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.