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Scalar-Valued Score Functions and their use in Parametric Estimation
Fabián, Zdeněk
2022 - English
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
Keywords:
core random variable; score mean; score variance; score distance; score correlation
Available on request at various institutes of the ASCR
Scalar-Valued Score Functions and their use in Parametric Estimation
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic ...
A New Look to Information and Uncertainty of Continuous Distributions
Fabián, Zdeněk
2022 - English
We define information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the differential entropy.
Keywords:
Differential entropy; information function; uncertainty function; mean information of distribution
Available at various institutes of the ASCR
A New Look to Information and Uncertainty of Continuous Distributions
We define information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their ...
Large Perimeter Objects Surrounded by a 1.5D Terrain
Keikha, Vahideh
2022 - English
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k > 0, we design an FPTAS that efficiently approximates such polygons within a factor (1 − ǫ). For the special case of the´largest-perimeter contained triangle in T , we design an O(n log n) time exact algorithm that matches the same result for the area measure.
Available in digital repository of the ASCR
Large Perimeter Objects Surrounded by a 1.5D Terrain
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k ...
DC 5.3 Fundamental large scale statistical model
Brabec, Marek; Malý, Marek; Malá, I.; Hladká, Adéla
2021 - Czech
This document describes suite of fundamental large-scale statistical models developed from data provided by CHMI (Czech Hydrometeorological Institute). The models were constructed in several variants, differing in complexity, detail and computational demands. Spatial models will be, after some further developments and modifications (necessary not only from the natural model evolution but also due to systematic changes brought e.g. by covid outbreak influences) used as the main input for optimization algorithms constructed for selection of measurement stations on the principles of statistical design theory and methods. BIBLIOGRAFICKÉ ÚDAJE: Výzkumná zpráva č. SS02030031-V94, evidenční č. ENV/2021/118018. Praha: ICS CAS, 2021. 47 s. ANOTACE: Obsahem tohoto dokumentu je popis prostorového statistického modelu velkého měřítka vyvinutého z dosavadních dat poskytnutých ČHMÚ. Prostorový model bude (po nezbytných aktualizacích a případných modifikacích daných jak časovým vývojem samotného znečištění, který lze očekávat např. v souvislosti s dopady pandemie covid-19, tak dalším vývojem statistické metodologie) v dalších letech používán jako podklad pro vývoj algoritmu prostorové optimalizace umístění měřicích stanic na základě statistického designu. Jde o několik variantních řešení, která zohledňují různé aspekty statistického chování pole koncentrací vybraných znečišťujících látek.
Keywords:
spatial field of pollutant concentration; geostatistics; GAM; INLA; spatially varying covariance model; Bayesian modeling
Available in digital repository of the ASCR
DC 5.3 Fundamental large scale statistical model
This document describes suite of fundamental large-scale statistical models developed from data provided by CHMI (Czech Hydrometeorological Institute). The models were constructed in several variants, ...
City simulation software for modeling, planning, and strategic assessment of territorial city units
Svítek, M.; Přibyl, O.; Vorel, J.; Garlík, B.; Resler, Jaroslav; Kozhevnikov, S.; Krč, Pavel; Geletič, Jan; Daniel, Milan; Dostál, R.; Janča, T.; Myška, V.; Aralkina, O.; Pereira, A. M.
2021 - English
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software for modeling, planning, and strategic assessment of territorial city units. 1.1. Prague: CTU & ICS CAS, 2021. Technical Report. ABSTRACT: The Smart Resilience City concept is a new vision of a city as a digital platform and eco-system of smart services where agents of people, things, documents, robots, and other entities can directly negotiate with each other on resource demand principals providing the best possible solution. It creates the smart environment making possible self-organization in sustainable or, when needed, resilient way of individuals, groups and the whole system objectives.
Keywords:
Smart city; City simulation; Energy resource-demand modelling; Environmental modelling; Synthetic population; Transport modelling
Available on request at various institutes of the ASCR
City simulation software for modeling, planning, and strategic assessment of territorial city units
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software ...
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix
Turčičová, Marie; Mandel, J.; Eben, Kryštof
2021 - English
We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of covariance) and estimate its parameters together with the analysis mean by the Score Matching method. This procedure provides an explicit expression for parameter estimators. The resulting analysis step formula is the same as in the traditional ensemble Kalman filter.
