Jiří Vomlel

• PhD
• Senior Researcher at The Czech Academy of Sciences

This paper develops the traditional Failure Modes, Effects and Criticality Analysis (FMECA) for quantitative risk assessment from a Bayesian Network (BN)-based perspective. The main purpose consists in endowing FMECA with a framework for analysing causal relationships for risk evaluation and deriving probabilistic relations between significant risk...

In this paper, we consider two-layer Bayesian networks. The first layer consists of hidden (unobservable) variables and the second layer consists of observed variables. All variables are assumed to be binary. The variables in the second layer depend on the variables in the first layer. The dependence is characterised by conditional probability tabl...

Background: Acute myocardial infarction (AMI) is the leading cause of death world- wide and requires accurate models to predict the risk of heart disease and mortality from these accidents for early intervention and prevention. Objective: Bayesian networks (BNs) as a class of machine learning will not only significantly improve the prediction of h...

In this paper we discuss learning Bayesian networks whose conditional probability tables are either Noisy-OR models or general conditional probability tables. We refer to these models as Mixed Noisy-OR Bayesian Networks. To learn their structure, we modify the Bayesian Information Criterion used for standard Bayesian networks to reflect the number...

In this paper, we provide an approach to learning optimal Bayesian network (BN) structures from incomplete data based on the BIC score function using a mixture model to handle missing values. We have compared the proposed approach with other methods. Our experiments have been conducted on different models, some of them Belief Noisy-Or (BNO) ones. W...

One of the current drivers for transitioning from the traditional E-Government to the digital government is the ability to create and share new services in the governmental ICT landscape. The government must effectively communicate and offer its services to itself (G2G) and outside, be it an end-consumer or business (G2C, G2B). Since the government...

Across languages, verbs are known to be sensitive to their syntactic context. Their meaning may change, based on number, type of arguments, and role of argument. Alternatively, their meaning may remain constant (a paraphrase). Two main approaches have addressed this: i) The lexical-semantic approach (e.g. Levin 1986, 2015; Levin & Rappaport-Hovav 2...

We present an automatic verb classifier system that identifies inflectional classes in Abui (AVC-abz), a Papuan language of the Timor-Alor-Pantar family. The system combines manually annotated language data (the learning set) with the output of a morphological precision grammar (corpus data). The morphological precision grammar is trained on a full...

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, a 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 fami...

In this paper we study the problem of student knowledge level estimation. We use probabilistic models learned from collected data to model the tested students. We propose and compare experimentally several different Bayesian network models for the score prediction of student’s knowledge. The proposed scoring algorithm provides not only the expected...

This paper describes the aspectual classes in Abui, a Papuan language of the Timor-Alor-Pantar family. Abui innovated a system of aspectual stem pairing, realized by consonant mutation, vowel grading, and rime mutation. Although stem pairing is widespread (about 61% of the verbs alternate), about 38% of our 1,330 verb sample are unpaired and immuta...

This paper describes the aspectual classes in Abui, a Papuan language of the Timor-Alor-Pantar family. Abui innovated a system of aspectual stem pairing, realised by consonant mutation, vowel grading, and rime mutation. Although stem pairing is widespread (about 61% of the verbs alternate), about 38% of our 1330 verb sample are unpaired and immutab...

In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides a synergy between these two phases as it evaluates Bayesian network models used for computerized adaptive tes...

The contribution of the present paper aims to develop the traditional Failure Modes, Effects and Criticality Analysis (FMECA) for quantitative risk analysis from a Bayesian Network (BN)-based perspective. The main purpose of research consists in providing a framework for analysing causal relationships for risk evaluation and deriving probabilistic...

Learning parameters of a probabilistic model is a necessary step in machine learning tasks. We present a method to improve learning from small datasets by using monotonicity conditions. Monotonicity simplifies the learning and it is often required by users. We present an algorithm for Bayesian Networks parameter learning. The algorithm and monotoni...

Non-trivial minimal balanced systems (= collections) of sets are known to characterize through their induced linear inequalities the class of the so-called balanced (coalitional) games. In a recent paper a concept of an irreducible min-balanced (= minimal balanced) system of sets has been introduced and the irreducible systems have been shown to ch...

