École d’hiver 2024 - Les Diablerets

4-7 février 2024

Christian Mazza

Prof. Christian Mazza, Université de Fribourg

Mme Caroline Gillardin, Coordinatrice CUSO

Prof. Mariana Olvera-Cravioto, University of North Carolina, Chapel Hill, USA

Prof. Sofia Olhede, EPFL

Prof. Simon Wood, University of Edinburgh, UK

Prof. Mariana Olvera-Cravioto, University of North Carolina, USA Title : Processes on random graphs: Modeling the web, social networks and opinion dynamics. Abstract : This course will give an overview of how random graphs can be used to model complex networks, as well as processes that run on them. The main motivating examples are the analysis of network centrality and community structure on directed networks, such as the web, and the evolution of opinions on a social network. Both of these problems can be thought of as (stochastic) processes on a large graph, and the goal is to obtain tractable approximations for predicting their behavior based only on the network's statistical properties. On sparse graphs, such as the web and most social networks, the main tool enabling this kind of analysis is a concept known as "local weak convergence" for random graph sequences. Local limits allow us to understand the complex network in terms of simpler structures, such as trees, which for the two main examples the course will discuss, is enough to determine the behavior of the process that runs on the graph. The course will be structured into three main modules: 1) An introduction to random graphs and the most useful models for complex networks. 2) A description of the problems of interest as (stochastic) processes that run on a directed graph. 3) An overview of the techniques used to analyze processes on directed random graphs, including local weak convergence and some tools from interacting particles systems.

Lecture1

Lecture2

Lecture3

Prof. Sofia Olhede (EPFL). Title : Estimation and dependence in space and time. Abstract : Dependence and structured variation is key both to time series and random fields. The types of structure we expect to see in a sample are linked to a distributional shift invariance. This property unlocks a number of useful consequences, such as the spectral representation theorem, and estimation by various forms of averaging. We shall start in lecture one with defining various models satisfying stationarity, or difference stationarity, discuss the A. C. Harvey decomposition point-of-view of temporal processes, motivated by modelling drifter time series from physical oceanography, and define simple estimators. Special attention will be shown to the physical constraints of real-world data when modelling. We shall also cover the Whittle likelihood as a convenient and computationally efficient composite likelihood based way of defining estimators. Lecture two will discuss isotropy, anisotropy, and models in dimensions higher than one, motivated by geophysical observations of gravity and topography, while lecture 3 will end by briefly discussing the role of distributional invariance of defining models and methods, briefly linking to other representation theorems than the spectral representation (the Chaotic representation and Aldous-Hoover's theorem for exchangeable arrays). 

Lecture1

Lecture2

Lecture3

Prof. Simon Wood, University of Edinburgh, UK: topic :Generalized additive models. Abstract: Generalized additive models are GLM type regression models in which the linear predictor depends on smooth functions of covariates, and those smooth functions are the targets of inference. These lectures will outline an effective empirical Bayes framework for applied work with such models, in which the smooth function are represented by reduced rank spline functions, with smoothing parameters estimated using marginal likelihood or cross validation. Further model selection tools and model checking are also discussed. The framework is sufficiently general to cover location scale and shape models, in addition to simple mean regression, and to admit a rich range of smooth model components, including smooth interaction terms and linear functionals of smooth functions. The basic empirical Bayes approach can be extended to quite large data/model settings; refined if needed by stochastic simulation or INLA; and the frequent applied problem of un-modelled nuisance residual autocorrelation can be addressed using computationally efficient neighbourhood cross validation approaches. The framework discussed is that underpinning the mgcv package in R. Lectures :

Statistics

Advanced

Gam

Pen

Smoothers

Monday night, raclette evening in Chalet Téléthon (5 minutes walking from Eurotel Victoria) at 7:30 PM

Les Diablerets - Eurotel

Eurotel Victoria

1865 Les Diablerets (VD)

https://www.eurotel-victoria.ch/en

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)

Chalet Téléthon (soirée raclette lundi soir)

Tarif :

Non CUSO (ETHZ, etc)

Non CUSO (ETH) double room: 1300 CHF (price may fluctuate depending on the nb of registrations)

Non CUSO (ETH) single room: 1400 CHF (price may fluctuate depending on the nb of registrations)

You are responsible for your own transport costs

CUSO (UNINE, UNIGE, UNIL, UNIFR, UNIBE, IHEID)

Doctorant-e CUSO chambre double: 200 CHF

Doctorant-e CUSO chambre simple: 350 CHF

Post-doctorant-e CUSO chambre double: 300 CHF

Post-doctorant-e CUSO chambre simple: 450 CHF

Professeur-e CUSO chambre double: 400 CHF

Professeur-e CUSO chambre simple: 550 CHF

Non CUSO privé-e chambre double: 1300 CHF

Non CUSO privé-e 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.

If you register and are unable to attend, please contact us as soon as possible. Otherwise you might be billed for all nights in the hotel.

Versement sur compte postal (payment into postal account) :

CUSO

CCP 12-1873-8

Neuchâtel

BIC : POFICHBEXXX

IBAN : CH0509000000120018738. Merci d'écrire votre nom suivi du no" 24220002 " lors du paiement. Thank you to write your name on the payment wording and nb" 24220002".

IMPORTANT : si vous vous inscrivez, et que vous avez un empêchement, veuillez nous contacter dès que possible. Sinon le prix de toutes le nuitées à l'hôtel vous seront intégralement facturées si l'hôtel le demande. If you register and are unable to attend, please contact us as soon as possible. Otherwise you might be billed for all nights in the hotel.

40