Random split and merge processes

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Table of contents

Introduction 
0.1 Context
0.1.1 Natural language processing
0.1.2 Remarks on the shortcomings of standard models
0.1.3 Syntactic analysis
0.1.4 Markov substitute processes and toric grammars in a few words
0.2 Overview of the main results
0.2.1 Toric grammars
0.2.2 Markov substitute sets and processes
0.2.3 Model selection: finding a collection of Markov substitute sets
0.2.4 Parameter estimation
0.2.5 Invariant dynamics
1 Toric grammars and communication models 
1.1 Introduction to a new communication model
1.2 First definitions
1.2.1 Toric grammars
1.2.2 A roadmap towards a communication model
1.3 Operations on toric grammars
1.3.1 Non stochastic syntax splitting and merging
1.3.2 Random split and merge processes
1.3.3 Splitting rules and label identification
1.4 Parsing and generalization
1.5 Expectation of a random toric grammar
1.6 Language models
1.6.1 Communication model
1.6.2 Comparison with other models
1.7 A small experiment
1.8 The story so far…
1.A Proofs
1.A.1 Bound on the length of splitting and production processes .
1.A.2 Parsing Relations
1.A.3 Convergence to the expectation of a random toric grammar .
1.B Language produced by a toric grammar
2 Markov substitute Sets 
2.1 Presentation of the model
2.1.1 Motivation
2.1.2 What is a Markov substitute set
2.1.3 Weak Markov substitute sets
2.1.4 Basic properties of Markov substitute sets
2.1.5 Interpretation in terms of random parsing
2.2 Invariant dynamics
2.2.1 Metropolis invariant dynamics on sentences
2.2.2 Reflecting a reversible dynamics on the boundary of a finite domain
2.2.3 Compound dynamics
2.2.4 A simple example of recursive structure
2.2.5 Crossing-over reversible dynamics on texts
2.3 Exponential families of Markov substitute processes
2.4 Testing Markov substitute sets
2.4.1 Alternative construction of a test function
2.5 Weakening the Markov substitute assumption
2.6 Testing using a parse process
2.6.1 Probability of false rejection
2.6.2 Probability of false acceptance of the hypothesis
2.7 Testing Markov substitute sets without parsing
2.7.1 Definition of the test and probability of false rejection .
2.7.2 Testing for the weak Markov substitute property
2.7.3 Computation of the test
2.7.4 Some numerical examples
2.7.5 Probability of false acceptance of the test
2.8 Estimation of the substitute measure
3 Markov substitute sets and language 
3.1 Production rules and Markov substitute sets
3.1.1 Markov grammars
3.1.2 Parse trees
3.1.3 General introduction to parsing
3.2 Substitute measures and reversible dynamics
3.2.1 Parametrization of substitute measures
3.2.2 Estimating substitute measures
3.2.3 Simulating substitute measures
3.2.4 Reversible dynamics for the language distribution
3.2.5 Crossing-over dynamics
3.3 Crossing-over dynamics and the maximum likelihood estimator .
3.4 Building a Markov ruleset
3.4.1 Adding new rules
3.4.2 Reducing the context space
3.4.3 Saturation
3.4.4 Identification of labels
3.5 Toric grammars
3.5.1 Split and merge processes using parsing
3.5.2 Reversible split and merge process
3.6 Estimating the language distribution
3.A Support of the split and merge process and substitutions
3.B Parsing using a ruleset
3.B.1 Parsing general syntagms
3.B.2 Parsing inside syntagms of certain type
3.C Building crossing-over tree kernels
3.D Building general Metropolis reversible dynamics
4 Conclusion 
4.1 Possible uses of Markov substitute sets
4.2 Further considerations on the scope of the model
Bibliography