Latent Tree Models

Lecturer: Piotr Zwiernik (University Pompeu Fabra, Barcelona)


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.

An introduction to backward SDEs and applications in finance and economics

Lecturer: Dylan Possamai  (Columbia University)


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.

Joint Seminar with Vienna Graduate School on Computational Optimization – 29 Sep 2016

Joint Seminar with Vienna Graduate School on Computational Optimization headed by Professor Georg Pflug (

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.

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 by 29.9.2016.

PhD student position in Jyväskylä

PhD-Position in Stochastics

Within the project of the Academy of Finland

Stochastic Analysis and Nonlinear Partial Differential Equations, Interactions and Applications (2016-2020) there is an open PhD-position. We look for a doctoral student that works in the area of Stochastic Analysis and related fields with a possible emphasize on Backward Stochastic Differential Equations.

Site of research: Department of Mathematics and Statistics University of Jyväskylä (Finland)

Earliest date for starting: September 1, 2016

Contact: Stefan Geiss
Department of Mathematics and Statistics

University of Jyväskylä (Finland)

Workshop at Aalto 7-9 Dec 2016: Nonlinear, nonlocal problems and stochastic methods

Dear Colleagues,
We are pleased to announce the workshop on
Nonlinear, nonlocal problems and stochastic methods
taking place
December 7-9, 2016
at Aalto University, Helsinki/Espoo, Finland.
Invited Speakers
Lisa Beck (Universität Augsburg)
Pierre Cardaliaguet (Université Paris – Dauphine)
Bartłomiej Dyda (Politechnika Wrocławska)
Benjamin Gess * (Max Planck Institute for Mathematics in the Sciences)
Michael Hinz (Universität Bielefeld)
Martina Hofmanová (Technische Universität Berlin)
Cyril Imbert (CNRS)
Grzegorz Karch (Uniwersytet Wrocławiski)
Tadele Mengesha (University of Tennessee)
Armin Schikorra (Albert-Ludwigs-Universität Freiburg)
Joaquim Serra * (Universitat Politècnica de Catalunya)
Nizar Touzi (École Polytechnique)
Rico Zacher (Universität Ulm)
Aleksandra Zimmermann (Universität Duisburg-Essen)
* to be confirmed
Juha Kinnunen (Aalto University)
Tuomo Kuusi (Aalto University)
Jonas Tölle (Aalto University)
Mikko Parviainen (University of Jyväskylä)
Moritz Kaßmann (Universität Bielefeld)
We gratefully acknowledge sponsoring by the Academy of Finland,
the Department of Mathematics and Systems Analysis, School of Science, Aalto University,
and the Collaborative Research Center “Spectral Structures and Topological Methods in Mathematics” (SFB 701) of the German Research Foundation (DFG) at Bielefeld University.
for more info. You can register here:
There is no registration fee.
There will be the possibility to contribute a poster. Interested participants may provide the title of their poster to the contact email address below (additionally to the registration).
Best regards,
Jonas Tölle (Aalto University)