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aim. Here, we aim at studying the magnetic nature of umbr...

Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Here, we aim at studying the magnetic nature of umbra-penumbra bou...

Our research reported in this paper is twofold. In the first part of the paper we use standard statistical methods to analyze medical records of patients suffering myocardial infarction from the third world Syria and a developed country-the Czech Republic. One of our goals is to find whether there are statistically significant differences between t...

Artificial intelligence is present in many modern computer science applications. The question of effectively learning parameters of such models even with small data samples is still very active. It turns out that restricting conditional probabilities of a probabilistic model by monotonicity conditions might be useful in certain situations. Moreover...

Influence diagrams are decision-theoretic extensions of Bayesian networks. In this paper we show how influence diagrams can be used to solve trajectory optimization problems. These problems are traditionally solved by methods of optimal control theory but influence diagrams offer an alternative that brings benefits over the traditional approaches....

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Goddard problem. We present results of numerical experiments with this problem and compare the solutions provided by influence diagrams with the optimal solution.

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Brachistochrone problem. We present results of numerical experiments on this problem, compare the solution provided by the influence diagram with the optimal solution. The R code used for the experiments i...

Influence diagrams have been applied to diverse decision problems. In this paper, we describe their application to the speed profile optimization problem – a problem traditionally solved by the methods of optimal control theory. Influence diagrams appeared to be well-suited to these types of problems. It is mainly due to their ability to perform co...

In this work, we study the performance of di�erent structure learning algorithms in the context of inferring gene networks from transcription data. We consider representatives of di�erent structure learning approaches, some of which perform unrestricted searches, such as the PC algorithm and the Gobnilp method, and some of which introduce prior inf...

This paper provides a common framework, a generic model, for Computerized Adaptive Testing (CAT) for different model types. We present question selection methods for CAT for this generic model. We use three different types of models, Item Response Theory, Bayesian Networks, and Neural Networks, that instantiate the generic model. We illustrate the...

This paper follows previous research we have already performed in the area of Bayesian networks models for CAT. We present models using Item Response Theory (IRT - standard CAT method), Bayesian networks, and neural networks. We conducted simulated CAT tests on empirical data. Results of these tests are presented for each model separately and compa...

Computerized adaptive testing (CAT) is an interesting and promising approach to testing human abilities. In our research we use Bayesian networks to create a model of tested humans. We collected data from paper tests performed with grammar school students. In this article we first provide the summary of data used for our experiments. We propose sev...

In this paper, we generalize the noisy-or model. The generalizations are threefold. First, we allow parents to be multivalued ordinal variables. Second, parents can have both positive and negative influences on their common child. Third, we describe how the suggested generalization can be extended to multivalued child variables. The major advantage...

Influence diagrams are decision theoretic extensions of Bayesian networks. They are applied to diverse decision problems. In this paper we apply influence diagrams to the optimization of a vehicle speed profile. We present results of computational experiments in which an influence diagram was used to optimize the speed profile of a Formula 1 race c...

A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In this paper we show that, most CPTs from real applications of Bayesian networks can actually be very well approxi...

We propose an approximate probabilistic inference method based on the CP-tensor decomposition and apply it to the well known computer game of Minesweeper. In the method we view conditional probability tables of the exactly ℓ-out-of-k functions as tensors and approximate them by a sum of rank-one tensors. The number of the summands is min {l + 1,k −...

Exact inference in Bayesian networks with nodes having a large parent set is not tractable using standard techniques as are the junction tree method or the variable elimination. However, in many applications, the conditional probability tables of these nodes have certain local structure than can be exploited to make the exact inference tractable. I...

The specification of conditional probability tables (CPTs) is a difficult task in the construction of probabilistic graphical models. Several types of canonical models have been proposed to ease that difficulty. Noisy-threshold models generalize the two most popular canonical models: the noisy-or and the noisy-and. When using the standard inference...

We propose an efficient method for Bayesian network inference in models with functional dependence. We generalize the multiplicative factorization method originally designed by Takikawa and D Ambrosio(1999) FOR models WITH independence OF causal influence.Using a hidden variable, we transform a probability potential INTO a product OF two - dimensio...

