of Data Sciences

You can retrieve the draft of the book:

Gabriel PeyrÃ©, Mathematical Foundations of Data Sciences.

The Latex sources of the book are available.

It should serve as the mathematical companion for the Numerical Tours of Data Sciences, which presents Matlab/Python/Julia/R detailed implementations of all the concepts covered here.

This book draft presents an overview of important mathematical and numerical foundations for modern data sciences. In particular, it covers the basics of signal and image processing (Fourier, Wavelets, and their applications to denoising and compression), imaging sciences (inverse problems, sparsity, compressed sensing) and machine learning (linear regression, logistic classification, deep learning). The focus is on the mathematically-sound exposition of the methodological tools (in particular linear operators, non-linear approximation, convex optimization, optimal transport) and how they can be mapped to efficient computational algorithms.

- Shannon Theory
- Fourier Transforms
- Wavelets
- Linear and Non-linear Approximation
- Compression
- Denoising
- Variational Priors and Regularization
- Inverse Problems
- Theory of Sparse Regularization
- Compressed Sensing
- Machine Learning
- Optimization & Machine Learning: Smooth Optimization
- Optimization & Machine Learning: Advanced Topics
- Deep-Learning
- Convex Analysis
- Non Smooth Optimization

Dedicated course notes covering specifically optimization and its applications in ML is available as a separate PDF file. There is also a short note on PAC learning.

Dedicated course notes covering specifically optimal transport is available as a separate PDF file. You can also check the dedicated book for a more detailed treatment of the algorithmic aspects.