Web and Data Science

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Web and Data Science by Mind Map: Web and Data Science

1. Onto

1.1. [VL1/VL2 Logic, Logic, Logic]

1.1.1. FOL Semantics Interpretation Entailment Syntax Terms Formulars Compactness of Topology Löwenheim-Skolem-Property First Lindström Theorem Pro und Contra von FOL Complexity FOL in PSPACE FOL in AC^0 (pratical Scenarios)

1.1.2. Proof Calculi Resolution Prenex Normal Form Skolem Form (Skolemization) Clausal Normal Form Correctness & Completness Semi-Decidability

1.2. [VL3/VL4 Finite Model Theory]

1.2.1. Inexpressibility Tools Games Ehrenfeucht-Fraissé Games Quantifier Rank Locality Bounded Number of Degree Property Gaifman Locality Hanf Locality Reductions FOL has the 0-1 Law

1.2.2. Fixed-Point Logics Datalog

1.3. [VL5/VL6 Data Exchange]

1.3.1. Main Setting Consistency Materialization Goodness

1.3.2. Materialization Marked NULLs

1.3.3. Representations

1.3.4. Certain Answears

1.3.5. Solutions Universal Solutions Homomorphism Core Solutions

1.3.6. Mappings Source Schema Target Schema Source-target dependencies st-tgd Target dependencies tgd edg

1.3.7. Chase Terminating With Solution Without Solution Not Terminating Simple Dependency Graphs

1.4. [VL7/VL8 Ontology Based Data Access]

1.4.1. Closed Word Assumption NULLs

1.4.2. Open World Assumption

1.4.3. Ontologies Signature Constants Concepts Roles Terminological Box (TBox) Assertional Box (ABox)

1.4.4. Reasoning Services Model Satisfiability Coherence Concept satisfiability Subsumption Instance Check Query Answering

1.4.5. Certain Answers

1.4.6. Descriptions Logics (DLs) Lightweight DLs

1.4.7. Tableaux

1.4.8. Rewriting Perfect Rewriting Termination Correctnis Completness Unifications Annonymization Reduction

1.4.9. Unfolding

1.5. [VL9/VL10 Ontology Integration]

1.5.1. Motivation Import Merge Versioning

1.5.2. Belief Revision Consequence Operator Tarskian Consequence Operator Belief Set AGM Belief Revision Expansion Contraction Revision Criticism Remainder Set Selection Function Partial Meet

1.5.3. Ontology Change Goals Overcome Heterogenity Combine Ontologies Modify Ontologies Operations Ontology Mapping Ontology Merge Ontology Evolution Ontology Learning

1.5.4. Iterated Belief Revision

1.6. [VL11 Stream Processing]

2. Data Mining

2.1. [VL1-3]: Bayesian Networks

2.1.1. Agent Rational Autonomous Social Simple information retrieval

2.1.2. Triple Tradeoff Complexity/Capacity of H: c(H) Training set size: N Generalization error: E As N increases, E decreases As c(H) increases, first E decreases, then E increases again (overfitting)

2.1.3. Conditional Probability

2.1.4. Bayes Rule

2.1.5. Bayesian Network Conditional Probability Table (CPT) Full Joint Distribution P(X_1, ..., X_n)

2.1.6. Inference Tasks Simple queries Conjunctive queries Optimal decisions Value of information Sensitivity analysis Explanation

2.1.7. Exact Inference Inference by Enumeration Variable Elimination Pearl's Belief Propagation Algorithm \lambda messages \pi message

2.1.8. Approximate Inference Sampling from empty network Rejection sampling Likelihood weighting Markov Chain Monte Carlo Markov Blanket

2.1.9. Learning Bayesian Networks Known structure Full Bayesian Learning MAP Learning Maximum Likelihood Learning Unknown structure Model selection

2.1.10. Learning BNs with hidden variables Known structure Expectation-Maximization Unknown structure Structural EM

2.2. [VL4-7]: Structured Causal Models

2.2.1. General concepts Confounder Mediator Exogenous/Endogenous Exogenous Endogenous Simpson's paradox d-separation Network structure Chain Fork Collider Equivalent graphs V-Structure Skeleton Conditioning

2.2.2. IC algorithm

2.2.3. Intervention Blocking conditions Backdoor criterion Frontdoor criterion General Causal Effect Inverse Probability Weighing Average Causal Effect/Causal Effect Difference Specific Causal Effect Controlled Direct Effect Adjusting

