Bachelor theses
Statistical modelling of Covid-19 time series
Author
Oleh Kuznetsov
Year
2021
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Radomír Žemlička
Department
Summary
In the years 2020-2021, the whole world is experiencing difficulties caused by the global epidemic of the new SARS-CoV-2 virus. This thesis aims at the statistical analysis of the time series related to the COVID-19 pandemic in the Czech Republic. It explores the usability of the Facebook Prophet and Seasonal Autoregressive Integrated Moving Average (SARIMA) models to analyze and predict the development of pandemic processes. Moreover, this thesis connects the global changes that occurred in the selected time series with the provided government restrictions (lockdown, wearing a face mask, and so on).
Modeling and properties of autoregressive processes
Author
Artem Tokarevskikh
Year
2021
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Karel Klouda, Ph.D.
Department
Summary
Streaming data has recently attracted attention in numerous fields such as IoT, social networks, and e-Commerce. Streaming data is the data that is continuously generated by some sources and there is a need for their real-time processing. Given that the frequency of a stream may be very high, the methods for its processing must be computationally cheap and have low memory requirements. Autoregressive (AR) models are one of the fundamental approaches to time series modelling. The idea behind the autoregressive models is that the current value of the series is linearly dependent on its most recent past values. Thanks to its structure, AR models are able to effectively process streaming data even in situations when more complex models cannot achieve the desired performance for their computational and memory burden. This thesis investigates AR processes and their properties, outlines the theory behind them, and provides an illustrative example of AR modelling on real data related to the COVID-19 pandemic course in Czech Republic.
Comparison of national COVID-19 time series
Author
Michael Kolínský
Year
2021
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Radomír Žemlička
Department
Summary
This thesis analyses the national time series of newly infected people by COVID-19. The data are taken from the World Health Organization. In the preprocessing phase are the national time series scaled to respect the size of the population. The dimension is reduced using the Piecewise aggregate approximation and just the trend component of the time series is taken into account. In the thesis, there are defined four measures of time series (dis)similarity like Dynamic Time Warping (DTW), Edit Distance With Real Penalty (ERP), Longest Common Subsequence Similarity LCSS, and Discrete Fréchet distance. In the following phase, the preprocessed data are clustered using the agglomerative hierarchical clustering algorithm with the use of the average linkage that exploits the defined measures. In the last phase, the resulting count of clusters is chosen for each metric using the dendrogram. In the conclusion of this thesis, there are the resulting plots, which are further discussed together with the properties of the distance measures.
Approximations in logistic regression
Author
Eliáš El Frem
Year
2022
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
Department
Summary
Logistic regression is a classification method used in machine data processing. This thesis deals with the optimization of the Bayesian estimate of the parameters of the logistic model using Laplace approximation. The state-of-the-art methods usually rely on suboptimal Laplace-type approximations. This thesis goes one step further. It investigates the impact of a more precise approximation on the estimation quality. The results obtained by computationally intensive optimization are compared with the traditional less intensive but also more imprecise.
Multiple target tracking with PHD filters
Author
Petr Jechumtál
Year
2023
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
This thesis focuses on the problem of tracking multiple targets, which is still a very challenging discipline. It deals with the uncertainty about the measurement-target association in a noisy-cluttered-environment. Furthermore, targets can appear and disappear more or less randomly. The solution described in this thesis is based on the Bayesian inference and consists of the probability hypothesis density (PHD) filters. This approach involves modeling the relevant sets of targets and
measurements as random finite sets. The probability density recursions (PHDs) are used to propagate the posterior intensity, which is a first-order statistic of a random finite set of targets, over time.
Statistical and sentiment-based prediction of UFC results
Author
Roman Isaev
Year
2023
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
RNDr. Vladimíra Sečkárová, Ph.D.
Department
Summary
This work explores theory of Sentiment Analysis and investigates the possibilities of utilization of sentiments left on social media platforms for forecasting of UFC fight outcomes. Further, it utilizes already proposed approaches for usage of past statistics for prediction of future fights. This work proves that sentiments left online can be of great value for UFC outcome forecasting, as it achieves high accuracy for the case study which is conducted with the usage of posts from Twitter social media platform.
Design and implementation of a book recommender system
Author
Damián Baraník
Year
2023
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
RNDr. Vladimíra Sečkárová, Ph.D.
