Training for Research

• Study for the weekly research seminar
• Mar. 2, 2021 ~ Feb. 1, 2022

1. Neural Networks Basics

• Neural Networks, Logistic Regression, Gradient Descent

| Presentation |

2. Pattern formation

• Lengyel-Epstein model (1D, 2D)

| Presentation | Code |

3. Gradient Descent

• Convex optimization, Newton-method, Lagrange multiplier
• Rosenbrock function

| Presentation | Code |

4. Wavelet Transform

• Wavelet Transform and Windowed Fourier transform, Orthonormal wavelet bases : Multiresolution analysis
  | Presentation |
• Hilbert Space and Fourier Analysis
  | Presentation |
• Continuous windowed FT, operators, and Mathematical theorem related to wavelet transformation
  | Presentation |

[1] Daubechies, Ingrid. Ten lectures on wavelets. Society for industrial and applied mathematics, 1992.
[2] Harris, Terri Joan. "HILBERT SPACES AND FOURIER SERIES." (2015).

5. Monte-Carlo methods

• Markov chain Monte-Carlo (MCMC), MCMC Analysis of Diffusion model, Kinetic/Dynamic Monte-Carlo

| Presentation | Code |

6. Adam optimization

• Mini-batch gradient descent, exponentially weighted averages, bias correction, momentum, RMSprop, Adam

| Presentation | Code |

7. Hierarchical structure in financial markets

• Correlation coefficient, Minimal spanning tree (MST), Subdominant ultrametric distance matrix

| Presentation | Code |

8. Dynamical asset trees

• MST, four moments, central vertex, vertex degree, power law, multi-step survival ratio

| Presentation | Code |