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Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (p. 127-134) and index.

1. Introduction -- 1.1 Structure and contribution of this book -- 1.2 Background: a timeline of IR models -- 1.3 Notation -- 1.3.1 The notation issue "term frequency" -- 1.3.2 Notation: Zhai's book and this book --

2. Foundations of IR models -- 2.1 TF-IDF -- 2.1.1 TF variants -- 2.1.2 TFlog: Logarithmic TF -- 2.1.3 TFfrac: fractional (ratio-based) TF -- 2.1.4 IDF variants -- 2.1.5 Term weight and RSV -- 2.1.6 Other TF variants: lifted TF and pivoted TF -- 2.1.7 Semi-subsumed event occurrences: a semantics of the BM25-TF -- 2.1.8 Probabilistic IDF: The probability of being informative -- 2.1.9 Summary -- 2.2 PRF: the probability of relevance framework -- 2.2.1 Feature independence assumption -- 2.2.2 Non-query term assumption -- 2.2.3 Term frequency split -- 2.2.4 Probability ranking principle (PRP) -- 2.2.5 Summary -- 2.3 BIR: binary independence retrieval -- 2.3.1 Term weight and RSV -- 2.3.2 Missing relevance information -- 2.3.3 Variants of the BIR term weight -- 2.3.4 Smooth variants of the BIR term weight -- 2.3.5 RSJ term weight -- 2.3.6 On theoretical arguments for 0.5 in the RSJ term weight -- 2.3.7 Summary -- 2.4 Poisson and 2-Poisson -- 2.4.1 Poisson probability -- 2.4.2 Poisson analogy: sunny days and term occurrences -- 2.4.3 Poisson example: toy data -- 2.4.4 Poisson example: TREC-2 -- 2.4.5 Binomial probability -- 2.4.6 Relationship between Poisson and binomial probability -- 2.4.7 Poisson PRF -- 2.4.8 Term weight and RSV -- 2.4.9 2-Poisson -- 2.4.10 Summary -- 2.5 BM25 -- 2.5.1 BM25-TF -- 2.5.2 BM25-TF and pivoted TF -- 2.5.3 BM25: literature and Wikipedia end 2012 -- 2.5.4 Term weight and RSV -- 2.5.5 Summary -- 2.6 LM: language modeling -- 2.6.1 Probability mixtures -- 2.6.2 Term weight and RSV: LM1 -- 2.6.3 Term weight and RSV: LM (normalized) -- 2.6.4 Term weight and RSV: JM-LM -- 2.6.5 Term weight and RSV: Dirich-LM -- 2.6.6 Term weight and RSV: LM2 -- 2.6.7 Summary -- 2.7 PIN's: probabilistic inference networks -- 2.7.1 The Turtle/Croft link matrix -- 2.7.2 Term weight and RSV -- 2.7.3 Summary -- 2.8 Divergence-based models and DFR -- 2.8.1 DFR: divergence from randomness -- 2.8.2 DFR: sampling over documents and locations -- 2.8.3 DFR: binomial transformation step -- 2.8.4 DFR and KL-divergence -- 2.8.5 Poisson as a model of randomness: P(Kt [greater than] 0/d,c): DFR-1 -- 2.8.6 Poisson as a model of randomness: P(Kt [equals] TFd/d,c): DFR-2 -- 2.8.7 DFR: elite documents -- 2.8.8 DFR: example -- 2.8.9 Term weights and RSV's -- 2.8.10 KL-divergence retrieval model -- 2.8.11 Summary -- 2.9 Relevance-based models -- 2.9.1 Rocchio's relevance feedback model -- 2.9.2 The PRF -- 2.9.3 Lavrenko's relevance-based language models -- 2.10 Precision and recall -- 2.10.1 Precision and recall: conditional probabilities -- 2.10.2 Averages: total probabilities -- 2.11 Summary --