Department
Summary
Recommender systems are now an almost everyday part of our lives. Searching for a new book based on personal reading preferences takes considerable effort. To simplify the process, the majority of online retailers are utilizing the power of recommender systems to promote more products to their customers. In this thesis, we show the state-of-the-art recommender systems and analyze the different approaches for the recommendation process. Based on this analysis, we implement a recommendation system for books. Our system combines multiple recommendation algorithms and provides the user with the possibility to control the niche level of the recommendations.
Medicin avalability information system
Author
Dominik Kyjevský
Year
2024
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Pavel Náplava, Ph.D.
Department
Summary
This bachelor thesis deals with the analysis of publicly available data from the State Institute for Drug Control (SÚKL), in particular data on medicines and historical data on drug supply and dispensing, with the aim of proposing a model for predicting future supply and dispensing.
A web application was implemented that allows users to search for medicines or substances and provides key information including statistical graphs of supply, dispensing and forecasting.
The economic and management evaluation of the application includes an analysis of the costs of development and operation, proposals for funding and options for further development of the application. The evaluation results in a high profit potential in case of paid cooperation with pharmacies.
The benefit of this application is the high accuracy of the prediction of future dispensing and supply of medicines, based on which users can react to possible future shortages in advance.
Analysis of progression in lung cancer patients
Author
Martin Skala
Year
2024
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Marko Šidlovský
Department
Summary
The main goal of this paper was to analyse and determine possible predictions of lung cancer progression. Based on these results, the progression of patients with lung cancer can be predicted. It was possible to achieve a high success rate using the random forest with boosting machine learning model with astonishing results, achieving a balanced accuracy of 94.75% and F1 score of 92.47%. The research confirms the important role of machine learning in healthcare, where the right model can make easier the work of doctors and medical professionals.
Kubaturní Kalmanův filtr v inženýrské praxi
Author
Petr Fiedler
Year
2024
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
Department
Summary
This thesis explores the cubature Kalman filter, an algorithm designed for estimating system states in real-time within nonlinear models. While the filter possesses solid theoretical foundations, the original exposition of this algorithm may present accessibility challenges due to its reliance on advanced mathematical concepts. This thesis aims to present its derivation comprehensively, making it more accessible while explaining its core mathematical principles. Additionally, the cubature Kalman filter is compared with other algorithms for nonlinear filtering to highlight its unique features. Through practical examples, this thesis demonstrates the filter's effectiveness and operation in various scenarios.
Statistical loan management system
Author
Jaroslav Urban
Year
2024
Type
Bachelor thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
RNDr. Vladimíra Sečkárová, Ph.D.
Department
Summary
The thesis deals with the problem of effective loan management in an online loan market environment. The market consists of subjects willing to provide loans and subjects that create demand. Both sides share some information about themselves, their preferences, and requirements. With respect to the available information, the market seems to be a solid challenge for the development of an automated system that would manage the loans. The bachelor thesis aims to propose and, if possible, implement a loan management system that relies on statistical modeling methods.
Master theses
Electricity price forecasting based on weather conditions
Author
Jan Dejdar
Year
2019
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vondra, Ph.D.
Department
Summary
This thesis deals with electricity price forecasting based on weather conditions. The research of this topic is of great interest because accurate forecasting is essential for both the electricity producers and consumers. Due to the inability of storing a large amount of electricity efficiently and the necessity to balance between production and consumption, the short-term electricity price tends to be very volatile, which makes it difficult to predict it accurately.
There are many factors that affect the electricity price. Especially in Central and Western Europe, very important factor is the weather, due to increasing number of solar and wind power plants. This thesis aims to analyze available data about weather forecasts and the electricity prices and create predictive models for this data.
Fusion of heterogeneous models in agent networks
Author
Martin Šmíd
Year
2020
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Department
Summary
This thesis looks into the ways of enhancing the local predictions in agent networks using the information shared by their neighbouring nodes. Agents locally employ different models, thus the diversity of information to share is limited. Multiple variants of improving the predictions are proposed, some of them taking the prediction certainty into consideration. These are then implemented and compared on both simulated and real-world data.
Sequential Bayesian Poisson regression
Author
Radomír Žemlička
Year
2020
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Department
Summary
The Poisson regression is a popular generalized linear model used to model discrete count variables. This thesis is focused on the problem of its sequential estimation under potentially slowly time-varying regression coefficients. A convenient approximation by normal distribution is used to do so in the Bayesian setting. Also, a calibration technique is discussed to enhance the estimation quality. Finally, a use case of the proposed approach in the signal processing domain is suggested, in particular, its application in diffusion networks to perform distributed collaborative estimation.
