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Modeling the spread of loanwords in South-East Asia using sailing navigation software and Bayesian networks
Kratochvíl, F. ; Kratochvíl, Václav ; Saad, G. ; Vomlel, Jiří
A loanword is a word permanently adopted from one language and incorporated into another language without translation. In this paper, we study loanwords in the South-East Asia Archipelago, home to a large number of languages. Our paper is inspired by the works of Hoffmann et al. (2021) Bayesian methods are applied to probabilistic modeling of family trees representing the history of language families and by Haynie et al. (2014) modeling the diffusion of a special class of loanwords, so-called Wanderw ̈orter in languages of Australia, North America, and South America. We assume that in the South-East Asia Archipelago Wanderwörter spread along specific maritime trade routes whose geographical characteristics can help unravel the history of Wanderwörter diffusion in the area. For millennia trade was conducted using sailing ships which were constrained by the monsoon system and in certain areas also by strong sea currents. Therefore rather than the geographical distances, the travel times of sailing ships should be considered as a major factor determining the intensity of contact among cultures. We use sailing navigation software to estimate travel times between different ports and show that the estimated travel times correspond well to the travel times of a Chinese map of the sea trade routes from the early seventeenth century. We model the spread of loanwords using a probabilistic graphical model - a Bayesian network. We design a novel heuristic Bayesian network structure learning algorithm that learns the structure as a union of spanning trees for graphs of all loanwords in the training dataset. We compare this algorithm with BIC optimal Bayesian networks by measuring how well these models predict the true presence/absence of a loanword. Interestingly, Bayesian networks learned by our heuristic spanning tree-based algorithm provide better results than the BIC optimal Bayesian networks.
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Subjective well-being and the individual material situation in Central Europe: A Bayesian network approach
Švorc, Jan ; Vomlel, Jiří
The objective of this paper is to explore the associations between the subjective well-being (SWB) and the subjective and objective measures of the individual material situation in the four post-communist countries of Central Europe (the Czech Republic, Hungary, Poland, and Slovakia). The material situation is measured by income, relative income compared to others, relative income compared to one’s own past, perceived economic strain, financial problems, material deprivation, and housing problems. Our analysis is based on empirical data from the third wave of European Quality of Life Study conducted in 2011. Bayesian networks as a graphical representation of the relations between SWB and the material situation have been constructed in five versions. The models have been assessed using the Bayesian Information Criterion (BIC) and SWB prediction accuracy, and compared\nwith Ordinal Logistic Regression (OLR). Expert knowledge, as well as three different algorithms (greedy, Gobnilp, and Tree-augmented Naive Bayes) were used for learning the network structures. Network parameters were learned using the EM algorithm. Parameters based on OLR were learned for a version of the expert model. The Gobnilp model, the Markov equivalent to the greedy model, is BIC optimal. The OLR predicts SWB slightly better than the other models. We conclude that the objective material conditions' influence on SWB is rather indirect, through the subjective situational assessment of various aspects related to the individual material conditions.
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Bayesian Networks for the Analysis of Subjective Well-Being
Švorc, Jan ; Vomlel, Jiří
We use Bayesian Networks to model the influence of diverse socio-economic factors on subjective well-being and their interrelations. The classical statistical analysis aims at finding significant explanatory variables, while Bayesian Networks can also help sociologists to explain and visualize the problem in its complexity. Using Bayesian Networks the sociologists may get a deeper insight into the interplay of all measured factors and their influence on the variable of a special interest. In the paper we present several Bayesian Network models -- each being optimal from a different perspective. We show how important it is to pay a special attention to a local structure of conditional probability tables. Finally, we present results of an experimental evaluation of the suggested approaches based on real data from a large international survey. We believe that the suggested approach is well applicable to other sociological problems and that Bayesian Networks represent a new valuable tool for sociological research.
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Question Selection Methods for Adaptive Testing with Bayesian Networks
Plajner, Martin ; Magauina, A. ; Vomlel, Jiří
The performance of Computerized Adaptive Testing systems, which are used for testing of human knowledge, relies heavily on methods selecting correct questions for tested students. In this article we propose three different methods selecting questions with Bayesian networks as students’ models. We present the motivation to use these methods and their mathematical description. Two empirical datasets, paper tests of specific topics in mathematics and Czech language for foreigners, were collected for the purpose of methods’ testing. All three methods were tested using simulated testing procedure and results are compared for individual methods. The comparison is done also with the sequential selection of questions to provide a relation to the classical way of testing. The proposed methods are behaving much better than the sequential selection which verifies the need to use a better selection method. Individually, our methods behave differently, i.e., select different questions but the success rate of model’s predictions is very similar for all of them. This motivates further research in this topic to find an ordering between methods and to find the best method which would provide the best possible selections in computerized adaptive tests.
