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].

References:

  1. F. V. Jensen, Bayesian networks and decision graphs, Springer Verlag, 2001.

  2. M. Gómez, Real-World Applications of Influence Diagrams. In Advances in Bayesian Networks, edited by J. A. Gámez, S. Moral, and A. Salmerón. Studies in Fuzziness and Soft Computing, Springer Berlin Heidelberg, pp. 161-180, 2004, doi: 10.1007/978-3-540-39879-0_9

  3. V. Kratochvíl, J. Vomlel, Influence diagrams for the optimization of a vehicle speed profile. In Proceedings of the Twelfth Annual Bayesian Modeling Applications Workshop, Amsterdam, Netherlands, 2015

  4. J. Vomlel, V. Kratochvíl, Influence diagrams for speed profile optimization: computational issues. In Proceedings of the 10th Workshop on Uncertainty Processing (Wupes 2015). September 16-19, 2015, Monínec, Czech Republic.

  5. J. Vomlel and V. Kratochvíl. Solving Trajectory Optimization Problems by Influence Diagrams. In A. Antonucci et al. (Eds.): ECSQARU 2017, Springer LNAI 10369, pp. 125–134, 2017. https://dx.doi.org/10.1007/978-3-319-61581-3

  6. P. Shenoy, J. West, Inference in hybrid Bayesian networks using mixtures of polynomials. International Journal of Approximate Reasoning, 52(5):641--657, 2011.

  7. B. Kveton, M. Hauskrecht, C. Guestrin, Solving factored MDPs with hybrid state and action variables. Journal of Artificial Intelligence Research, 27:153--201, 2006. https://dx.doi.org/10.1613/jair.2085

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

  • find efficient computational methods for canonical models
    (suitable candidates seem to be methods used for the decomposition of tensors),

  • compare different inference methods for canonical models according to

    1. the computational complexity and

    2. the accuracy of the calculation.

  • design and test methods for learning canonical models from data.

References:

  1. F. V. Jensen, Bayesian networks and decision graphs, Springer Verlag, 2001.

  2. S. L. Lauritzen, Graphical Models, Clarendon Press, Oxford, 1996.

  3. F. V. Jensen and S. L. Lauritzen and K. G. Olesen, Bayesian updating in recursive graphical models by local computation. Computational Statistics Quarterly, 1990, Vol. 4, pp. 269-282.

  4. F. J. Díez and M. J. Druzdzel. Canonical Probabilistic Models for Knowledge Engineering. Technical Report CISIAD-06-01, UNED, Madrid, Spain, 2006.

  5. P. Savický and J. Vomlel, Exploiting tensor rank-one decomposition in probabilistic inference, Kybernetika, 2007, Vol. 43, Number 5, pp. 747-764.

  6. J. Vomlel and P. Tichavský, Probabilistic inference with noisy-threshold models based on a CP tensor decomposition, International Journal of Approximate Reasoning (2014), Volume 55, Issue 4, pp. 1072-1092.

  7. P. Tichavský, J. Vomlel. Representations of Bayesian networks by low-rank models, International Conference on Probabilistic Graphical Models, 11-14 September 2018, Prague. Proceedings of Machine Learning Research, Volume 72, pp. 463-474.

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.

References:

  1. Jiří Vomlel and Václav Kratochvíl. Dynamic Bayesian Networks for the Classification of Sleep Stages. In Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18), Třeboň, Czech Republic, 2018, pp. 205-215, http://staff.utia.cas.cz/vomlel/vomlel-kratochvil-2018.pdf

  2. Junming Zhang and Yan Wu. A New Method for Automatic Sleep Stage Classification. IEEE Transactions on Biomedical Circuits and Systems, Vol. 11, No. 5, October 2017.

  3. Erik Bresch, Ulf Großekathöfer, Gary Garcia-Molina. Recurrent Deep Neural Networks for Real-Time Sleep Stage Classification From Single Channel EEG. Frontiers in Computational Neuroscience. Vol. 12, 2018. https://www.frontiersin.org/article/10.3389/fncom.2018.00085

  4. Patrick Krauss, Claus Metzner, Nidhi Joshi, Holger Schulze, Maximilian Traxdorf, Andreas Maier, Achim Schilling. Analysis and visualization of sleep stages based on deep neural networks, Neurobiology of Sleep and Circadian Rhythms, Vol. 10, 2021, https://doi.org/10.1016/j.nbscr.2021.100064

  5. Mustafa Radha, Pedro Fonseca, Arnaud Moreau, Marco Ross, Andreas Cerny, Peter Anderer, Xi Long, Ronald M. Aarts. Sleep stage classification from heart-rate variability using long short-term memory neural networks. Sci Rep 9, 14149 (2019). https://doi.org/10.1038/s41598-019-49703-y

  6. Kristína Blašková, Machine learning methods for sleep analysis, MSc. Thesis, České vysoké učení technické v Praze, Fakulta jaderná a fyzikálně inženýrská, 2020, https://drive.google.com/file/d/1GA4AXBP0RQYAZBPuf8a1SNia76cvgUS7/view?usp=sharing

  7. Hongyang Li & Yuanfang Guan, DeepSleep convolutional neural network allows accurate and fast detection of sleep arousal. https://doi.org/10.1038/s42003-020-01542-8

  8. National Sleep Research Resource, Sleep Heart Health Study, https://doi.org/10.25822/ghy8-ks59

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.

References:

  1. T. Hastie, R. Tibshirani and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, 2009.

  2. O. Zamaraeva, F. Kratochvíl, E. M. Bender, F. Xia & K. Howell. Computational Support for Finding Word Classes: A Case Study of Abui. In Proceedings of the 2nd Workshop on the Use of Computational Methods for Endangered Languages, Honolulu, Hawaii, March 6-7, 2017, 130-140. Association for Computational Linguistics (ACL).

  3. F. Kratochvíl, D. Moeljadi, David, B. Delpada, V. Kratochvíl, and Vomlel, Jiří. Aspectual pairing and aspectual classes in Abui. STUF - Language Typology and Universals, vol. 74, no. 3-4, 2021, pp. 621-657. https://doi.org/10.1515/stuf-2021-1046