Distributed Kalman filtering under partially heterogeneous models
Author
Thanh Quang Mai
Year
2021
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
Department
Summary
This thesis explores the problem of distributed Kalman filtering under partially heterogeneous models. A modification to the existing diffusion Kalman filter is proposed, enabling the employment of partially heterogeneous models in the diffusion networks. The performance of the less complex models is futher improved by the implementation of a node failure detection heuristic, resetting the failling nodes, and giving them a chance at a recovery.
Bayesian filtering of state-space models with unknown covariance matrices
Author
Tomáš Vlk
Year
2021
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
Department
Summary
This thesis explores the problem of distributed Bayesian sequential estimation of unknown state-spacemodels with unknown processes and measurement noise covariance matrices. This is a frequent problem in real-world scenarios, where the information about noise covariance matrices for specific sensors may not be available. The solution proposed in this thesis is built upon the variational Bayesian paradigm, which is used for the estimation of the states, as well as the unknown measurement noise covariance matrix. From performance improvements, the measurements and posterior estimates are shared between the adjacent node in the network. It also shows a way of optimizing the process noise covariance matrix.
Performance and robustness analysis of Bayesian filters
Author
Mykyta Boiko
Year
2023
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
As is well-known, state-space models are widely used to model different observable processes in various fields, from finance to biology. Based on the observed sequence, the main interest is to deduce the sequence of hidden states that gave rise to them. The primary goal of this thesis is to study the performance and robustness of various Bayesian algorithms used for online state filtering under both well-specified and misspecified state-space models. This is due to the fact that in practice, for various reasons, there is often a lack of knowledge of process noise or measurements. This thesis, in particular, touches on the rather popular case where the measurement model is misspecified. As part of this work, the emphasis is placed on an introduction to the filters from the most popular family, the Kalman family, and consider them from a Bayesian perspective, also not without the particle filter, which is regarded as more stable in the context of application to misspecified models. Attention will also be paid, and experiments will be conducted with so-called approximate Bayesian filters, which allow complete ignorance of the noise distribution of measurements. The result of the thesis should be the coverage of the theory of all of the above and the results of experiments, not excluding the definition of plans for the future development of this topic.
Explainability in Time Series Classification
Author
Narek Vardanjan
Year
2023
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
RNDr. Vladimíra Sečkárová, Ph.D.
Department
Summary
Time series classification is used in a wide variety of
real-world problems, from health analysis to food quality assurance. Despite its
usage, the extent of understanding the reasons for the classification determined
by the model is insufficient. This thesis proposes a novel type of explainable
classifier based on ARIMA models, which are heavily used for time series
forecasting. The time series dataset is converted to ARIMA coefficients and
classified using random forests classifier. The explainability is provided by
established explanation methods for tabular data. Besides the ARIMA models,
the thesis additionally provides a method for explaining raw time series data,
built upon the LIME method.
Multiple target tracking with external information
Author
Andrey Babushkin
Year
2023
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
The thesis focuses on the multi-target tracking problem in cluttered environments with the uncertainty on the number of targets and using Bayesian inference. In this work, we mainly focus on the popular Gaussian mixture probability hypothesis density (GM-PHD) filter and introduce a technique to include additional information for cases when a sensor fails to detect targets due to environmental or physical limitations. We provide all required theoretical background from the basics of probability theory to the discussion of various multi-target tracking methods and the introduction of the Finite Set Statistics (FISST) framework. We also conclude with an extensive performance measurement and analysis of results, where we demonstrate that the proposed fusion technique significantly improves tracking results. Finally, we discuss the limitations of the filter and propose possible measures to overcome them.
Distributed multiple target tracking
Author
Jan Novák
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
This thesis focuses on the topic of distributed multiple-target tracking. It presents the necessary mathematical concepts needed to understand the subject. Then, it introduces the concept of hidden state estimation with the hidden Markovian model and measurement model. Next, it introduces and derives the Kalman filter using the exponential family of distributions. The Kalman filter is then gradually evolved into the PDA filter, IPDA filter and JIPDA filter. Once these concepts are established, they deal with collaborative filtering methods, focusing mainly on the diffusion approach. The diffusion approach is initially described in a general manner. After that, a diffusion algorithm based on the JIPDA filter is proposed. The performance of the proposed algorithm is then evaluated in several experiments.