2.2.4. Linear SCMs Exogenous variables for Linear SCMs Total effect in Linear SCMs Path coefficients Regression coefficients Instrumental Variable Conditional Instrumental Variables Instrumental Sets Wright's Rule

2.2.5. Counterfactuals Consistency rule Counterfactuals can simulate intervention Additive Intervention

2.3. [VL8]: Junction Trees

2.3.1. Junction Tree Property

2.4. [VL9]: Inference in Probabilistic Graphical Models

2.4.1. Markov Networks (=Markov Random Fields)

2.5. [VL10]: Computational Learning Theory

2.5.1. PAC Learning Computational Complexity Sample complexity VC Dimension Shattering Dichotomy

2.5.2. Mistake Bounds Optimal Mistake Bounds

2.6. [VL11]: Learning FOL definable concepts

2.6.1. Parameter Learning

2.6.2. Model Learning

3. Autonomous Agents and Information Retrieval

3.1. [VL1]: Agents and Documents

3.1.1. Documents Document Zones Incidence matrices for overlap matching Term weighting Term frequency Term scarcity Document length Inverse document frequency Vector space model tf.idf scarcity considered document frequency considered normalize to document length Latent Semantic Indexing (LSI) Dimension reduction Sigular Value Decomposition (Eigenwertzerlegung) Relevance feedback Precision Recall F-Score Kappa measure Rocchio algorithm

3.2. [VL2]: Probabilistic Information Retrieval

3.2.1. Odds

3.2.2. Probability Ranking Principle Binary Independence Retrieval Retrieval Status Value (RSV) Binary Independence Indexing

3.2.3. Bayesian Network Information Retrieval

3.2.4. Language Models Ponte and Croft LM Lavrenko and Croft LM

3.3. [VL3]: Topic Modeling

3.3.1. Naive Bayes: Plate Notation C: topics/classes N: number of words in considered documents W_i: one specific word in corpus M: documents W: words now in document

3.3.2. Multinomial Naive Bayes

3.3.3. Probabilistic LSI/LSA Hyperlink modeling using pLSI

3.3.4. Latent Dirichlet Allocation (LDA) Dirichlet Distributions Smoothed LDA Parameter Learning Variatonal EM Gibbs Sampling Hyperlink modeling using LDA

3.3.5. Relational Topic Model (RTM) Collapsed Gibbs Sampling for RTM

3.4. [VL4]: Probabilistic Reasoning over Sequential Structures

3.4.1. Probablisitic Temporal Models Dynamic Bayesian Networks Parameter Learning via EM Hidden Markov Models Kalman Filters

3.4.2. Inference Tasks Filtering Prediction Smoothing Most likely explanation

3.4.3. Viterbi Algorithm

3.5. [VL5]: Word Semantics and Latent Relational Structures

3.5.1. Pointwise Mutual Information (P)PMI-Matrix

3.5.2. Word representation: word2vec Continuous Bag of Words (CBOW) Skip-Grams (SG) Leaning method: Negative Sampling (SGNS) GloVe Dynamic Context Windows Context Distribution Smoothing

3.6. [VL6]: Multi-Relational LSA

3.6.1. Polarity Inducing LSA (PILSA)

3.6.2. Multi-Relational LSA (MRLSA) Encode Relations in Tensor Tensor decomposition (sim. to SVD)

3.7. [VL7]: Probablisitic Relational Models

3.7.1. Markov Networks (MRFs)

3.7.2. Markov Logic Networks (MLNs)

3.7.3. Inductive Logic Programming Inductive Learning: FOIL

3.8. [VL8]: Lifted Inference in PRMs

3.8.1. Lifted Junction Tree Algorithm

3.9. [VL9]: Game Theory / Social Choice Theory

3.9.1. Game Theory Game Agents Actions Outcomes Payoffs Multiagent Systems: Criteria Social welfare Surplus Pareto efficiency Individual rationality Stability Symmetry Strategies Dominant strategies Vickrey Auctions Nash Equilibrium

3.9.2. Social Choice Theory Agenda paradox Condorcet principle Borda count principle Inverted-order paradox Arrow's Theorem

3.10. [VL10]: Mechanism Design

3.10.1. Direct mechanisms

3.10.2. Incentive-compatible

3.10.3. Dominant strategies implementation Revelation principle

3.10.4. Social choice functions

3.10.5. Groves Mechanism