École d’été 2024

1-4 septembre 2024

Christian Mazza

Prof. Christian Mazza, Université de Fribourg

Mme Caroline Gillardin, coordinatrice CUSO

Co organisation avec l'EPFL

Prof. Bartek Blaszczyszyn, INRIA, Paris, France

Prof. Roland Langrock, Bielefeld University, Allemagne

Prof. Antonietta Mira, Università della Svizzera italiana, Suisse

Prof. Bartek Blaszczyszyn, INRIA, Paris, France

Title : Ergodic Learning of Spatial Geometric Structures

Abstract:

Ergodicity serves as a crucial link between probability theory and

statistics. In spatial statistics, it connects various spatial

averages to their corresponding mathematical expectations. A

remarkable—and perhaps underemphasized—implication of ergodicity is

that, in theory, a single complete realization of a stationary ergodic

model almost surely allows one to estimate the underlying distribution

of the model.

In the first lesson, we will revisit these foundational results in the

context of point processes. The second lesson will explore how

ergodicity can be leveraged to develop generative models for point

processes, learned from a single realization. In the final lesson, we

will narrow our focus to learning some striking feature of the model,

namely hyperuniformity, and provide mathematical limiting results that

justify this approach to ergodic learning.

**Bibliography for the course:**

1. Blaszczyszyn, B. *Lecture Notes on Random Geometric Models*; hal:cel-01654766.

2. Brochard, A., Blaszczyszyn, B., Mallat, S., and Zhang, S. (2022). *Particle Gradient Descent Model for Point Process Generation*. *Statistics and Computing*; arXiv:2010.14928.

3. Mastrilli, G., Blaszczyszyn, B., Lavancier, F. (2024). *Estimating the Hyperuniformity Exponent of Point Processes*. arXiv:2407.16797.

LECTURES

LECTURES2

LECTURES3

Prof. Roland Langrock, Bielefeld University, Allemagne

Title : Hidden Markov models Abstact : Hidden Markov models (HMMs) are flexible statistical models for sequences of observations that are driven by underlying states. Over the last two decades, this class of models has become increasingly popular in applied statistics since many real-world phenomena naturally translate to the HMM framework: for example, observed animal movement depends on not directly observed behavioural modes, financial share returns depend on the underlying market volatility, and medical measurements depend on the patient's underlying health state. In such scenarios, HMMs allow for comprehensive statistical inference, including forecasting, state decoding and investigations of the system's response to internal and external drivers.This mini-course will introduce the HMM framework, covering the following topics: – overview & basic model formulation– fitting an HMM to data – model selection & model checking

– state decoding

– incorporating covariates, random effects and seasonality

– extensions of the basic model formulation

LECTURES

Prof. Antonietta Mira, Università della Svizzera italiana, Suisse

Title : How can Bayesian statistics help in dimensionality reduction?

Abstract : I will introduce the Bayesian paradigm to statistical inference, and then explain how it can be exploited to estimate the intrinsic dimension (ID) of data, and to answer questions related to dimensionality reduction that are becoming more pressing as the size of available data becomes larger. Indeed, real-world datasets tend to show a high degree of (possibly) non-linear correlations and constraints between their features. This means that, despite a very large embedding dimensionality, data typically lie on a manifold characterized by a much lower ID. which, in the presence of noise, may depend on the scale at which the data is analysed. This fact rises interesting questions: How many variables, or combinations there of, are necessary to describe a real-world data set without significant information loss? What is the appropriate scale at which one should analyze and visualize the data? These two issues, which are often considered unrelated, are actually strongly entangled, and can be addressed within a unified framework. We introduce an approach in which the optimal number of variables and the optimal scale are determined self-consistently, recognizing and bypassing the scale at which the data are affected by noise. To this aim we estimate the data ID in an adaptive way, and exploit it as a summary statistics in Approximate Bayesian Computation for inference in network type data. Sometimes, within the same dataset, it is possible to identify more than one ID meaning that different subsets of the data points lie onto manifolds with different IDs. Identifying these manifold provides a clustering of the data, and in many real world applications a simple topological feature, like the ID, allows to uncover a rich data structure and improves our insight into subsequent statistical analysis. Examples of these applications range from gene expression to protein folding, pandemic evolution, FMRI, all the way to finance, sport data and the analysis of the representations of neural networks.

LECTURE1

LECTURE2

slides 1 and slides 2 for the Bayesian part of the lectures

CODE_CH1 and CODE_CHE2

https://youtu.be/UTjmU8TRnQE?si=gP_TlucKln6BdhHw

 https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf

Program (can be changed)

Conférences and coffee breaks in : Hôtel des Masques (2 mns walk from Hôtel Eden), Place du Village 7, 1972 Anzère

Wecome tea Sunday : Hôtel Eden

Apero Sunday : Bar Hôtel Eden

Breakfast, lunch and dinner : Hôtel Eden

Anzère - Eden Resort - Alpes valaisannes

Hôtel : Eden Resort Anzère

Adress : Route d'Anzère 34, 1972 Anzère, Canton du Valais

Tel +41 (0)27 399 31 00 L'hôtel est situé dans les Alpes valaisannes. Il y a des chambres et des suites.

Accès à Anzère en voiture: Google Map

EN AVION Aéroports internationaux de: - Genève (180 km) - Zürich (290 km) - Bâle (270 km)

En transport public Horaires Swiss Train :

De: Aéroport de Genève : Train jusqu'à Sion. A la gare de Sion : car postal Sion - Anzère centre (36 mns)

Swiss Train schedule : From: Geneva airport, To: Sion. From Sion station : postal bus to Anzère centre. Travel time: Genève - Sion (1 hour and 55 minutes); Sion - Anzère (36 minutes).

Visa pour la Suisse (demande de visa suisse en ligne)

Météo en suisse (meteoswiss.admin.ch)

Tarif :

CUSO (UNINE, UNIGE, UNIL, UNIFR, UNIBE, IHEID, HES-SO)

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. Si vous vous inscrivez et que vous ne pouvez pas participer, veuillez nous contacter dès que possible. Dans le cas contraire, toutes les nuits d'hôtel pourraient vous être facturées.

*Condition d'annulation :

Pour une annulation effectuée entre la date de réservation et 30 jours avant l'arrivée aucun frais d'annulation ne sera prélevé.Pour une annulation effectuée entre 7 et 30 jours avant l'arrivée un montant équivalent à 30 % de la réservation sera prélevé.Pour une annulation effectuée entre 7 jours avant l'arrivée et le jour de l'arrivée la Totalité de la réservation sera prélevé.

Pour une annulation effectuée entre le jour de l'arrivée et le no show la Totalité de la réservation sera prélevé.

Pour cause d'accident ou maladie, etc, merci de nous livrer un certificat médical.

*Cancellation policy:

For cancellations made between the reservation date and 30 days before arrival, no cancellation fee will be charged.

For cancellations made between 7 and 30 days before arrival, an amount equivalent to 30% of the reservation will be charged.

For cancellations made between 7 days and the day of arrival, the full amount of the reservation will be charged.

For cancellations made between the day of arrival and no-show, the full amount of the reservation will be charged.

In the event of accident or illness, etc, please provide a medical certificate.

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" 24220001 " lors du paiement. Thank you to write your name on the payment wording and nb" 24220001".

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