Topics for students' thesis

Topics for PhD Thesis

Decision diagrams [1] are an extension of Bayesian networks for decision problems, where the goal is to maximize a given utility function. Decision diagrams have already been applied in decision-making problems in various areas (economic decision-making, health expert systems, risk analysis, etc.) [2]. Relatively recently, decision diagrams have been applied to optimize a speed profile [3,4,5]. However, the theory of decision diagrams is not sufficiently developed for cases where the model variables are not only discrete but also continuous (so-called mixed decision diagrams) and utility functions are nonlinear. The aim of the dissertation is a theoretical design of computational methods for mixed decision diagrams and their application in the tasks of optimizing the speed profile of vehicles. An already established computer model for a Formula 1 car on the Silverstone circuit can be used for the initial tests [3]. One of the possibilities for theoretical research is to follow up on works [6] and [7]. 

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Bayesian networks [1] are an example of a probabilistic graphical model [2] successfully used in various real-world applications where uncertainty decision support is needed. The basic advantage of Bayesian networks is that they make it possible to model the relationships between quantities using an oriented graph and then use these relationships for effective computations of conditional probabilities in the model (ie for probabilistic inference) [3]. This allows to employ them in applications where it is necessary to model the relationships between hundreds of quantities. One of the active areas of research is the search for methods of exact or approximate inference, in situations where the use of conditional independence is not sufficient. These are mainly Bayesian networks, where conditional probability tables take the form of so-called canonical models [4,5,6,7]. 

The aim of the dissertation is to 

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Bayesian networks (BNs) represent an AI model capable of reasoning under uncertainty and possesing good explainability. BNs were applied in diverse domains. They seem to be a proper model for e-learning and evaluation systems in education, see [Conati, 1997], [Vomlel, 2012], and [Plajner, 2021].

In order to simplify parameter estimations, BNs containing conditional probability tables of a special type (e.g., noisy-or and noisy-and) are used. In recent works, models whose conditional probability tables (CPTs) satisfy the monotonicity requirement were considered [Plajner, 2020]. The use of probability tables of a special type not only makes learning easier but it also allows computationally efficient inference. At the same time, it brings new challenges such as finding new methods for structural learning of BNs with special type CPTs [Kratochvíl, 2022]. 

In the thesis new learning methods should be developed that build on standard methods for learning the structure of BNs [Cussens, 2017] and [de Campos, 2011] and modify them so that they learn well-behaving BNs with special type CPTs. These models should be applied and tested in an e-learning or assessment system in education.

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[de Campos, 2011] C. P. de Campos and Q. Ji, Q, Efficient structure learning of Bayesian networks using constraints, Journal of Machine Learning Research, vol. 12, pp. 663-689, 2011. http://jmlr.org/papers/v12/decampos11a.html

[Conati, 1997] C. Conati, A. S. Gertner, K. VanLehn, and M. J. Druzdzel, On-line student modeling for coached problem solving using Bayesian networks, in User modeling,  Lecture Notes in Computer Science, vol 1839, Springer, pp. 231-242, 1997. https://doi.org/10.1007/978-3-7091-2670-7_24

[Cussens, 2017] J. Cussens, M. Järvisalo, J. H. Korhonen, and M. Bartlett. Bayesian network structure learning with integer programming: Polytopes, facets and complexity, Journal of Artificial Intelligence Research, vol. 58, pp. 185–229, 2017. https://doi.org/10.1613/jair.5203

[Kratochvíl, 2022] F. Kratochvíl, V. Kratochvíl, and J. Vomlel, Learning Noisy-Or Networks with an Application in Linguistics, In Proceedings of The 11th International Conference on Probabilistic Graphical Models (PGM 2022), Proceedings of Machine Learning Research (PMLR), vol. 186, pp. 277-288, 2022. https://proceedings.mlr.press/v186/kratochvil22a/kratochvil22a.pdf

[Plajner, 2020] M. Plajner and J. Vomlel, Learning bipartite Bayesian networks under monotonicity restrictions, Int. J. of General Systems, Vol. 49, No. 1, pp. 88-111, 2020. https://doi.org/10.1080/03081079.2019.1692004

[Plajner, 2021] M. Plajner, J. Vomlel, Bayesian Networks for the Test Score Prediction: A Case Study on a Math Graduation Exam. In: Vejnarová J., Wilson N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science, vol 12897. Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-86772-0_19

[Vomlel, 2012] J. Vomlel, Bayesian networks in educational testing, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, Vol. 12, Supplementary Issue 1, 2004, pp. 83-100. https://doi.org/10.1142/S021848850400259X

Topics for MSc and Bc Thesis

Sleep analysis is a traditional application area of ​​probabilistic methods. Typical examples are Hidden Markov Models and their generalizations - Dynamic Bayesian Networks [1]. Recently, models from the neural network family have been applied in this area: convolutional neural networks [2], recurrent deep neural networks [3,4]. A special case of recurrent networks are long short-term memory neural networks [5]. Bayesian networks usually do not achieve the quality of prediction of deep neural networks, but their advantage is the ability to provide an explanation of their conclusions. In the diploma thesis [6], dynamic Bayesian networks were modified by relaxing the assumption of time invariance (i.e. stationarity) of parameters so that the probabilities in the transition matrix depended on the length of stay in a given sleep phase. The aim of this work will be to further improve dynamic Bayesian networks by including the detection of several sleep phenomena such as awakening (sleep arousals) [7], K-complexes and spindles. The proposed method will be tested and compared with other methods used in this area, such as Random Forests and the Support Vector Machines method. Extensive data from the Sleep Heart Health Study (SHHS) [8] containing sleep data from 5804 adults will be used for comparisons.

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More than half of the world's languages are at risk and a large number are expected to die out this century. Such languages usually do not have a written form and at the same time it is not clear how much data needs to be collected in order to reliably capture their complex nature. Moreover, such languages are often studied by only one linguist, which casts doubt on the objectivity of the conclusions drawn and the credibility of the description. The aim of the work is the application of machine learning methods [1] in order to speed up and improve the analysis of endangered languages [2]. In cooperation with linguists from the Faculty of Arts of Palacký University in Olomouc, the work would focus on the issue of verb classes in Indonesian and two endangered Papuan languages Abui and Sawila [3]. Due to their typological properties, these languages are important for the question of verb classes.

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