Here I share some works done during my studies.

Some works done during my research Master (MVA)

Project for the course on Kernel Methods with the questions.

Project on a unifying framework for representer theorems.

Homeworks (1, 2 and 3) related to the course “Probabilistic Graphical Models”

Poster done for a Machine-Learning project on classification by diffusion.

A list of good references that I read during my master and my PhD with some comments

• General references on the theoretical aspects of Machine Learning and data-science
  – A large list of nice Theoretical Computer Science references are available here.
  – I recommand also the book recently written by Francis Bach “Learning from first Principles”
• Markov chains
  – Meyn & Tweedie’s book: A good reference for theoretical aspects on (discrete time) Markov chains on general state space
  – Levin’s book on mixing time for Markov chains. This book deals mainly with Markov chain with finite state space and introduces important notions related to mixing like the spectral gap of a transition kernel or the Cheeger constant.
  – For a friendly version of the previous book, I recommend the lectures of Justin Salez (from a course at Sorbonne University).
  – For hidden Markov chains, one can read the book wirtten by Eric Moulines on the subject.
• Concentration of measure
  – P.Massart’s book is the main reference on the subject
  – I also recommand the lecture notes from Ana Ben Amou to get a more synthetic introduction to this topic.
• Convex Optimization
  – S. Bubeck’s book is a nice reference to understand the most important algorithms in convex optimization.
  – Boyd’s book is one of the most famous reference in the field of convex optimization.
• General books on Optimization
  – Numerical Optimization from Nocedal and Wright
  – Convex Analysis and Monotone Operator Theory in Hilbert Spaces from Combettes and al. is a great reference to understand ADMM, proximal algorithms or Douglas Rachford algorithm.
• High dimensional statistics
  – The book from R. Vershynin introduces important concepts of high dimensional statistics with a specific focus on geometry and concentration of measure and their interactions. This book presents in particular sub-gaussian and exponential random variables, concentration inequalities for quadratic forms (Hanson Wright’s inequality), Slepian, Gordon, Sudakov and Dudley inequalities (and much more).
  – To focus specifically on Random Matrices, there exists the Saint Flour lecture notes of Alice Guionnet.
  – Wainwright, High-Dimensional Statistics: A Non-Asymptotic Viewpoint This book covers a larger number of topics compared to the previous one with chapters on RKHS or PCA. I also spends several chapters presenting theoretical results for sparse linear models in high dimensions. The author takes the framework the more general possible which makes some sections difficult to grasp.
  – Giraud, Introduction to High-Dimensional Statistics
  – Giné, Mathematical Foundations of Infinite-Dimensional Statistical Models
• Non parametric statistics
  – Non parametric inference, Tsybakov
  – Lecture Notes written by John Duchi were also really helpful for me.
• Sparsity and compressed sensing
  – Statistical Learning with Sparsity, Hastie: one of the few books that present some “recent” and important topics such as Post-selection inference and the polyhedral lemma.
  – Books from Sara Van de Geer are widely used in the community (but are technically difficult).
  – Claire Boyer’s lecture notes on compressed sensing
• Multiple testing procedures
  – Lecture notes from Emmanuel Candès offer a really nice historical overview of the subject. A specific attention is given to the work personally done by Pr. Candès (such as the Knockoff filter).
  – The recent handbook “Handbook of Multiple Comparisons” edited by Cui, Dickhaus and al. presents advanced research topics.
• Probability theory
  – Books from Billingsley are often used as references for master courses on probability theory and limit theorems.
  – Giné, Decoupling – From dependence to independence : Book introducing decoupling methods.
• Stochastic Calculus
  – Marc Yor’s book on Continuous Martingales and brownian motion describes in detail a variety of techniques used by probabilists in the field of random processes. This is not a book for beginners on the subject and is more intended for doctoral students or reseachers in the field.
  – Jean-François Le Gall’s lecture notes are a great reference for people that do not work precisely on Stochastic Calculus.
• Optimal Transport
  – A nice reference that was the purpose of a reading group during my master MVA with Professor Vianney Perchet is the book written by Santambrogio: Optimal transport.
  – For a more computational view point (and maybe a more easy to grasp presentation of concepts from a theoretical point of view), I recommend the book from Gabriel Peyré and Marco Cuturi: “Computational Optimal Transport”.
  – Lectures Notes from Lenaic Chizat give an impressive well-structured summary of the two previous references.