Posted on February 28, 2024
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Theses by Arianna Casanova Flores (edited by H. Diego Estrada-Lugo & Alexander Erreygers)
In my thesis, we further explore the potential of desirability theory, a very powerful uncertainty formalism developed within the context of imprecise probabilities, pursuing three primary research directions. Firstly, we provide joint foundations for the fields of social choice and probabilistic opinion pooling using desirability. This strategy offers a fresh perspective on traditional results in those fields and provides a tool for comparing their formulations. Secondly, we examine the relationship between desirability and information algebras. The latter are general algebraic structures introduced to manage information at an abstract level, providing general formulations of architectures for inference. This investigation reveals that desirability formally induces an instance of these structures, thereby offering a novel algebraic perspective on desirability and augmenting it with the inference machinery provided by information algebras. Thirdly, we explore relaxations of desirability’s foundational axioms to allow for a more realistic interpretation of its main tools. Specifically, we analyze different sets of axioms and reinterpret them as binary (usually nonlinear) classification problems. Drawing inspiration from machine learning, we define feature mappings that enable us to reformulate the aforementioned nonlinear classification problems as linear ones in higher-dimensional spaces.
Read morePosted on April 11, 2023
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Theses by Dominik Hose (edited by Henna Bains)
On May 20th in 2022, I successfully defended my PhD thesis [1] entitled “Possibilistic Reasoning with Imprecise Probabilities: Statistical Inference and Dynamic Filtering”. This dissertation is the result of five wonderful years at the Institute of Engineering and Computational Mechanics at the University of Stuttgart under the enthusiastic supervision of my “Doktorvater” Michael Hanss. Apart from him, my committee was also composed of Scott Ferson and Ryan Martin—but we will get to that.
Read morePosted on September 12, 2022
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Theses by Tathagata Basu (edited by Henna Bains)
After three years of research and extensive brainstorming with my supervisors; Jochen Einbeck and Matthias Troffaes, I finally defended my thesis on 15th December 2020. The thesis, entitled “High dimensional statistical modelling under limited information” was examined by Dr Hailiang Du and Dr Erik Quaghebeur in the presence of Dr Ostap Hryniv.
Read morePosted on March 9, 2016
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Theses by Jasper De Bock
On 13 May 2015, after four years of intensive research under the enthousiastic supervision of Gert de Cooman, I succesfully defended my PhD Thesis, entitled “Credal Networks under Epistemic Irrelevance: Theory and Algorithms”. The jury was composed of Fabio Cozman, Enrique Miranda, Serafín Moral, Joris Walraevens, Dirk Aeyels, Dries Benoit, Jan Van Campenhout and Rik Van de Walle. My dissertation presents a detailed study of credal networks under epistemic irrelevance, which are probabilistic graphical models that can compactly and intuitively represent the uncertainty that is associated with the key variables in some domain, and which can then be used to answer various domain-specific queries (compute inferences) that are of interest to the user. They share many of the nice features of Pearl’s celebrated Bayesian networks, but have the added advantage that they can represent uncertainty in a more flexible and realistic way.
Read morePosted on June 24, 2014
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Theses by Ignacio Montes
This thesis, supervised by Enrique Miranda and Susana Montes, was defended on May 16th. The jury was composed of Susana Díaz, Serafín Moral and Bernard De Baets. This thesis deals with the problem of comparing alternatives defined under some lack of information, that is considered to be either uncertainty, imprecision or both together.
Read morePosted on April 24, 2014
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Theses by Andrea Wiencierz
My PhD thesis deals with the statistical problem of analyzing the relationship between a response variable and one or more explanatory variables when these quantities are only imprecisely observed. Regression methods are some of the most popular and commonly employed methods of statistical data analysis. Like most statistical tools, regression methods are usually based on the assumption that the analyzed data are precise and correct observations of the variables of interest. In statistical practice, however, often only incomplete or uncertain information about the data values is available.
Read morePosted on January 9, 2014
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Theses by Dennis D. Mauá
My PhD thesis is about connecting three hard computational problems that arise in tasks involving graph-based probabilistic reasoning, namely, the problems of maximum a posteriori (MAP) inference in Bayesian networks, planning with influence diagrams, and belief updating in credal networks under strong independence (or simply strong credal networks). Roughly speaking, in the MAP inference problem we seek the most probable explanation of a complex phenomena represented as a Bayesian network, a graph-based description of a multivariate joint probability distribution where nodes are identified with random variables and local conditional probability distributions.
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