Network anomaly detection based on traceroute data
Author
Jan Peřina
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
doc. Ing. Tomáš Čejka, Ph.D.
Department
Summary
Network anomaly detection is crucial for identifying issues in computer networks, with particular significance in large-scale global networks like the Worldwide LHC Computing Grid, that is used for processing data from CERN experiments.
This thesis aims to enhance or replace the existing heuristic network anomaly detection algorithm, primarily designed to identify routing changes based on traceroute measurements between global datacenters, generated through the perfSonar software.
The work demonstrates the informational richness of traceroute measurements and proposes several Bayesian inference-based models to improve anomaly detection in traceroute data.
PHD filter-based monitoring of birds migration
Author
Tomáš Holas
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
The swift advancement of miniature devices with GNSS positioning and communication capabilities has spurred their widespread utilization in biological research. Specifically, the real-time or near-real-time tracking of wild animals enables a thorough examination of their behavior within their natural environment and throughout migration patterns. This study focuses on localizing birds cataloged in the Research Institute for Nature and Forest (INBO) database BOP\_RODENT. This localization approach employs the~probability hypothesis density (PHD) filter in its standard configuration and an adapted version tailored for individual bird tracking. The primary motivations for choosing this filter include its ability to localize multiple targets simultaneously, resilience to external noise and false positives, and independence from prior knowledge of target quantity. The~original contributions of this research are twofold: proposing a PHD-based method for bird tracking and enhancing the basic PHD filter to facilitate track formation.
Estimation of detection probability in multitarget filters using object advanced image processing techniques
Author
Michal Seibert
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
Department
Summary
This thesis focuses on the problem of multi-target tracking with noisy measurements in a cluttered environment. Algorithms for tracking multiple targets with the uncertainty in the number of targets and their survival are often sensitive to the correct setting of parameters relative to the environment. One of the key parameters is the detection probability, which is often constant. In this work, a method to estimate this probability for each target at any time step is demonstrated through tracking objects in video footages. Advanced deep-learning algorithms for image processing are utilized to provide targets' measurements. Outputs of these methods are then exploited to calculate the detection probability. To analyse the capability of the proposed method, the Gaussian mixture probability hypothesis density (GM-PHD) filter is used. This filter falls among fundamental random finite sets statistics-based ultitarget algorithms. The appropriateness of the proposed method is then discussed with regards to its limitations and possible future improvements.
Improvement of multi-target tracker performance by on-demand external sensors
Author
Anna Tesaříková
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
This thesis focuses on the problem of multi-target tracking, especially on the probability hypothesis density (PHD) filter, and on methods of improving its performance in regions where the sensor is affected by significant misdetections or high clutter rate. To this end, the information from on-demand external sensors is employed. We introduce three approaches to include additional information from single-target trackers -- probabilistic data association (PDA) filters. We provide all required theoretical background for single-target tracking, multi-target tracking, and information fusion methods. We evaluate the performance of proposed approaches and demonstrate that they improve tracking results.
Track coalescence in JPDA filters and its suppression
Author
Artem Tokarevskikh
Year
2024
Type
Master thesis
Supervisor
doc. Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Tomáš Vlk
Department
Summary
Multi-target tracking (MTT) plays a crucial role in various applications, from autonomous vehicles and robotics to surveillance and air traffic control. Joint Probabilistic Data Association (JPDA) filters have been widely employed for MTT due to their efficiency and ability to handle data association uncertainties in cluttered environments. However, JPDA filters are susceptible to track coalescence, where closely spaced target tracks tend to merge, leading to inaccurate state estimation and potential track loss.
This thesis investigates the problem of track coalescence in JPDA filters and proposes a novel suppression technique that combines adaptive validation gating with hypothesis pruning. Our method dynamically adjusts the validation gate size based on target proximity and estimated states, effectively limiting association possibilities and reducing the likelihood of track merging. Through simulations and experiments, we demonstrate the effectiveness of our proposed approach in improving localization accuracy and overall tracking performance compared to baseline JPDA and JPDA* with pruning.
While our method shows significant advantages, it exhibits a higher misdetection rate in extreme scenarios. We discuss potential explanations for this limitation and propose directions for future research, including adaptive gating parameter selection, alternative gating strategies, and advanced track management techniques. By addressing these aspects, we aim to further enhance the robustness and reliability of JPDA-based tracking systems for handling complex multi-target scenarios.