École d’été 2021

12-15 septembre 2021

Prof. Sebastian Engelke, UNIGE; Caroline Gillardin Coordinatrice CUSO

Prof. Afonso S. Bandeira (ETH Zürich)

Prof. Henry Lam (Columbia University)

Prof. Yves Tillé (Université de Neuchâtel)

Prof. Afonso S. Bandeira (ETH Zürich)

Title : Community Detection in Networks and other Inference Problems: Statistical and Computational considerations

Detecting communities in a graph is a central problem in network science. We will study this problem under a mathematical model of random graphs with underlying communities, the stochastic block model, allowing us to formulate this task as a statistical inference one. We will use this problem as a starting point to explore not only statistical limits but also algorithmic challenges that are present in many other inference questions. (we will start by following parts of Chapter 8 here: PDF). Link for udated versions : https://people.math.ethz.ch/~abandeira//BandeiraSingerStrohmer-MDS-draft.pdf

Prof. Henry Lam (Columbia University)

Title : Variance Reduction and Rare-Event Simulation

Monte Carlo simulation is a common tool for model-based prediction and inference. In many important problems, however, naive implementation of Monte Carlo is inefficient, sometimes practically infeasible, which calls for an umbrella of so-called variance reduction techniques for efficiency enhancement. This lecture will present the motivation, statistical mechanism, comparative strengths, and also limitations that drive the current research of these techniques. The lecture is roughly divided into two parts:

- The first part will give a general overview on the set of problems that necessitates the use of variance reduction despite modern computing power. Besides introducing these techniques (including importance sampling, control variates and multi-level Monte Carlo) and discussing how to configure them efficiently, we will also illustrate their applications in recent problems in machine learning and statistics, including in stochastic optimization, gradient estimation and reinforcement learning. 

- The second part will focus on rare-event simulation, namely the quantification of extremal probabilities in stochastic systems where naive Monte Carlo is often infeasible. Building efficient variance reduction procedures here often requires some level of understanding on system tail behaviors. We will discuss both techniques based on large deviations theory (both light and heavy-tailed) and also versatile approaches using particle methods (such as multi-level splitting) and sequential stochastic search (such as cross-entropy). 

Lectures 1-2-3

Prof. Yves Tillé (Université de Neuchâtel)

Title : Sampling from Finite Populations

The objective of the course is to examine methods for selecting a sample for extrapolation to the entire population. We begin by presenting a number of applications where sampling is necessary. Then we examine how extrapolation can be justified using a sampling design, a model or both. After a brief review of the most classical methods (simple random sampling, stratification), we explain the interest and the difficulties of unequal probability sampling. We show how these methods can be implemented. We then develop algorithms for selecting the balanced samples. Finally we present methods to obtain a sample that is spread in space. We then return to the examples to show how sampling can be optimized.

PDF Lectures 1-2-3

Program (may be changed)

Les Diablerets à l'Eurotel Victoria

Eurotel Victoria

1865 Les Diablerets (VD)

www.eurotel-victoria.ch/diablerets/

Accès aux Diablerets :

EN VOITURE Autoroute A9, direction Grand St-Bernard, sortie Aigle. Puis la route Aigle - Les Diablerets - Col du Pillon (20km). 

EN AVION Aéroports internationaux de: - Genève (120 km) - Zürich (250 km) - Bâle (200 km)

EN TRAIN  (HORAIRE DES TRAINS - RAILWAY TIMETABLE)  International TGV Paris - Lausanne. En hiver, TGV des Neiges Paris - Lausanne - Aigle.

Swiss Train schedule : From: Geneva airport, To: Les Diablerets, gare. Trains directs jusqu'à Aigle. Ensuite train de montagne A.S.D (Aigle - Sépey - Diablerets) Durée des trajets: Lausanne - Aigle (30 minutes), Aigle - Les Diablerets (50 minutes).

Visa pour la Suisse (Swiss Online Visa application)

Météo en suisse (meteoswiss.admin.ch)

Adresse salle de gym Maison des congrès : Chemin des Grandes Isles, 1865 Ormont-Dessus (Entre la gare les Diableret et l'Eurotel)

Tarifs si l'activité a lieu en présentiel :

Doctorant CUSO chambre double: 200 CHF

Doctorant CUSO chambre simple: 350 CHF

Post-doctorant CUSO chambre double: 300 CHF

Post-doctorant CUSO chambre simple: 450 CHF

Professeur CUSO chambre double: 400 CHF

Professeur CUSO chambre simple: 550 CHF

Non CUSO universitaire chambre double: 850 CHF

Non CUSO universitaire chambre simple: 1000 CHF

Non CUSO privé chambre double: 1300 CHF

Non CUSO privé chambre simple: 1500 CHF

Lors de votre inscription, merci de bien vouloir indiquer dans la zone commentaire si vous désirez une chambre simple, ou double et le nom de la personne avec qui vous souhaiteriez partager votre chambre. Dans le cas où rien n'est indiqué, une chambre simple sera réservée.

Versement sur compte postal (seulement si l'activité à lieu en présentiel):

CUSO

CCP 12-1873-8

Neuchâtel

BIC : POFICHBEXXX

IBAN : CH0509000000120018738. Merci d'écrire votre nom suivi du no" 21220001 " lors du paiement. Thank you to write your name on the payment wording and nb"21220001".

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