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Lazy Learning of Environment Model from the Past
Štěch, J. ; Guy, Tatiana Valentine ; Pálková, B. ; Kárný, Miroslav
The paper addresses a lazy learning (LL) approach to decision making (DM) problem described in fully probabilistic way. The key idea of LL is to simplify the actual DM problem by using past DM problems similar to the current one. The approach can decrease computation complexity and increase quality of learning when no rich alternative information available. The proposed LL approach helps to learn the environment model based on a proximity of the past and current DM problem with Kullback-Leibler divergence serving as a proximity measure. The implemented algorithm is verified on the real data. The results show that the proposed approach improves prediction quality.
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On Linear Probabilistic Opinion Pooling Based on Kullback-Leibler Divergence
Sečkárová, Vladimíra
In this contribution we focus on the finite collection of sources, providing their opinions about a hidden (stochastic) phenomenon, that is not directly observable. The assumption on obtaining opinions yields a decision making process commonly referred to as opinion pooling. Due to the complexity of the space of possible decisions we consider the probability distributions over this set rather than single values, exploited before, e.g., in [2]. The final decision (result of pooling) is then a combination of probability distributions provided by sources.
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Recursive Estimation of High-Order Markov Chains: Approximation by Finite Mixtures
Kárný, Miroslav
A high-order Markov chain is a universal model of stochastic relations between discrete-valued variables. The exact estimation of its transition probabilities suers from the curse of dimensionality. It requires an excessive amount of informative observations as well as an extreme memory for storing the corresponding su cient statistic. The paper bypasses this problem by considering a rich subset of Markov-chain models, namely, mixtures of low dimensional Markov chains, possibly with external variables. It uses Bayesian approximate estimation suitable for a subsequent decision making under uncertainty. The proposed recursive (sequential, one-pass) estimator updates a product of Dirichlet probability densities (pds) used as an approximate posterior pd, projects the result back to this class of pds and applies an improved data-dependent stabilised forgetting, which counteracts the dangerous accumulation of approximation errors.
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DEMO: What Lies Beneath Players' Non-Rationality in Ultimatum Game?
Avanesyan, Galina ; Kárný, Miroslav ; Knejflová, Zuzana ; Guy, Tatiana Valentine
The rational strategy suggested by the game theory predicts a human playing Ultimatum Game (UG) would have tendency to decide in accordance with the assumption of self-interested rationality, i.e. to choose more for oneself and offer the least amount possible for co-players [2]. This “utilitarian” and gametheoretically correct “rational” behaviour is however rarely observed when experiments are conducted with human beings [1]. Long-term research in experimental economics indicates that humans do not behave as selfish as traditional economics assume them to do. In UG, human-responders reject offers they find too low while human-proposers often offer more than the smallest amount. An intuitively plausible interpretation of this phenomenon is that responders would rather give up some profit than be treated unfairly. This “non-rational” behaviour provides an insight into human’s motivation as a social being. The work challenges this view and insists on human rationality.
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On Approximate Fully Probabilistic Design of Decision-Making Units
Kárný, Miroslav
An efficient support of a single decision maker is vital in constructing scalable systems addressing complex decision-making (DM) tasks. Fully probabilistic design (FPD) of DM strategies, an extension of dynamic Bayesian DM, provides a firm basis for such a support. The limited cognitive and evaluation resources of the supported decision maker cause that theoretically optimal solutions are realised only approximately. Thus, the truly efficient support has to include reliable means for constructing approximate solutions of DM subtasks. The current paper deals with the design of the approximately optimal DM strategy for a known environment model and adequately described DM preferences. The design relies on: a) the explicit minimiser found within FPD; b) randomised nature of the strategy provided by FPD.
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A unified view on roots of imperfection
Kárný, Miroslav
Decision making (DM), broadly interpreted as an active choice among alternatives, is ubiquitous. A range of normative theories has arisen aiming at support and analysis of DM. Classical Savage's axiomatisation led to Bayesian DM, which suits DM with a non-negligible uncertainty. Observed discrepancies between recommendations of the normative theory and DM practice represent the major challenge of the related research. The talk discusses these discrepancies, and: a) respects the presence of imperfect decision maker; b) considers neglecting of importance of closed-loop behaviour as their major cause; c) provides tasks where a) and b) do matter and where a unified view on imperfection roots can help.
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Estimating Efficiency Offset between Two Groups of Decision-Making Units
Macek, Karel
The comparison of two groups of decision-making units (DMUs) has been already subject of scientific reflection. So far, some statistical tests have been developed. This article addresses estimating the difference between expected outputs of two groups of DMUs. In contrast to other efficiency evaluation methods, this publication focuses on quantitative assessment of this difference, not on the hypothesis testing. The article focuses on single output DMUs and the designed statistical tests are examined on various simulated data sets as well as on one realworld example. Some of them stem from the data envelopment analysis, others are related to the local regression.
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A note on weighted combination methods for probability estimation
Sečkárová, Vladimíra
To successfully learn from the information provided by avail- able information sources, the choice of automatic method combining them into one aggregate result plays an important role. To respect the reliability in the source’s performance each of them is assigned a weight, often subjectively influenced. To overcome this issue, we briefly describe the method based on Bayesian decision theory and elements of infor- mation theory. In particular we consider discrete-type information, rep- resented by probability mass functions (pmfs) and obtain an aggregate result, which has also form of pmf. This result of decision making pro- cess is found to be a weighted linear combination of available information. Besides the brief description of the novel method, the paper focuses on its comparison with other combination methods. Since we consider the available information and unknown aggregate as pmfs, we mainly focus on the case when the parameter of binomial distribution is of interest and the sources provide appropriate pmfs.
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Scalable Decision Making: Uncertainty, Imperfection, Deliberation, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD 2013)
Guy, Tatiana Valentine ; Kárný, Miroslav
Machine learning (ML) and knowledge discovery both use and serve to decision making (DM), which has to cope with uncertainty, incomplete knowledge, problem and data complexity and imperfection (limited cognitive and evaluating capabilities) of the involved heterogeneous multiple participants (aka agents, decision makers, components, controllers, classifiers, etc.). Contemporary DM deals with complex systems characterised by heterogeneous components and their goal-motivated dynamic interactions. The individual participants are selfish, i.e. follow their individual goals. There is no well-justified way to influence or describe the resulting collective behaviour of such a system via a well-proved combination of the selfish components. Economic and natural sciences describe concepts governing the functioning of systems of selfish participants as well as ways influencing their behaviour. However, the majority of solutions rely on the human moderator/manager controlling such a system.
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