Mgr. Petr Novák, Ph.D.

Mgr. Petr Novák, Ph.D.

Ing. Jitka Hrabáková, Ph.D.

Department of Applied Mathematics

The bachelor's thesis focuses on the implementation of regression parameter estimation in a semiparametric accelerated failure time model. The thesis first introduces survival analysis, the approach to survival analysis using counting processes, and then regression modeling in survival analysis. Subsequent chapters provide detailed descriptions of the chosen methods for estimating regression parameters of semiparametric accelerated failure time model and the constructed R package. The selected methods are tested at the end using both real and simulated data. An extensive simulation study was conducted on simulated data, where were selected methods tested with different scenarios including different procentual number of censoring, number of observations and different distributions of model deviations. The practical result of the thesis is an implemented R package that executes selected methods for estimating regression coefficients and includes all necessary tools for the semiparametric analysis of censored data.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

Ing. Jitka Hrabáková, Ph.D.

Department of Applied Mathematics

This thesis investigates recently published iterative approaches to estimate the parameters of robust M-estimators, which do not have explicit solutions. The focus is on the stagewise truncated IRLS method (STIR) and its variant with gradient descent updates (STIR-GD). We test the new methods on a common benchmark Stack Loss dataset, and synthetic data with different types of adversarial corruption. The new methods are compared to the classical methods in terms of relative error of the parameter estimates, number of iterations, and runtime. The results show that the new methods provide improved robustness to adversarial corruption compared to ordinary least squares and classical IRLS M-estimation with Huber loss. The new methods also show faster convergence compared to the classical IRLS, especially when starting from a bad initial estimate. The main contribution of this thesis is the implementation and optimization of the new iterative methods for robust regressions.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

Ing. Mgr. Ladislava Smítková Janků, Ph.D.

Department of Applied Mathematics

This thesis designs an LLM-based pipeline that extracts structured features from the cryptocurrency news stream and empirically evaluates which of those features improve short-horizon realized-volatility forecasts. The engineering contribution is a real-time data collection system gathering articles from RSS feeds, Telegram channels, and the daily Crypto Fear and Greed Index into a ClickHouse database, plus a multi-agent LLM extractor that separates material-event detection (Fact Classifier) from emotional-tone measurement (Emotion Classifier). The empirical contribution combines OLS HAR-X regression with NeweyWest HAC standard errors, joint Wald F-tests for feature blocks, and the BenjaminiHochberg FDR multiple-comparison correction across the 21-feature non-HAR inventory; three experiments are reported at H = 4 h on Cardano (ADA) and Solana (SOL): a directional-prediction null on the LLM's binary BULLISH/BEARISH labels, a HAR-X significance test concluded by a coverage-proxy audit on the one LLM-semantic feature that initially passes BH-FDR, and an illustrative rolling z-score anomaly characterisation on the surviving feature. The headline finding is that news amplification (log_2(1+n_articles) · log_2(1+n_sources)), a deterministic news-volume statistic that does not invoke the LLM, is the only pipeline-delivered non-HAR feature that survives BH-FDR on both coins with a positive coefficient and a defensible interpretation after the audit; the apparent fact_factual_confidence signal is a coverage-proxy artifact caused by the LLM not being invoked on no-article buckets, and no LLM-semantic feature replicates a positive sign across both coins after that audit.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

Ing. Karel Klouda, Ph.D.

Department of Applied Mathematics

In this bachelor thesis, a regression model was developed to predict the number of points for NHL players in the regular season based on data from the corresponding season. Additionally, clustering of player statistics was performed and cluster identifiers were obtained, which were incorporated into the regression models as new features to improve MSE. Among all tested clustering algorithms, the k-means algorithm provided the greatest benefit, as its identifiers helped reduce the validation MSE of the ridge regression from 42.76 to 40.56. The best results among all tested regression models were achieved by a neural network without the use of cluster identifiers, which correctly predicted the number of points within a five-point tolerance for 79.85% of players in the test dataset.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

Ing. Jana Vacková, Ph.D.

Department of Applied Mathematics

The aim of this bachelor's thesis is to develop an algorithm that predicts the results of table tennis matches in Czech leagues. The predictions are based on match data from the previous season. The theoretical part examines the foundations of statistics in table tennis and the applicability of machine learning methods in sports. The data necessary for training the models was acquired through custom automated collection from the official STIS portal and subsequently appropriately preprocessed. Three algorithms were tested within the thesis: logistic regression, random forest, and XGBoost. Logistic regression achieved the highest accuracy with 75.42 % on the test set. This model was subsequently utilized in the proposed algorithm predicting the overall outcome of a team match. It reached a prediction accuracy of 80 % in the professional Extraliga and 65 % in lower leagues.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

Ing. Jitka Hrabáková, Ph.D.

Department of Applied Mathematics

This thesis investigates and seeks to identify the optimal method for predicting victory in the team-based game League of Legends. The study employs Logistic Regression, Feedforward Neural Networks and Recurrent Neural Networks. The research involved obtaining and processing a large dataset of around 165,000 League of Legends matches. The models were compared based on accuracy, F1 score and expected calibration error (ECE). The logistic regression model emerged as the most effective, achieving an accuracy of 72.49% and an ECE of 0.0062 on the test data. The main outcome of this work is a mapping of the suitability of different machine learning approaches for the problem of predicting victory in League of Legends during the match.

Thesis on DSpace

Mgr. Petr Novák, Ph.D.

doc. Ing. Pavel Hrabák, Ph.D.

Department of Applied Mathematics

This bachelor's thesis focuses on modeling trends in the population development of world countries. The work explores and applies modern statistical methods for time series modeling with an emphasis on utilizing explanatory variables. The theoretical part introduces basic concepts of time series, statistical characteristics, stochastic processes, and models suitable for population prediction, such as linear regression, ARIMA models, and random forests. The practical part describes the collection and preprocessing of population data and relevant socioeconomic indicators from public sources. Subsequently, three different models with various approaches are trained and compared on this data, including addressing seasonality, change point detection, and outlier detection. Model performance is evaluated using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) metrics. Based on these metrics, the ARIMAX model proved to be the most accurate, achieving the lowest MAPE values for both short-term (0.0092) and long-term predictions (0.0200), thus effectively combining the time structure of the data with the influence of exogenous variables.

Thesis on DSpace