Gilles Teyssière's Website

Teaching and Supervision

Online Teaching Material

2010-: Institut Mines-Télécom Atlantique, Brest, lectures (in French) on nonstationary processes (Mathematical and Computational Engineering Lectures).
My 3^rd year lectures on nonstationary processes for the academic year 2020-2021 will take place in March 2021. They have been quite rewritten from scratch, after reviewing a long series of papers and books (over 70 and counting) on these issues for Mathematical Reviews®. The new section on deep learning and AI is obviously expanding. The writing of the book supporting these lectures is in progress.
List of past lectures for the academic year 2018-2019:
- Lecture 1 (Tuesday 10^th January 2019): Volatility models. GARCH model: definition, properties, dependence structure, QML estimation. Slides
- Lecture 2 (Friday 11^th January 2019): Exponential GARCH model. Bootstrap methods and their application to model-free prediction and inference of univariate models. Multivariate models. Change-point models. Slides
- Lecture 3 (Monday 25^th February 2019): Long-range dependent and multifractal volatility models. Wavelet analysis of volatility processes. Slides
- Lecture 4 (Tuesday 26^th February 2019): Volatility estimation of high frequency time series. Deep Learning: convolutional, recurrent and hybrid architectures. Slides
2009: Aarhus University, PhD lectures, based on the draft version of the book Large Sample Inference for Long Memory Processes (2012) Imperial College Press. In 2013, I wrote the review of this book for Mathematical Reviews®. If you are a MathSciNet subscriber, you could read this review from my author profile
Additional material not covered in that book: Slides
2006-2007: Ensae, lectures (in French) on Long-range dependence and change-points, Applications to univariate and multivariate financial time series,
- Leçon 1 : Processus fortement dépendants, Transparents
- Leçon 2 : Tests de détection de longue portée et estimateurs du paramètre de longue portée, Transparents
- Leçon 3 : Tests de détection de ruptures, Transparents
- Leçon 4 : Méthodes statistiques robustes aux ruptures, Transparents
- Leçon 5 : Modèles multivariés, Transparents
1993-1996: Lectures on optimization techniques with Maple. I have typed a 200 pages document, that obviously needs to be upgraded.

Machine Learning and AI

The Machine learning with provable guarantees research group at Princeton University. See also Sanjeev Arora's ICM 2018 plenary lecture on The mathematics of machine learning and deep learning.
The December 2019 issue of the Notices of the American Mathematical Society contains the paper entitled Machine Learning: Mathematical Theory and Scientific Applications (2019), vol 66, 1813-20, Pdf
The Spring 2020 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:
- 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.

Computing Science Resources

The first class requires a good working knowledge of R.
Since the academic year 2016-2017, students undertaking their dissertation on Machine Learning, deep learning, etc., are using either Python with the PyTorch, TensorFlow, and scikit-learn libraries, or Torch for R.
The efficiency of the running of Python programs is substantially improved by calling them within a Julia program.
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, T_eX 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, Pdf file. 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.
BOINC, the Berkeley Open Infrastructure for Network Computing, is an open-source software for volunteer and grid computing. BOINC projects are covering several fields: physics, astronomy, mathematics, biology, artificial intelligence, cryptography, computer science, etc. If your project is computationally very intensive, and intellectually attractive, you can transform it into a BOINC project.

Other Teaching and Supervision Resources

Open Math Notes is a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students.
The January 2013 and May 2011 issues of the Notices of the American Mathematical Society contain two introductory papers on wavelets: Wavelets (2013), vol 60, 66-76, Pdf file, and Discrete wavelet transformations and undergraduate education (2011), vol 58, 656-666, Pdf file.
See also the interview with Yves Meyer published in May 2018 in the Notices of the American Mathematical Society Pdf, and the lecture, in French, by Yves Meyer entitled Les ondelettes et la révolution numérique.
Two lectures by Benoît Mandelbrot on Fractals:
- L'anneau fractal de l'art à l'art à travers la géométrie, la finance et les sciences,
- Fractals in Science, Engineering and Finance (Roughness and Beauty).
Three books on the art of writing mathematics: the two standard texts by respectively Paul Halmos, How to write mathematics (1970) Pdf file, and Donald Knuth, Tracy L. Larrabee, and Paul M. Roberts Mathematical Writing, Mathematical Association of America, 1989, with the updates by Donald Knuth. Steven Krantz has recently issued the second edition of his book A Primer of Mathematical Writing, American Mathematical Society, 2017.
Jean-Pierre Serre considers the other side of the issue with his funny lecture: How to Write Mathematics Badly. In the same spirit, the parody of scientific publication by Georges Perec: Experimental demonstration of the tomatotopic organization in the Soprano (Cantatrix sopranica L.).
MathJax is an open source Javascript library that uses LaTeX and MathML for displaying mathematics on webpages, which works on all modern browsers and that I'm using for my web pages. Further details are provided by the paper published in the Notices of the American Mathematical Society MathJax: A Platform for Mathematics on the Web (2012), vol 59, 312-316, Pdf file.
Mathematical Reviews (MathSciNet®), edited by the American Mathematical Society, is a useful reference tool for mathematicians (Every decent mathematician is indexed there). Its practical use is given in this tutorial. See also the AMS blog Beyond Reviews.
The following video gives an account on the origins and the current running of Mathematical Reviews:
The Scholarly Open Access website contains a critical analysis of scholarly open-access publishing, and in particular provides a list of predatory journals and publishers that must be avoided. Further details are given in J. Beall Predatory publishers are corrupting open access, Nature 489, 179, (13 September 2012) DOI.
Plagiarism.org: This organization provides research institutes and academic places with a database for deterring and detecting plagiarism.