Thesis supervisor: Marianna Bolla
Location of studies (in Hungarian): Department of Stochastics, Institute of Mathematics, BME Abbreviation of location of studies: BME
Description of the research topic:
Graphical models provide a framework for describing statistical dependencies in (possibly large) collections of random variables. At their core lie various correspondences between the conditional independence properties of a random vector and the structural properties of the graph used to represent interactions (directed or undirected) between the vertices assigned to the random variables. These so-called causality models have been investigated since the 1980s, the first steps were made by J. Pearl. However, it was S. L. Lauritzen who showed how loglinear models can be used to estimate joint, marginal, and conditional probabilities taking into consideration the graph structure. The candidate is assumed to master some routine in hierarchical and decomposable loglinear models, based on the book of S. L. Lauritzen (Graphical Models, Oxford Univ. Press, 1995). Then the task of the candidate would be to develop the models and algorithms in the following. The underlying variables are usually categorical (e.g., symptoms, medical diagnoses), but so-called mixed models, incorporating continuously distributed random variables (mainly Gaussian, conditioned on the deiscrete ones) are also proposed in the above book. The estimation methods could be extended to these mixed types of models, via standard methods of multivariate statistics working with covariances. The models are applicable in machine learning for building artificial intelligence
(e.g., in medical diagnostic systems), so testing the models on real-life data is also welcome.
Required language skills: english Further requirements: to be graduated in introductory Probability, Statistics, and Graph Theory
Number of students who can be accepted: 1
Deadline for application: 2018-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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