MMS2018-backup

Tutorials

DALALYAN, Arnak (ENSAE ParisTech - CREST, France)

Title - Outlier-robust estimation of a high-dimensional mean vector

Abstract: In these lectures, we will review some recent results on the estimation of the mean of a Gaussian distribution when the sample contains outliers. Different mathematical frameworks for modeling outliers will be presented. Then, we will show that in a p-dimensional problem with s outliers out of n observations, the minimax quadratic risk is at least of order (p/n) + (s/n)^2. This turns out to be the optimal rate, since it is achieved by the Tukey’s median. We will then present some computationally tractable estimators, which have provably better rates of convergence than the standard estimators such as the (coordinatewise or geometric) median.

ZHOU, Harrisson (Yale University, USA)

Title - Spectral method, Lloyd Algorithm, EM, and Variational Bayes for Clustering

Abstract: In this talk, I will review some recent attempts to understand spectral method, Lloyd algorithm, EM, and variational Bayes for clustering. Our goal is to have a more or less complete answer to the question whether and when each of the four algorithms attains the optimal statistical accuracy for Gaussian mixtures. This is a joint work with Matthias Loffler, Yu Lu, Tal Sarig, Yihong Wu, and Anderson Zhang.

Program

Monday 17 Tuesday 18 Wednesday 19 Thursday 20
Friday 21

8:55- Opening
9:00 - 9:45
Podolskij

Break

10:00 - 12:00
Mukherjee
Ermakov
Paris


9:15 - 10:15
A. Dalalyan 2/2


Break

10:30 - 12:00
Altmeyer
Loffler



9:15 - 10:15
H. Zhou 1/2


Break

10:30 - 12:30
Wu
Belitser
Berthet

9:15 - 10:15
H. Zhou 2/2


Break

10:30 - 12:00
Derumigny
Enikeeva


9:00 - 10:30
Bellec
Tsybakov

Break

10:45 - 12:15
Panov
Mao
Lunch Lunch Lunch Lunch Lunch

16:00 - 17:00
A. Dalalyan 1/2



16:00 - 17:30
Rigollet
Stepanova



16:00 - 17:30
Gao
Suvorikova


Break Break
Break

17:15 - 19:15
Rivoirard
Duval
Mariucci


17:45 - 19:15
Steinberger
Ndaoud


17:45 - 19:15
Salmon
Chinot

Talk titles

Altmeyer
Nonparametric Estimation for Stochastic Partial Differential Equations (SPDEs)
Belitser
Robust inference for general projection structures
Bellec
The variance of the sparsity of the Lasso is at most (n∧s*log(p/s)), and other surprises from Stein's formula
Berthet

Chinot
Derumigny
About the estimation of conditional Kendall's tau and Kendall's regression
Duval
Compound Poisson approximation to estimate the Levy density
Enikeeva
Bump detection in linear Gaussian models
Ermakov On consistency and inconsistency of nonparametric tests
Gao

Loffler
Spectral Tresholding for the estimation of transition densities of discretely observed elliptic SDEs
Mao
Optimal estimation of two-dimensional totally positive densities
Mariucci
Gaussian approximation for the small jumps of Levy processes
Mukherjee
Ndaoud
Sharp optimal recovery in the Gaussian mixture model
Panov
Towards optimal estimation in mixed membership stochastic block models
Paris
Learning minimizers of functionals on metric spaces
Podolskij
High dimensional problems for diffusion models: A short survey and future challenges
Pontil
Rigollet

Rivoirard Hawkes processes: Frequentist and Bayesian inference
Salmon
Generalized Concomitant Multi-Task Lasso for sparse multimodal regression
Steinberger
Geometrizing rates of convergence under local differential privacy
Stepanova
On binary classification in sparse models
Suvorikova
Central Limit Theorem in Bures-Wasserstein space with applications
Tsybakov
Adaptive robust estimation under sparsity in non-gaussian sequence model
Wu
Efficient random graph matching via degree profiles

Participants

Organizing Committee