CodPy Book

Chapter 2:

  • Chapter 2: Basic notions on reproducing kernels
    • 2.2 Reproducing kernels and transformation maps
    • 2.3 1D Periodic Function Extrapolation
    • 2.3.2 Applying maps to kernels
    • 2.4 2D Periodic Function Extrapolation
    • 2.6.2 A study of the discrepancy functional

Chapter 3:

  • Chapter 3: Discrete operators based on reproducing kernels
    • 3.3.2 Partition of unity
    • 3.4.1 Gradient Operator
    • 3.4.2 Divergence Operator
    • 3.4.3 Inverse Laplace operator
    • 3.4.4 Integral operator - inverse gradient operator
    • 3.4.5 Integral operator - inverse divergence operator
    • 3.4.6 Leray-orthogonal operator
    • 3.4.7 Leray operator and Helmholtz-Hodge decomposition

Chapter 4:

  • Chapter 4: Clustering strategies
    • 4.2 Clustering

Chapter 5:

  • Chapter 5: Optimal transport and statistical kernel methods
    • 5.2 Optimal Transport: LSAP (Linear Sum Assignment Problem)
    • 5.3.3 Kernel Conditional Density
    • 5.3.4 Kernel Conditional Expectation
    • 5.6.a Application of OT in Disitribution Sampling : 1D
    • 5.6.b Application of OT in Disitribution Sampling : 2D
    • 5.6.c Application of OT in Disitribution Sampling : High-Dimensional case
    • 5.6.d Exploration Data Analysis of the Latent Space: Spherical Data
    • 5.6.e Exploration Data Analysis of the Latent Space: Spherical Data - 2
    • 5.7. Conditional Sampling

Chapter 6:

  • Chapter 6: Applications to machine learning : supervised, unsupervised and generative methods
    • 6.1 Supervised learning: reproducibility illustration with housing prices
    • 6.2 Supervised learning: benchmarks of methods with MNIST
    • 6.3 Unsupervised learning: Clustering - MNIST
    • 6.4 Unsupervised learning: Clustering - Fraud detection
    • 6.4.1 Generating complex distributions
    • 6.4.1 Generating complex distributions from celebA dataset
    • 6.4.5 Conditioning on discrete distributions of celebA dataset
    • 6.5 Unsupervised learning: Clustering - Stock Clustering
    • 6.7. Conditional Sampling

Chapter 7:

  • Chapter 7: Application to partial differential equations
    • 7.01 Inverse Laplace Operator
    • 7.02 Denoising
    • 7.03 Heat Equation
    • 7.04 Lagrange Heat Equation
    • 7.05 Convex Hull Algorithm
    • 7.06 Automatic Differentiation

Chapter 8:

  • KQLearning
  • Chapter 8: Reinforcement learning.
    • 8.1 Using KAgents
    • 8.2 Experiments - Cartpole
    • 8.3 Experiments - LunarLander

Chapter 9:

  • Chapter 9: Mathematical Finance.
    • 9.01 Free time series modeling
    • 9.02 Random walks
    • 9.03 ARMA(p,1) model
    • 9.04 GARCH(1,1) model
    • 9.05 Lagrange interpolation model
    • 9.06 Additive noise map
    • 9.07 Conditionning model
    • 9.08 Stochastic volatility model
    • 9.09 Heston Process - Reproducibility
    • 9.10 Heston Process - Path comparison
    • 9.11 Heston Process - Intraday interpolation
    • 9.12 Price extrapolation using KRR and Taylor
    • 9.13 Greeks output after correction
    • 9.13 Reverse Stress Test
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© Copyright 2024, Philippe G. LeFloch , Jean-Marc Mercier, and Shohruh Miryusupov.

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