To perform efficient inference in Bayesian networks by means of a Junction Tree method, the network graph needs to be triangulated. The quality of this triangulation largely determines the efficiency of the subsequent inference, but the triangulation problem is unfortunately NP-hard. It is common for existing methods to use the treewidth criterion...

The basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain uniquely determined vector, called the standard imset. In a recent paper [18], it was shown that the set S of standard imsets is the set of vertices (=extreme points) of a certain polytope P and natural geometric neig...

Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of-k functions. These tables appear naturally in real-world applications when we observe a state of a variable that d...

Whenever objects and their interaction is modelled via undirected graphs, it is often of great interest to know the cliques of the graph. For several problems the graph changes frequently over time, and we therefore seek methods for updating the information about the cliques in a dynamic fashion to avoid expensive recomputations. This dynamic probl...

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (=extreme points) of a certain polytope. Motivated by the ge...

A BN2O network is a Bayesian network having the structure of a bipartite graph with all edges directed from one part (the top level) toward the other (the bottom level) and where all conditional probability tables are noisy-or gates. In order to perform efficient inference, graphical transformations of these networks are performed. The efficiency o...

Abstract A standard graphical representative of a Bayesian network structure is a special chain graph, known as an essential graph. An alternative algebraic approach to the mathematical description of this statistical model uses instead a certain integer-valued vector, known as a standard imset. We give a direct formula for the translation of any c...

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...

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived...

We recall the basic idea of an algebraic approach to learning a Bayesian network (BN) structure, namely to represent every BN structure by a certain (uniquely determined) vector, called standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (= extreme points) of a certain polytope. Motivated by the ge...

The topic of this chapter is conditional independence models. We review mathematical objects that are used to generate conditional independence models in the area of probabilistic reasoning. More specifically, we mention undirected graphs, acyclic directed graphs, chain graphs, and an alternative algebraic approach that uses certain integer-valued...

We propose a new additive decomposition of probability tables tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a produc...

I discuss an application of a family of Bayesian network models—known as models of independence of causal influence (ICI)—to classification tasks with large numbers of attributes. An example of such a task is categorization of text documents, in which attributes are single words from the documents. The key that enabled application of the ICI models...

We propose a new additive decom- position of probability tables - tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same do- main as the original table but can be expressed as a...

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We apply tensor rank-one decomposition (Savicky and Vomlel, 2005) to conditional probability tables representing Boolean functions. We present a numerical algorithm that can be used to find a minimal tensor rank-one decomposition together with the results of the experiments performed us-ing the proposed algorithm. We will pay special attention to a...

Autonomous agents that communicate using probabilistic information and use Bayesian networks for knowledge representation need an update mechanism that goes beyond conditioning on the basis of evidence. In a related paper (M. Valtorta, Y.G. Kim, and J. Vomlel, International Journal of Approximate Reasoning ,v ol. 29, no. 1, pp. 71-106, 2002), we de...

Bayesian networks and other graphical probabilistic models became a popular framework for reasoning with uncertainty. Ecient methods have been developed for revising beliefs with new evidence.

In this paper we discuss the process of building a joint probability distribution from an input set of low-dimensional probability distributions. Since the solution of the problem for a consistent input set of probability distributions is known we concentrate on a setup where the input probability distributions are inconsistent. In this case the it...

Bayesian networks became a popular framework for reasoning with uncertainty. Efficient methods have been developed for probabilistic reasoning with new evidence. However, when new evidence is uncertain or imprecise, different methods have been proposed. The original contribution of this paper are guidelines for the treatment of different types of u...

We propose a framework for building decision strategies using Bayesian network models and discuss its application to adaptive testing. Dynamic programming and the AO* algorithm are used to find optimal adaptive tests. The proposed AO* algorithm is based on a new admissible heuristic function.

