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# Résultats de recherche

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## Klopp - Sparse Network Estimation

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of the statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. We will also discuss the problem of graphon estimation when the probability matrix is sampled according to the graphon model. For these two problems, the minimax optimal rates of convergence in Frobenius norm are achieved by the least squares estimator which is known to be NP-hard. In this talk we will present two alternatives to the least squares: ... Voir la vidéole (58m34s)

## Tropp 1/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ... Voir la vidéole (59m6s)

## Tropp 2/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ... Voir la vidéole (1h18s)

## Bubeck 3/9 - Some geometric aspects of randomized online decision making

This course is concerned with some of the canonical non-stochastic models of online decision making. These models have their origin in works from the 1950's and 1960's, and went through a resurgence in the mid-2000's due to many applications in the internet economy. This course focuses on a set of challenging conjectures around these models from the 1980's and 1990's. We present a unified approach based on a combination of convex optimization techniques together with powerful probabilistic tools, which will allow us to derive state of the art results in online learning, bandit optimization, as well as some classical online ... Voir la vidéole (55m13s)

## Bubeck 4/9 - Some geometric aspects of randomized online decision making

This course is concerned with some of the canonical non-stochastic models of online decision making. These models have their origin in works from the 1950's and 1960's, and went through a resurgence in the mid-2000's due to many applications in the internet economy. This course focuses on a set of challenging conjectures around these models from the 1980's and 1990's. We present a unified approach based on a combination of convex optimization techniques together with powerful probabilistic tools, which will allow us to derive state of the art results in online learning, bandit optimization, as well as some classical online ... Voir la vidéole (41m33s)

## Massoulié - Planting trees in graphs, and finding them back

In this talk we consider detection and reconstruction of planted structures in Erdős-Rényi random graphs. For planted line graphs, we establish the following phase diagram. In a low density region where the average degree λ of the initial graph is below some critical value λc, detection and reconstruction go from impossible to easy as the line length K crosses some critical value f(λ)ln(n), where n is the number of nodes in the graph. In the high density region λ>λc, detection goes from impossible to easy as K goes from o(\sqrt{n}) to ω(\sqrt{n}), and reconstruction remains impossible so long as K=o(n). We show similar properties for planted D-ary trees. These results are in contrast with the ... Voir la vidéole (42m3s)

## Verzelen - Clustering with the relaxed K-means

This talk is devoted to clustering problems. It amounts to partitionning a set of given points or the nodes of a given graph, in such a way that the groups are as homogeneous as possible. After introducing two random instances of this problem, namely sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM), I will explain how convex relaxations of the classical $K$-means criterion achieve near optimal performances. Emphasis will be put on the connections between the clustering bounds and relevant results in random matrix theory. Voir la vidéole (57m49s)

## Tropp 3/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ... Voir la vidéole (1h21s)