t = 0.5. This means that each term has even odds of appearing in a relevant document, and so the p t and 1 − p t factors cancel out in the expression for RSV. Such an estimate is weak, but doesn’t disagree violently with our hopes for the search terms appearing in many but not all relevant documents. Combining this method with our earlier approximation for u t , the document ranking is determined simply by which query terms occur in documents scaled by their idf weighting. For short documents titles or abstracts in situations in which iterative searching is undesirable, using this weighting term alone can be quite satisfactory, although in many other circumstances we would like to do better. 3. Greiff 1998 argues that the constant estimate of p t in the Croft and Harper 1979 model is theoretically problematic and not observed empirically, and argues that a much better estimate is found by simply estimating p t from collection level statistics about the occurrence of t, as p t = df t N. Preliminary draft c 2008 Cambridge UP 228 11 Probabilistic information retrieval Iterative methods of estimation, which combine some of the above ideas, are discussed in the next subsection.11.3.4 Probabilistic approaches to relevance feedback
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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