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Inference in Bayesian Networks
Šimeček, Josef ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
This master's thesis deals with demonstration of various approaches to probabilistic inference in Bayesian networks. Basics of probability theory, introduction to Bayesian networks, methods for Bayesian inference and applications of Bayesian networks are described in theoretical part. Inference techniques are explained and complemented by their algorithm. Techniques are also illustrated on example. Practical part contains implementation description, experiments with demonstration applications and conclusion of the results.
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An empirical comparison of popular algorithms for learning gene networks
Djordjilović, V. ; Chiogna, M. ; Vomlel, Jiří
In this work, we study the performance of different algorithms for learning gene networks from data. We consider representatives of different structure learning approaches, some of which perform unrestricted searches, such as the PC algorithm and the Gobnilp method and some of which introduce prior information on the structure, such as the K2 algorithm. Competing methods are evaluated both in terms of their predictive accuracy and their ability to reconstruct the true underlying network. A real data application based on an experiment performed by the University of Padova is also considered. We also discuss merits and disadvantages of categorizing gene expression measurements.
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Proceedings of the 10th Workshop on Uncertainty Processing
Kratochvíl, Václav
WUPES 2015 is organized jointly by the Institute of Information Theory and Automation of the Czech Academy of Sciences and by the Faculty of Management, University of Economics, Prague. It is quite natural that such a meeting could not materialize if it were not for the hard work of many our colleagues and friends. This is why we want to express our gratitude to all the members of both the Programme and Organizing Committees. Last but not least, we also want to acknowledge the fact that this workshop is organized, due to the fact that the research of several members of the Organizing Committee is financially supported by grants GA CR no 15-00215S and 13-20012S.
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A generalization of the noisy-or model to multivalued parent variables
Vomlel, Jiří
In this paper we propose a generalization of the noisy-or model to multivalued parent variables. Albeit the proposed generalization is more restrictive than previous proposals, it has several nice properties. In this paper we suggest a method for learning this model and report results of experiments on the Reuters text classification data.
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Experimentální srovnání triangulačních heuristik na transformovaných sítích BN2O
Vomlel, Jiří ; Savický, Petr
In this paper we present results of experimental comparisons of several triangulation heuristics on bipartite graphs. Our motivation for testing heuristics on the family of bipartite graphs is the rank-one decomposition of BN2O networks. A BN2O network is a Bayesian network having the structure of a bipartite graph with all edges directed from the top level toward the bottom level and where all conditional probability tables are noisy-or gates. After applying the rank-one decomposition, which adds an extra level of auxiliary nodes in between the top and bottom levels, and after removing simplicial nodes of the bottom level we get so called BROD graph. This is an undirected bipartite graph. It is desirable for efficiency of the inference to find a triangulation of the BROD graph having the sum of table sizes for all cliques of the triangulated graph as small as possible. From this point of view, the minfill heuristics perform in average better than other tested heuristics (minwidth, h1, and mcs).
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Využití imsetů při učení bayesovských sítí
Vomlel, Jiří ; Studený, Milan
This paper describes a modification of the greedy equivalence search (GES) algorithm. The presented modification is based on the algebraic approach to learning. The states of the search space are standard imsets. Each standard imset represents an equivalence class of Bayesian networks. For a given quality criterion the database is represented by the respective data imset. This allows a very simple update of a given quality criterion since the moves between states are represented by differential imsets. We exploit a direct characterization of lower and upper inclusion neighborhood, which allows an efficient search for the best structure in the inclusion neighborhood. The algorithm was implemented in R and is freely available.
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Noisy-or classifier
Vomlel, Jiří
We discuss application of the noisy-or model to classification with large number of attributes. An example of such a task is categorization of text documents, where attributes are single words from the documents.
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Two applications of Bayesian networks
Vomlel, Jiří
We present two recent applications of Bayesian networks: adaptive testing and troubleshooting man-made devices. We review briefly the underlying theory and provide a general framework for building strategies using Bayesian network models. We discuss applications of the framework to adaptive testing and troubleshooting. The paper is based on our experience with two projects.
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Possibilistic Laws of Large Numbers
Kramosil, Ivan
We consider sequences of samples defined on spaces endowed by a possibilistic measure, looking for relatively small sets of such sequences which are important or interesting, in a sense, and which occur with possibility degree equal to one or tending to one with the length of the sample sequence increasing.
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Thoughts on belief and model revision with uncertain evidence
Vomlel, Jiří
Bayesian networks and other graphical probabilistic models became a popular framework for reasoning with uncertainty. Efficient methods have been developed for revising beliefs with new evidence. However, when the evidence is uncertain, i.e. represented by a probability distribution, different methods have been proposed. In this paper we analyze and compare these methods. The goal is to show in what cases they can be used correctly.
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