here<\/a>.
– I recommand also the book recently written by Francis Bach “Learning from first Principles”<\/li>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.<\/li>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.<\/li>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.<\/li>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.<\/li>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
– Gin\u00e9, Mathematical Foundations of Infinite-Dimensional Statistical Models<\/li>Non parametric statistics
– Non parametric inference, Tsybakov
– Lecture Notes written by John Duchi were also really helpful for me.<\/li>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<\/li>Multiple testing procedures
– Lecture notes from Emmanuel Cand\u00e8s offer a really nice historical overview of the subject. A specific attention is given to the work personally done by Pr. Cand\u00e8s (such as the Knockoff filter).
– The recent handbook “Handbook of Multiple Comparisons” edited by Cui, Dickhaus and al. presents advanced research topics.<\/li>Probability theory
– Books from Billingsley are often used as references for master courses on probability theory and limit theorems.
– Gin\u00e9, Decoupling – From dependence to independence : Book introducing decoupling methods.<\/li>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-Fran\u00e7ois Le Gall’s lecture notes are a great reference for people that do not work precisely on Stochastic Calculus.<\/li>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 Peyr\u00e9 and Marco Cuturi: “Computational Optimal Transport”.
– Lectures Notes from Lenaic Chizat give an impressive well-structured summary of the two previous references.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"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<\/p>\n
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