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Representations of Bayesian Networks by Low-Rank Models
Tichavský, Petr ; Vomlel, Jiří
Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks defined as the product of these CPTs may become intractable by conventional methods of BN inference because of their dimensionality. In many cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in the so-called Kruskal form as a sum of rank-one components. Such representation would be equivalent to adding one artificial parent to all random variables and deleting all edges between the variables. The most difficult task is to find such a representation given a set of marginals or CPTs of the random variables under consideration. In the former case, it is a problem of joint canonical polyadic (CP) decomposition of a set of tensors. The latter fitting problem can be solved in a similar manner. We apply a recently proposed alternating direction method of multipliers (ADMM), which assures that the model has a probabilistic interpretation, i.e., that all elements of all factor matrices are nonnegative. We perform experiments with several well-known Bayesian networks.\n\n
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Gradient Descent Parameter Learning of Bayesian Networks under Monotonicity Restrictions
Plajner, Martin ; Vomlel, Jiří
Learning parameters of a probabilistic model is a necessary step in most machine learning modeling tasks. When the model is complex and data volume is small the learning process may fail to provide good results. In this paper we present a method to improve learning results for small data sets by using additional information about the modelled system. This additional information is represented by monotonicity conditions which are restrictions on parameters of the model. Monotonicity simplifies the learning process and also these conditions are often required by the user of the system to hold. \n\nIn this paper we present a generalization of the previously used algorithm for parameter learning of Bayesian Networks under monotonicity conditions. This generalization allows both parents and children in the network to have multiple states. The algorithm is described in detail as well as monotonicity conditions are.\n\nThe presented algorithm is tested on two different data sets. Models are trained on differently sized data subsamples with the proposed method and the general EM algorithm. Learned models are then compared by their ability to fit data. We present empirical results showing the benefit of monotonicity conditions. The difference is especially significant when working with small data samples. The proposed method outperforms the EM algorithm for small sets and provides comparable results for larger sets.
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Employing Bayesian Networks for Subjective Well-being Prediction
Švorc, Jan ; Vomlel, Jiří
This contribution aims at using Bayesian networks for modelling the relations between the individual subjective well-being (SWB) and the individual material situation. The material situation is approximated by subjective measures (perceived economic strain, subjective evaluation of the income relative to most people in the country and to own past) and objective measures (household’s income, material deprivation, financial problems and housing defects). The suggested Bayesian network represents the relations among SWB and the variables approximating the material situation. The structure is established based on the expertise gained from literature, whereas the parameters are learnt based on empirical data from 3rd edition of European Quality of Life Study for the Czech Republic, Hungary, Poland and Slovakia conducted in 2011. Prediction accuracy of SWB is tested and compared with two benchmark models whose structures are learnt using Gobnilp software and a greedy algorithm built in Hugin software. SWB prediction accuracy of the expert model is 66,83%, which is significantly different from no information rate of 55,16%. It is slightly lower than the two machine learnt benchmark models.
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Dynamic Bayesian Networks for the Classification of Sleep Stages
Vomlel, Jiří ; Kratochvíl, Václav
Human sleep is traditionally classified into five (or six) stages. The manual classification is time consuming since it requires knowledge of an extensive set of rules from manuals and experienced experts. Therefore automatic classification methods appear useful for this task. In this paper we extend the approach based on Hidden Markov Models by relating certain features not only to the current time slice but also to the previous one. Dynamic Bayesian Networks that results from this generalization are thus capable of modeling features related to state transitions. Experiments on real data revealed that in this way we are able to increase the prediction accuracy.
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A machine learning method for incomplete and imbalanced medical data
Salman, I. ; Vomlel, Jiří
Our research reported in this paper is twofold. In the first part of the paper we use\nstandard statistical methods to analyze medical records of patients suffering myocardial\ninfarction from the third world Syria and a developed country - the Czech Republic.\nOne of our goals is to find whether there are statistically significant differences between\nthe two countries. In the second part of the paper we present an idea how to deal with\nincomplete and imbalanced data for tree-augmented naive Bayesian (TAN). All results\npresented in this paper are based on a real data about 603 patients from a hospital in\nthe Czech Republic and about 184 patients from two hospitals in Syria.
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O problémech seřazení při řízení servisních operací
Lín, Václav ; Vomlel, Jiří (vedoucí práce) ; Jiroušek, Radim (oponent) ; Kouba, Zdeněk (oponent) ; Ottosen, Thorsten Jorgen (oponent)
Jedním z témat operačního managementu je udržení provozuschopnosti produkčních systémů a rychlé obnovení provozu v případě poruchy. V předkládané práci se zabýváme problémem optimálního seřazení dostupných servisních operací při odstraňování poruchy produkčního systému. Cílem je nalezení posloupnosti operací s nejnižší očekávanou cenou nebo dobou opravy. Studujeme několik variant tohoto problému známých z literatury. Zabýváme se výpočetní složitostí, algoritmy a vztahem k teorii rozvrhů.
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