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Graphical Models for Complex Multivariate Data

Project description

An improved statistical method of multivariate data analysis

Modern scientific experiments often produce data that require the analysis of more than two variables per observation. The EU-funded GRAPHMODE project plans to develop efficient methods for the statistical analysis of such data. For their study, researchers will rely on probabilistic graphical models that express the conditional dependence structure between random variables. These models are the state-of-the-art approach for the detailed exploration of cause–effect relationships. The project will place a special focus on algebraic and statistical issues related to latent (unmeasured) variables and feedback loops in graphical models.

Objective

Modern science increasingly relies on insights gained from sophisticated analyses of large data sets. An ambitious goal of such data-driven discovery is to understand complex systems via statistical analysis of multivariate data on the activity of their interacting units. Probabilistic graphical models, the topic of this project, are tailored to the task. The models facilitate refined yet tractable data exploration by using graphs to represent complex stochastic dependencies between considered variables. Models based on directed graphs, in particular, provide the state-of-the-art approach for detailed exploration of cause-effect relationships. However, modern applications of graphical models face numerous challenges such as key variables being latent (i.e. unobservable/unobserved), lacking temporal resolution in studies of feedback loops, and limited experimental interventions. Often arising in combination, these issues generally result in observed stochastic structure that cannot be characterized using the established notion of conditional independence. As a result, we are left with only a partial understanding of which aspects of a system can be inferred from the available data, and we lack effective methods for fundamental problems such as inference in the presence of feedback loops. The aim of the new project is to move beyond conditional independence structure to obtain a deeper understanding of the inherent limitations on what can be inferred from imperfect measurements, and to design novel statistical methodology to infer estimable quantities. The unique feature of the proposed work is a focus on algebraic relations among moments of probability distributions and the subtle statistical issues arising when such relations are to be exploited in practical methodology.

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Programme(s)

Topic(s)

Funding Scheme

ERC-ADG - Advanced Grant

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Call for proposal

(opens in new window) ERC-2019-ADG

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Host institution

TECHNISCHE UNIVERSITAET MUENCHEN
Net EU contribution
€ 1 971 296,00
Address
Arcisstrasse 21
80333 Muenchen
Germany
Region
Bayern Oberbayern München, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
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Total cost
€ 1 971 296,00

Beneficiaries (1)