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2018-10-02
14:38
Multi-Objective Optimization Problems with Random Elements - Survey of Approaches
Kaňková, Vlasta
Many economic and financial situations depend simultaneously on a random element and a decision parameter. Mostly, it is possible to influence the above mentioned situation only by an optimization model depending on a probability measure. This optimization problem can be static (one-stage), dynamic with finite or infinite horizon, single-objective or multi-objective. We focus on one-stage multi-objective problems corresponding to applications those are suitable to evaluate simultaneously by a few objectives. The aim of the contribution is to give a survey of different approaches (as they are known from the literature) of the above mentioned applications. To this end we start with well-known mean-risk model and continue with other known approaches. Moreover, we try to complete every model by a suitable application. Except an analysis of a choice of the objective functions type we try to discuss suitable constraints set with respect to the problem base, possible investigation and relaxation. At the end we mention properties of the problem in the case when the theoretical "underlying" probability measure is replaced by its "deterministic" or "stochastic" estimate.

Úplný záznam
2018-10-02
14:38
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains
Sladký, Karel
In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.

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2018-10-02
14:38
Problem of competing risks with covariates: Application to an unemployment study
Volf, Petr
The study deals with the methods of statistical analysis in the situation of competing risks in the presence of regression. First, the problem of identification of marginal and joint distributions of competing random variables is recalled. The main objective is then to demonstrate that the parameters and, in particular, the correlation of competing variables, may depend on covariates. The approach is applied to solution of a real example with unemployment data. The model uses the Gauss copula and Cox’s regression model.

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2018-10-02
14:38
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

Úplný záznam
2018-10-02
14:38
Two Algorithms for Risk-averse Reformulation of Multi-stage Stochastic Programming Problems
Šmíd, Martin ; Kozmík, Václav
Many real-life applications lead to risk-averse multi-stage stochastic problems, therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, Coin-OR, APML or, for smaller problems, Excel), it is, however, mostly up to researcher to reformulate the problem into its deterministic equivalent. Moreover, such solutions are usually one-time, not easy to modify for different applications. We overcome these problems by providing a front-end software package, written in C++, which enables to enter problem definitions in a way close to their mathematical definition. Creating of a deterministic equivalent (and its solution) is up to the computer. In particular, our code is able to solve linear multi-stage with Multi-period Mean-CVaR or Nested Mean-CVaR criteria. In the present paper, we describe the algorithms, transforming these problems into their deterministic equivalents.

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2018-07-30
11:02
On attempts to characterize facet-defining inequalities of the cone of exact games
Studený, Milan ; Kroupa, Tomáš ; Kratochvíl, Václav
The sets of balanced, totally balanced, exact and supermodular games play an important role in cooperative game theory. These sets of games are known to be polyhedral cones. The (unique) non-redundant description of these cones by means of the so-called facet-defining inequalities is known in cases of balanced games and supermodular games, respectively. The facet description of the cones of exact games and totally balanced games are not known and we present conjectures about what are the facet-defining inequalities for these cones. We introduce the concept of an irreducible min-balanced set system and conjecture that the facet-defining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facet-defining inequalities for this cone are those which correspond to irreducible min-balanced systems on strict subsets of the set of players and their conjugate inequalities. A consequence of the validity of the conjectures would be a novel result saying that a game m is exact if and only if m and its reflection are totally balanced.

Úplný záznam
2018-07-30
11:02
Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter
Jiroušek, R. ; Kratochvíl, Václav
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the Dempster-Shafer theory of evidence. Up to now, there was no direct way to get the expected value of a utility function in D-S theory. If eeded, one had to find a probability mass function corresponding to the considered belief function, and then - using this probability mass function - to compute the classical probabilistic expectation. In this paper, we take four different approaches to defining probabilistic representatives of a belief function and compare which one yields to the best approximations of Shenoy’s expected values of various utility functions. The achieved results support our conjecture that there does not exist a probabilistic representative of a belief function that would yield the same expectations as the Shenoy’s new operator.

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2018-07-30
11:02
About Two Consonant Conflicts of Belief Functions
Daniel, M. ; Kratochvíl, Václav
General belief functions usually bear some internal conflict which comes mainly from disjoint focal elements. Analogously, there is often some conflict between two (or more) belief functions. After the recent observation of hidden conflicts (seminar CJS’17 [17]), appearing at belief functions with disjoint focal elements, importance of interest in conflict of belief functions has increased. This theoretical contribution introduces a new approach to conflicts (of belief functions). Conflicts are considered independently of any combination rule and of any distance measure. Consonant conflicts are based on consonant approximations of belief functions in general; two special cases of the consonant approach based on consonant inverse pignistic and consonant inverse plausibility transforms are discussed. Basic properties of the newly defined conflicts are presented, analyzed and briefly compared with our original approaches to conflict (combinational conflict, plausibility conflict and comparative conflict), with the recent conflict based on non-conflicting parts, as well as with W. Liu’s degree of conflict.

Úplný záznam
2018-07-30
11:02
Proceedings of the 11th Workshop on Uncertainty Processing
Kratochvíl, Václav ; Vejnarová, Jiřina
The Workshop on Uncertainty Processing, better known under its abbreviation WUPES, celebrates its 30-year anniversary this year. In 1988, when the first Workshop took place, Czechoslovakia was still a communist country and a part of the Soviet bloc. Since then, many things have changed. For example, Czechoslovakia no longer exists as a country (because in 1993 it was peacefully split into two independent countries - Czechia and Slovakia). From this perspective, it is hard to believe that we have several participants who have attended most workshops in the the thirty-year history of WUPES. As of now, the Program Committee has accepted, based on the extended abstracts, 21 papers to be presented at the Workshop, and 19 out of them are to be published in the present Conference Proceedings. These papers cover diverse topics, such as information processing, decision making, and data analysis; but what is common to most of them is that they are related to uncertainty calculus - Bayesian Networks, Dempster-Shafer Theory, Belief Functions, Probabilistic Logic, Game Theory, etc.

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2018-06-19
19:26
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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