Ing. Kamil Dedecius, Ph.D.

Theses

Bachelor theses

Comparison of national COVID-19 time series

Author
Michael Kolínský
Year
2021
Type
Bachelor thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Radomír Žemlička
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.

Statistical modelling of Covid-19 time series

Author
Oleh Kuznetsov
Year
2021
Type
Bachelor thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Radomír Žemlička
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).

Approximations in logistic regression

Author
Eliáš El Frem
Year
2022
Type
Bachelor thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
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.

Modeling and properties of autoregressive processes

Author
Artem Tokarevskikh
Year
2021
Type
Bachelor thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Karel Klouda, Ph.D.
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.

Master theses

Distributed Kalman filtering under partially heterogeneous models

Author
Thanh Quang Mai
Year
2021
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
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.

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.
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.
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.

Bayesian filtering of state-space models with unknown covariance matrices

Author
Tomáš Vlk
Year
2021
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
Reviewers
Ing. Ondřej Tichý, Ph.D.
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.

Sequential Bayesian Poisson regression

Author
Radomír Žemlička
Year
2020
Type
Master thesis
Supervisor
Ing. Kamil Dedecius, Ph.D.
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.