In this paper we discuss knowledge integration as a process of building a joint probability distribution from an input set of lowdimensional probability distributions starting with an initial joint probability distribution. Since the solution of the problem for a consistent input set of probability distributions is known we concentrate on a setup w...

mitelne reprezentaci nezavislost mezi velicinami pomoc acyklickych orientovanych grafu . Bayesovska st' je tvorena acyklickych orientovanym grafem G = (V, E), ke kaz- demu uzlu i V je prirazena jedna nahodna velicina X i s konecnou mnozinou X i navza- jem disjunktnch stavu a tabulka podmnene pravdepodobnosti P (X i (X j ) j#pa(i) ), kde pa(i) oznac...

 Troubleshooting is one of the areas where Bayesian networks are successfully applied [9]. In this paper we show that the generally defined troubleshooting task is NP-hard. We propose a heuristic function that exploits the conditional independence of all actions and questions given the fault of the device. It can be used as a lower bound of the exp...

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 exp...

Troubleshooting is one of the areas where Bayesian networks are successfully applied [9]. In this paper we show that the generally de ned troubleshooting task is NP-hard. We propose a heuristic function that exploits the conditional independence of all actions and questions given the fault of the device. It can be used as a lower bound of the expec...

We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation is the desire to let agents communicate with each other by exchanging beliefs, as in the Agent-Encapsulated Bayesian Network (AEBN) model, and soft evidential update (under several different names) is a...

In this paper we discuss applications of Bayesian networks to educational testing. Namely, we deal with the diagnosis of person's skills. We show that when modeling dependence between skills we can get better diagnosis faster. We present results of experiments with basic operations that use fractions. The experiments suggest that the test design ca...

The paper describes the task of performing ecient decision-theoretic troubleshooting of electro-mechanical devices. In general, this task is NP-complete, but under fairly strict assumptions, a greedy approach will yield an optimal sequence of actions, as discussed in the paper. This set of assumptions is weaker than the set proposed by Heckerman et...

The goal of decision-theoretic troubleshooting is to find a sequence of actions that minimizes the expected cost of repair of a device. If the device is complex then it is convenient to create several Bayesian Networks, each designed to solve a particular problem. At the beginning of a troubleshooting process, it is often necessary to help the user...

The goal of decision-theoretic troubleshooting is to find a sequence of actions that minimizes the expected cost of repair of a device. If the device is complex then it is convenient to create several Bayesian Networks, each designed to solve a particular problem. At the beginning of a troubleshooting process, it is often necessary to help the user...

this paper all random variables are supposed to be nite random variables (possiblymultidimensional).For V = f1; 2; : : : ; sg, P (X 1 ; : : : ; X s ) (abbreviated P V ) will denote s-dimensional probabilitydistribution of a s-dimensional random variablefX i g i2V:7! i2V X i :Thus for every x = (x 1 ; : : : x s ) 2 i2V X iP (x) = P (X 1 = x 1 ; : :...

In probabilistic models of knowledge based systems, the knowledge base is usually represented by a multidimensional probability distribution (Hájek et. al., 1992). Analogously, oligodimensional distributions (i.e. distributions of dimensionality cca1-5) can be considered partial knowledge. Within this framework the knowledge integration process cor...

The basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain (uniquely determined) vector, called the standard imset. In a recent paper [11], we have shown that the set S of standard imsets is the set of vertices (= extreme points) of a certain polytope P and introduced natural...

The game of Mastermind is a nice example of an adaptive test. We propose a modification of this game - a probabilistic Mastermind. In the probabilis- tic Mastermind the code-breaker is uncertain about the correctness of code-maker responses. This mod- ification better corresponds to a real world setup for the adaptive testing. We will use the game...

Anotace Předmětem práce je standardizace výsledkového ukazatele "Nemocniční mortalita při akutním infarktu myokardu" s využitím zjištěných závislostí mezi dílčími rizikovými faktory pacienta a úmrtím pacienta. Klíčová slova Standardizace rizika, hodnocení nemocniční péče, logistická regrese, strojové učení, dolování z dat.

In learning Bayesian networks one meets the problem of non-unique graphical description of the respective statistical model. One way to avoid this problem is to use special chain graphs, named essential graphs. An alternative algebraic approach uses certain integer-valued vectors, named standard imsets, instead. In this paper we present algorithms...