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Multi-dimensional trading problem in multi-participant settings
Zeman, Jan
The dimensionality of optimization problem arising within multi-market trading task grows exponentially with a growing number of markets. To prevent the dimensionality problem, multi-market trading is represented as a multi-participant decision making problem with finite common capital. Each local DM task is a single-market trading enriched by an ability to share a part of local capital with other local DM tasks (participants). The paper provides formulation of the problem and basic algorithmic steps. The approach is illustrated on the real market data.
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Sharing of knowledge and preferences among imperfect Bayesian decision makers
Kárný, Miroslav ; Guy, Tatiana Valentine
Bayesian decision theory provides a strong theoretical basis for a single-participant decision making under uncertainty, that can be extended to multi-participant problems. However Bayesian decision theory assumes unlimited abilities of a participant to probabilistically model participant´s environment and to optimise decision-making strategy. The paper proposes a methodology for sharing of knowledge and strategies among participants, that helps to overcome the non-realistic assumption on participant´s unlimited abilities.
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Bayesian vector auto-regression model with Laplace errors applied to financial market data
Šindelář, Jan
The article presents alternative version of Bayesian vector auto-regression model with Laplace distributed innovations. Bayesian estimation in such model is more computationally demanding than estimation in a model with normally distributed innovations, but because of the heavier tails of Laplace distribution, it is more robust. In the article I try to present the way of proceeding with the estimation, obtaining a full posterior distribution of the parameters as a result. At the end an efficient algorithm is sketched, but this part of the research is still unfinished.
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Komprese dvousměrných texturních dat založaná na víceůrovňové vektorové kvantizaci - doplňkový materiál
Havran, V. ; Filip, Jiří ; Myszkowski, K.
The Bidirectional Texture Function (BTF) is becoming widely used for accurate representation of real-world material appearance. In this paper a novel BTF compression model is proposed. The model resamples input BTF data into a parametrization, allowing decomposition of individual view and illumination dependent texels into a set of multidimensional conditional probability density functions. These functions are compressed in turn using a novel multi-level vector quantization algorithm. The result of this algorithm is a set of index and scale code-books for individual dimensions. BTF reconstruction from the model is then based on fast chained indexing into the nested stored code-books. In the proposed model, luminance and chromaticity are treated separately to achieve further compression. The proposed model achieves low distortion and compression ratios 1:233-1:2040, depending on BTF sample variability.
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Iterativní formulace cílů řízení v plně pravděpodobnostním návrhu
Jirsa, Ladislav ; Kárný, Miroslav ; Tesař, Ludvík
A control design converts knowledge about the controlled system, constraints and control aims into the controller. Control aims must be quantified in the way compatible to the design. A systematic quantification of the control aims, called aim elicitation, is the least supported step of the design process. We present a solution of this problem within the framework of a fully probabilistic design (FPD) [1]. Any controller modifies the closed-loop behaviour to reach the control aims. The controller is chosen in order to minimize a given loss function. The FPD selects the controller that minimizes the Kullback- Leibler divergence of the joint probability density function (pdf) describing closed-loop behaviour to the ideal pdf. The ideal pdf expresses both the desired closed-loop behaviour and constraints on system inputs. Thus within the FPD, the aim elicitation reduces to the choice of the ideal pdf. For complex multidimensional systems, the task to construct the ideal pdf may represent a nontrivial problem requiring an expert experienced both in practical treatment of the system and theory as well.
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