Synthetic Data and Generative AI

1st Edition - January 9, 2024
Author: Vincent Granville
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 2 1 8 5 7 - 6
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 2 1 8 5 6 - 9

Synthetic Data and Generative AI covers the foundations of machine learning with modern approaches to solving complex problems and the systematic generation and use of synthe… Read more

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Synthetic Data and Generative AI covers the foundations of machine learning with modern approaches to solving complex problems and the systematic generation and use of synthetic data. Emphasis is on scalability, automation, testing, optimizing, and interpretability (explainable AI). For instance, regression techniques – including logistic and Lasso – are presented as a single method without using advanced linear algebra. Confidence regions and prediction intervals are built using parametric bootstrap without statistical models or probability distributions. Models (including generative models and mixtures) are mostly used to create rich synthetic data to test and benchmark various methods.

Cover image
Title page
Table of Contents
Copyright
Chapter 1: Machine learning cloud regression and optimization
Abstract
1.1. Introduction: circle fitting
1.2. Methodology, implementation details, and caveats
1.3. Case studies
1.4. Connection to synthetic data: meteorites, ocean tides
References
Chapter 2: A simple, robust, and efficient ensemble method
Abstract
2.1. Introduction
2.2. Methodology
2.3. Implementation details
2.4. Model-free confidence intervals and perfect nodes
References
Chapter 3: Gentle introduction to linear algebra – synthetic time series
Abstract
3.1. Power of a matrix
3.2. Examples, generalization, and matrix inversion
3.3. Application to machine learning problems
3.4. Mathematics of autoregressive time series
3.5. Math for machine learning: must-read books
References
Chapter 4: Image and video generation
Abstract
4.1. Introduction
4.2. Applications
4.3. Python code
4.4. Visualizations
References
Chapter 5: Synthetic clusters and alternative to GMM
Abstract
5.1. Introduction
5.2. Generating the synthetic data
5.3. Classification and unsupervised clustering
5.4. Python code
References
Chapter 6: Shape classification and synthetization via explainable AI
Abstract
6.1. Introduction
6.2. Mathematical foundations
6.3. Shape signature
6.4. Shape comparison
6.5. Application
6.6. Exercises
References
Chapter 7: Synthetic data, interpretable regression, and submodels
Abstract
7.1. Introduction
7.2. Synthetic data sets and the spreadsheet
7.3. Damping schedule and convergence acceleration
7.4. Performance assessment on synthetic data
7.5. Feature selection
7.6. Conclusion
References
Chapter 8: From interpolation to fuzzy regression
Abstract
8.1. Introduction
8.2. Original version
8.3. Full, nonlinear model in higher dimensions
8.4. Results
8.5. Exercises
8.6. Python source code and data sets
References
Chapter 9: New interpolation methods for synthetization and prediction
Abstract
9.1. First method
9.2. Second method
9.3. Python code
References
Chapter 10: Synthetic tabular data: copulas vs enhanced GANs
Abstract
10.1. Sensitivity analysis, bias reduction and other uses of synthetic data
10.2. Using copulas to generate synthetic data
10.3. Synthetization: GAN versus copulas
10.4. Deep dive into generative adversarial networks (GAN)
10.5. Comparing GANs with the copula method
10.6. Data synthetization explained in one picture
10.7. Python code: GAN to synthesize medical data
References
Chapter 11: High quality random numbers for data synthetization
Abstract
11.1. Introduction
11.2. Pseudorandom numbers
11.3. Python code
11.4. Military-grade PRNG based on quadratic irrationals
References
Chapter 12: Some unusual random walks
Abstract
12.1. Symmetric unbiased constrained random walks
12.2. Related stochastic processes
12.3. Python code
References
Chapter 13: Divergent optimization algorithm and synthetic functions
Abstract
13.1. Introduction
13.2. Nonconverging fixed-point algorithm
13.3. Generalization with synthetic random functions
13.4. Smoothing highly chaotic curves
13.5. Connection to synthetic data: random functions
References
Chapter 14: Synthetic terrain generation and AI-generated art
Abstract
14.1. Introduction
14.2. Terrain generation and the evolutionary process
14.3. Python code
14.4. AI-generated art with 3D contours
References
Chapter 15: Synthetic star cluster generation with collision graphs
Abstract
15.1. Introduction
15.2. Model parameters and simulation results
15.3. Analysis of star collisions and collision graph
15.4. Animated data visualizations
15.5. Python code and computational issues
Chapter 16: Perturbed lattice point process: alternative to GMM
Abstract
16.1. Perturbed lattices: definition and properties
16.2. Cluster processes and nearest neighbor graphs
16.3. Statistical inference for point processes
16.4. Special topics
References
Chapter 17: Synthetizing multiplicative functions in number theory
Abstract
17.1. Introduction
17.2. Euler products
17.3. Finite Dirichlet series and generalizations
17.4. Exercises
17.5. Python code
References
Chapter 18: Text, sound generation, and other topics
Abstract
18.1. Sound generation: let your data sing!
18.2. Data videos and enhanced visualizations in R
18.3. Dual confidence regions
18.4. Fast feature selection based on predictive power
18.5. NLP: taxonomy creation and text generation
18.6. Automated detection of outliers and number of clusters
18.7. Advice to beginners
References
Glossary
Index

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Synthetic Data and Generative AI

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Vincent Granville