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## Other IR Models

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**Set Theoretic**Structured Models Fuzzy Extended Boolean Non-Overlapping Lists Proximal Nodes Browsing Flat Structure Guided Hypertext Other IR Models Classic Models boolean vector probabilistic Algebraic U s e r T a s k Generalized Vector Lat. Semantic Index Neural Networks Retrieval: Adhoc Filtering Probabilistic Inference Network Belief Network Browsing**Another Vector Model: Motivation**• Index terms have synonyms. [Use thesauri?] • Index terms have multiple meanings (polysemy). [Use restricted vocabularies or more precise queries?] • Index terms are not independent; think “phrases”. [Use combinations of terms?]**Latent Semantic Indexing/Analysis**• Basic Idea: Keywords in a query are just one way of specifying the information need. One really wants to specify the key concepts rather than words. • Assume a latent semantic structure underlying the term-document data that is partially obscured by exact word choice.**LSI In Brief**• Map from terms into lower dimensional space (via SVD) to remove “noise” and force clustering of similar words. • Pre-process corpus to create reduced vector space • Match queries to docs in reduced space**SVD for Term-Doc Matrix**Docs = Terms m x m m x d t x d t x m C = where m is the rank of X (<=min(t,d)), T is orthonornal matrix of eigenvectors for term-term correlation, D is orthonornal matrix of eigenvectors from transpose of doc-doc correlation**Reducing Dimensionality**• Order singular values in S0 by size, keep the k largest, and delete other rows/columns in S0, T0 and D0 to form • Approximate model is the rank-k model with best possible least-squares-fit to X. • Pick k large enough to fit structure, but small enough to eliminate noise – usually ~100-300.**Computing Similarities in LSI**• How similar are 2 terms? • dot product between two row vectors of • How similar are two documents? • dot product between two column vectors of • How similar are a term and a document? • value of an individual cell**Query Retrieval**• As before, treat query as short document: make it column 0 of C • First row of C provides rank of docs wrt query.**LSI Issues**• Requires access to corpus to compute SVD • How to efficiently compute for Web? • What is the right value of k ? • Can LSI be used for cross-language retrieval? • Size of corpus is limited: “one student’s reading through high school” (Landauer 2002).**Other Vector Model: Neural Network**• Basic idea: • 3 layer neural net: query terms, document terms, documents • Signal propagation based on classic similarity computation • Tune weights.**Query Terms**DocumentTerms Documents k1 d1 ka ka dj kb kb dj+1 kc kc dN kt Neural Network Diagram from Wilkinson and Hingston, SIGIR 1991**Computing Document Rank**• Weight from query to document term • Wiq = wiq sqrt ( i wiq ) • Weight from document term to document • Wij = wij sqrt ( i wij )**Probabilistic Models**Principle: Given a user query q and a document d in the collection, estimate the probability that the user will find d relevant. (How?) • User rates a retrieved subset. • System uses rating to refine the subset. • Over time, retrieved subset should converge on relevant set.**Computing Similarity I**probability that document dj is relevant to query q, probability that dj is non-relevant to the query q, probability of randomly selecting dj from set R probability that a randomly selected document is relevant**Computing Similarity II**probability that index term ki is present in document randomly selected from R, Assumes independence of index terms**Initializing Probabilities**• assume constant probabilities for index terms: • assume distribution of index terms in non-relevant documents matches overall distribution:**Improving Probabilities**Assumptions: • approximate probability given relevant as % docs with index i retrieved so far: • approximate probabilities given non-relevant by assuming not retrieved are non-relevant:**Classic Probabilistic Model Summary**• Pros: • ranking based on assessed probability • can be approximated without user intervention • Cons: • really need user to determine set V • ignores term frequency • assumes independence of terms**Probabilistic Alternative: Bayesian (Belief) Networks**A graphical structure to represent the dependence between variables in which the following holds: • a set of random variables for the nodes • a set of directed links • a conditional probability table for each node, indicating relationship with parents • a directed acyclic graph**Earthquake**Burglary Alarm JohnCalls Mary Calls Belief Network Example from Russell & Norvig**Earthquake**Burglary Alarm JohnCalls Mary Calls Belief Network Example (cont.) Probability of false notification: alarm sounded and both people call, but there was no burglary or earthquake**Inference Networks for IR**Random variables are associated with documents, index terms and queries. Edges from document node to term nodes increases belief in terms.**Computing rank in Inference Networks for IR**• q is keyword query. q1 is Boolean query. I is information need. • Rank of document is computed as P(q^dj)**Where do probabilities come from? (Boolean Model)**• uniform priors on documents • only terms in the document are active • query is matched to keywords ala Boolean model**Belief Network Formulation**• different network topology • does not consider each document individually • adopts set theoretic view