Descripción del proyecto
Un método estadístico mejorado de análisis de datos con múltiples variantes
Los experimentos científicos modernos a menudo generan datos que requieren el análisis de más de dos variables por observación. El proyecto GRAPHMODE, financiado con fondos europeos, prevé desarrollar métodos eficaces para el análisis estadístico de tales datos. Para su estudio, los investigadores se basarán en modelos gráficos probabilísticos que expresen la dependencia condicional entre variables aleatorias. Estos modelos son un método moderno para el estudio detallado de las relaciones causa-efecto. El proyecto prestará atención especial a cuestiones estadísticas y algebraicas relacionadas con variables latentes (no medidas) y bucles de retroalimentación en modelos gráficos.
Objetivo
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.
Palabras clave
Programa(s)
Régimen de financiación
ERC-ADG - Advanced GrantInstitución de acogida
80333 Muenchen
Alemania