Machine Learning & AI

• The Artificial Intelligence and Machine Learning research group at Princeton University. See also Sanjeev Arora's ICM 2018 plenary lecture on The mathematics of machine learning and deep learning.
• Both April and July 2024 issues of the Bulletin of the American Mathematical Society contain a collection of papers on Math and AI.
• Besides, the Notices of the American Mathematical Society have published more pedagogical papers on the mathematical foundations of Machine Learning:
  • Machine Learning and Invariant Theory (2023), vol 70, 1205-13,
  • Mathematizing Human Perception (2023), vol 70, 1081-88,
  • Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning (2022), vol 69, 1717-29,
  • Model Selection for Optimal Prediction in Statistical Machine Learning (2020), vol 67, 155-168,
  • Machine Learning: Mathematical Theory and Scientific Applications (2019), vol 66, 1813-20,
  • From Decoupling and Self-Normalization to Machine Learning (2019), vol 66, 1641-46,
• The Spring 2020 & 2021 lectures on deep learning by Yann LeCun at the NYU Center for Data Science.
• The lectures, in French, at the Collège de France, by Stéphane Mallat:
  • 2023-2024 : Apprentissage et génération par échantillonnage aléatoire,
  • 2021-2022 : Information and Complexity (Information et complexité),
  • 2020-2021 : Parsimonious representations (Représentations parcimonieuses),
  • 2019-2020: Multiscale models and convolutive neural networks (Modèles multi-échelles et réseaux de neurones convolutifs),
  • 2018-2019: Deep Learning (L'apprentissage par réseaux de neurones profonds),
  • 2017-2018: Learning and the Curse of Dimensionality.

Students attending my final year lectures must have a working knowledge of Python.

• Since the academic year 2016-2017, students undertaking their dissertation on Machine Learning, deep learning, etc., are using either Python with the PyTorch, fast.ai, TensorFlow, and scikit-learn libraries, or Torch for R.
• Some statistical procedures are using Octave, a matrix oriented programming language for numerical computing, the syntax of which is similar to Matlab, up to some changes in the syntax of a few functions.
• The C++ programming language is still the most powerful language. Valgrind is a useful tool for memory leak debugging, profiling, etc.
  NLopt is a free/open-source library for nonlinear optimization, callable from C, C++, Fortran, Python, Julia, R, Octave, and Matlab programs.
• Donald Knuth's home page. Don Knuth is the author of the celebrated books: The Art of Computer Programming You can find there everything important on semi-numerical and numerical algorithms, \(\TeX\) etc.
• The Digital Library of Mathematical Functions of the National Institute of Standards and Technology (NIST); See A special functions handbook for the digital age, R. Boisvert, C.W. Clark, D. Lozier, and F. Olver, Notices of the American Mathematical Society (2011), vol 58, 905-911, . This new online library supersedes the celebrated book by M. Abramowitz and I. Stegun: the Handbook of Mathematical Functions.
  The NIST Statistical Reference Datasets (NIST StRD) for assessing the numerical accuracy of statistical software packages. This database is very useful for checking parts of statistical procedures.
  Useful information on the issue of numerical accuracy of statistical software packages is available at B.D. McCullough's web page.