Stability and scaling limits for Markov processes and applications (1–3 cr)

Lecturer:
Prof Matthieu Jonckheere (U Buenos Aires)

Schedule:
Three lectures during 24–26 Sep 2018, every day 10:15–12:00 (Mon, Tue, Wed)

Location:
Krossi lounge (M220), 2nd floor, Otakaari 1, Aalto University

Description:
Markov processes allow to study models of almost any dynamics: population dynamics, data networks, physical systems evolutions, biological networks, etc. We will study techniques to answer stability questions including techniques allowing to link some Markov processes to simpler systems (often a deterministic dynamical system) via space-time scaling.

Topics:
1) Markov processes in discrete and continuous time
2) Stationary measures, reversibility
3) Martingales for Markov processes
4) Lyapunov functions
5) Scaling limits
6) Stochastic stability

Evaluation: You may get 1 cr for active participation at the lectures, and up to 3 cr by doing a project (to be agreed with the lecturer).

Registration: You can send an email to lasse.leskela@aalto.fi or just show up at the first lecture.

Lecturer: Piotr Zwiernik (University Pompeu Fabra, Barcelona)

Abstract: 

Latent tree models are graphical models defined on a tree, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This lecture offers a concise introduction to the theory of latent tree models. I will emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned.

This lecture course is divided into three parts. In part 1, I will present basic combinatorial concepts related to trees and tree metrics. In part 2, I will define latent tree graphical models and discuss their basic properties. I will also discuss linear latent tree models which provide a convenient general family of distributions whose second-order moment structure is tree-like. In the last part I will present main ideas used in the design of learning procedures for this model class. This includes the structural EM algorithm and various distance based methods.

This course will be based on my book
P. Zwiernik, “Semialgebraic statistics and latent tree models”, Chapman&Hall, 2015,
and a forthcoming chapter in “Handbook of Graphical Models”, see also arXiv:1708.00847.

Lecturer: Dylan Possamai  (Columbia University)

Abstract: 

Backward stochastic differential equations (BSDEs for short) have been introduced since the 90s, and have proved since then to be a fundamental tool in stochastic analysis, stochastic control, and even PDE analysis, with numerous applications in finance, economics and insurance. This course would be the occasion to provide an introduction to the theory as well as its latest developments. After going through some of the most important theoretical results, we will see as an illuminating application how BSDEs allow to treat in a general fashion several problems stemming from contract theory with moral hazard.

Stochastic Sauna is a traditional workshop that brings together researchers and students working on probability, statistics, and their applications. The workshop starts in the morning of Tue 20 Dec 2016 and ends at approximately 17.00 in the afternoon.

For more information and registration, see:

http://math.aalto.fi/en/research/stochastics/sauna2016/

Joint Seminar with Vienna Graduate School on Computational Optimization headed by Professor Georg Pflug (http://vgsco.univie.ac.at/faculty-members/georg-pflug-speaker/).

Other speakers include Profs. Ahti Salo (Aalto SCI), Lasse Leskelä (Aalto SCI), Juuso Liesiö (Aalto BIZ), Stefan Geiss (University of Jyväskylä), Leena Suhl (University of Paderborn).

Time and place: Thursday 29th September 11:00-16:00 at Aalto University, Otakaari 1, Espoo. Lecture hall U5.

http://sal.aalto.fi/en/gradschool/seminars/Otaniemi2016/

The seminar programme consist of
(i) presentations of the participating research groups and the organization of graduate and doctoral studies (11:00-12:00)
(ii) lunch (12:00-13:00)
(iii) talks on timely research topics in stochastic optimization and analysis, portfolio decision analysis, risk management, and logistics and production planning (13:00-16:00).

The seminar is open to all interested faculty and students, and it will be attended by some 15 student from Vienna. Participants from Finland are kindly requested to register by sending email to tuomas.j.lahtinen@aalto.fi by 29.9.2016.