Structured optimization problems

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Table of contents

1 Introduction 
1.1 Spatial data and geostatistics
1.2 Spatial data analysis
1.3 Characteristics of geostatistical data
1.4 The weighted graph framework
1.5 Variational aggregation on weighted graphs
1.6 Graph structured prediction
1.7 Organisation of the thesis
2 Proximal methods for structured optimization 
2.1 Introduction
2.2 Structured optimization problems
2.3 Proximal splitting for structured optimization
2.4 Generalized forward-backward
2.5 Experimental setup and results
2.6 Conclusion
3 Aggregating spatial statistics with a generalized forward-backward splitting algorithm 
3.1 Aggregation as an optimization problem
3.2 Interpretation
4 Cut Pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs 
4.1 Introduction
4.2 A working set algorithm for total variation regularization
4.3 Minimal partition problems
4.4 Experiments
4.5 Conclusion
5 Learning in graphical models 
5.1 Introduction
5.2 Undirected graphical models
5.3 Potts model
5.4 Continuous time Markov models
5.5 Conclusion
6 Continuously indexed Potts model 
6.1 Introduction
6.2 Continuous graph Potts models
6.3 Learning with continuous graphs
6.4 Experiments
6.5 Conclusion
A Converting spatial data to graph
A.1 Converting spatial data to graph
B Appendix of Chapter 2
Bibliography 
C Appendix of Chapter 4
D Appendix of Chapter 6