3. Relationships between IR models -- 3.1 PRF: the probability of relevance framework -- 3.1.1 Estimation of term probabilities -- 3.2 P(d - q): the probability that d implies q -- 3.3 The vector-space model (VSM) -- 3.3.1 VSM and probabilities -- 3.4 The generalised vector-space model (GVSM) -- 3.4.1 GVSM and probabilities -- 3.5 A general matrix framework -- 3.5.1 Term-document matrix -- 3.5.2 On the notation issue "term frequency" -- 3.5.3 Document-document matrix -- 3.5.4 Co-occurrence matrices -- 3.6 A parallel derivation of probabilistic retrieval models -- 3.7 The Poisson bridge: Pd(t/u) avgtf(t,u) [equals] PL(t/u) avgdl(u) -- 3.8 Query term probability assumptions -- 3.8.1 Query term mixture assumption -- 3.8.2 Query term burstiness assumption -- 3.8.3 Query term BIR assumption -- 3.9 TF-IDF -- 3.9.1 TF-IDF and BIR -- 3.9.2 TF-IDF and Poisson -- 3.9.3 TF-IDF and BM25 -- 3.9.4 TF-IDF and LM -- 3.9.5 TF-IDF and LM: side-by-side -- 3.9.6 TF-IDF and PIN's -- 3.9.7 TF-IDF and divergence -- 3.9.8 TF-IDF and DFR: risk times gain -- 3.9.9 TF-IDF and DFR: gaps between term occurrences -- 3.10 More relationships: BM25 and LM, LM and PIN's -- 3.11 Information theory -- 3.11.1 Entropy -- 3.11.2 Joint entropy -- 3.11.3 Conditional entropy -- 3.11.4 Mutual information (MI) -- 3.11.5 Cross entropy -- 3.11.6 KL-divergence -- 3.11.7 Query clarity: divergence(query collection) -- 3.11.8 LM = Clarity(query) - Divergence(query doc) -- 3.11.9 TF-IDF = Clarity(doc) - Divergence(doc query) -- 3.12 Summary --

4. Summary & research outlook -- 4.1 Summary -- 4.2 Research outlook -- 4.2.1 Retrieval models -- 4.2.2 Evaluation models -- 4.2.3 A unified framework for retrieval and evaluation -- 4.2.4 Model combinations and "new" models -- 4.2.5 Dependence-aware models -- 4.2.6 "Query-log" and other more-evidence models -- 4.2.7 Phase-2 models: retrieval result condensation models -- 4.2.8 A theoretical framework to predict ranking quality -- 4.2.9 MIR: math for IR -- 4.2.10 AIR: abstraction for IR --

Bibliography -- Author's biography -- Index.

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Information Retrieval (IR) models are a core component of IR research and IR systems. The past decade brought a consolidation of the family of IR models, which by 2000 consisted of relatively isolated views on TF-IDF (Term-Frequency times Inverse-Document-Frequency) as the weighting scheme in the vector-space model (VSM), the probabilistic relevance framework (PRF), the binary independence retrieval (BIR) model, BM25 (Best-Match Version 25, the main instantiation of the PRF/BIR), and language modelling (LM). Also, the early 2000s saw the arrival of divergence from randomness (DFR). Regarding intuition and simplicity, though LM is clear from a probabilistic point of view, several people stated: "It is easy to understand TF-IDF and BM25. For LM, however, we understand the math, but we do not fully understand why it works." This book takes a horizontal approach gathering the foundations of TF-IDF, PRF, BIR, Poisson, BM25, LM, probabilistic inference networks (PIN's), and divergence-based models. The aim is to create a consolidated and balanced view on the main models. A particular focus of this book is on the "relationships between models." This includes an overview over the main frameworks (PRF, logical IR, VSM, generalized VSM) and a pairing of TF-IDF with other models. It becomes evident that TF-IDF and LM measure the same, namely the dependence (overlap) between document and query. The Poisson probability helps to establish probabilistic, non-heuristic roots for TF-IDF, and the Poisson parameter, average term frequency, is a binding link between several retrieval models and model parameters.

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