Материал из MachineLearning.

Основная статья: Численные методы обучения по прецедентам (практика, В.В. Стрижов)

Содержание 1 General principles 2 Syllabus and goals 3 Theme 1: 3.1 Message 3.2 Basics 3.3 Application 3.4 Code 4 Theme 1: Manifolds 5 Code 6 Theme 1: ODE and flows 7 Theme 1: PDE 8 Fourier for fun and practice 1D 9 Fourier for fun and practice nD 10 Geometric Algebra 11 Theme 1: High order splines 12 Theme 1: Topological data analysis 13 Theme 1: Homology versus homotopy 14 Fundamental theorems

• Geometric deep learning
• Functional data analysis
• Applied mathematics for machine learning

General principles

1. The experiment and measurements defines axioms i

Syllabus and goals

Theme 1:

Message

Basics

Application

Code

https://papers.nips.cc/paper/2018/file/69386f6bb1dfed68692a24c8686939b9-Paper.pdf

Theme 1: Manifolds

Code

Surface differential geometry Coursera code video for Image and Video Processing

Theme 1: ODE and flows

• Neural Ordinary Differential Equations (source paper and code)
• W: Flow-based generative model
• Flows at deepgenerativemodels.github.io
• Знакомство с Neural ODE на хабре

Goes to BME

• Variational Inference with Normalizing Flows (source paper)
• Flow-based deep generative models

Theme 1: PDE

(after RBF)

Fourier for fun and practice 1D

Fourier Code

Fourier for fun and practice nD

See:

• Fourier analysis on Manifolds 5G page 49
• Spectral analysis on meshes

Geometric Algebra

experior product and quaternions

Theme 1: High order splines

Theme 1: Topological data analysis

Theme 1: Homology versus homotopy

W: Homology

Fundamental theorems

W: Inverse function theorem and Jacobian