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.
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.
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 |
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Break | Break | Break | ||
17:15 - 19:15 Rivoirard Duval Mariucci |
17:45 - 19:15 Steinberger Ndaoud |
17:45 - 19:15 Salmon Chinot |
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 |