Keywords:
Score matching; ensemble filter; Gaussian Markov random field; covariance modelling
Available at various institutes of the ASCR
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix
We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of ...
Assessment of Independent EEG Components Obtained by Different Methods for BCI Based on Motor Imagery
Húsek, Dušan; Frolov, A. A.; Kerechanin, J. V.; Bobrov, P.D.
2021 - English
Eight methods of decomposition of a multichannel EEG signal are compared in terms of their ability to identify the most physiologically significant components. The criterion for the meaningfulness of a method is its ability to reduce mutual information between components; to create components that can be attributed to the activity of dipoles located in the cerebral cortex; find components that are provided by other methods and for this case; and at the same time, these components should most contribute to the accuracy of the BCI based on imaginary movement. Independent component analysis methods AMICA, RUNICA and FASTICA outperform others in the first three criteria and are second only to the Common Spatial Patterns method in the fourth criterion. The components created by all methods for 386 experimental sessions of 27 subjects were combined into more than 100 clusters containing more than 10 elements. Additionally, the components of the 12 largest clusters were analyzed. They have proven to be of great importance in controlling BCI, their origins can be modeled using dipoles in the brain, and they have been detected by several degradation methods. Five of the 12 selected components have been identified and described in our previous articles. Even if the physiological and functional origins of the rest of identified components’ are to be the subject of further research, we have shown that their physiological nature is at least highly probable.\n
Keywords:
brain–computer interface; motor imagery; blind source separation; independent component analysis; common spatial patterns; cluster analysis; EEG pattern extraction; EEG analysis; ICA; CSP; BCI; motor imagery
Available at various institutes of the ASCR
Assessment of Independent EEG Components Obtained by Different Methods for BCI Based on Motor Imagery
Eight methods of decomposition of a multichannel EEG signal are compared in terms of their ability to identify the most physiologically significant components. The criterion for the meaningfulness of ...
Nearly All Reals Can Be Sorted with Linear Time Complexity
Jiřina, Marcel
2021 - English
We propose a variant of the counting sort modified for sorting reals in a linear time. It is assumed that the sorting key and pointers to the items being sorted are moved and individual items remain at the same place in the memory (in place sorting). In this case, the space complexity of the new variant of the algorithm is the same as the complexity of the quicksort. We also quantify the practical limits for possible sorting reals in a linear time. This possibility is assured under additional assumptions on the distribution of the sorting key, mainly the independence and identity of the distribution. Here we give a more general criteria easily applicable in practice. We also show that the algorithm is applicable for data that do not fulfill criteria for linear time complexity but even that the computation is faster than the system quicksort. A new, faster version of the algorithm is attached.
Keywords:
sorting; algorithm; real sorting key; time complexity; linear complexity
Available in digital repository of the ASCR
Nearly All Reals Can Be Sorted with Linear Time Complexity
We propose a variant of the counting sort modified for sorting reals in a linear time. It is assumed that the sorting key and pointers to the items being sorted are moved and individual items remain ...
Visual Images Segmentation based on Uniform Textures Extraction
Goltsev, A.; Gritsenko, V.; Húsek, Dušan
2020 - English
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. The main advantages of the proposed procedure are as follows. It is completely unsupervised, that is, it processes the input image without any prior knowledge of either the type of textures or the number of texture segments in the image. In addition, the procedure segments arbitrary images of all types. This means that no changes to the procedure parameters are required to switch from one image type to another. Another major advantage of the procedure is that in most cases it extracts the uniform ne-grained texture segments present in the image, just as humans do. This result is supported by series of experiments that demonstrate the ability of the procedure to delineate uniform ne-grained texture segments over a wide range of images. At a minimum, image processing according to the proposed technique leads to a signficant reduction in the uncertainty of the internal structure of the analyzed image.
Keywords:
Texture feature; Texture window; Homogeneous ne-grained texture segment; Texture segment extraction; Texture segmentation
Available at various institutes of the ASCR
Visual Images Segmentation based on Uniform Textures Extraction
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. ...
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Vlček, Jan; Lukšan, Ladislav
2020 - English
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
Keywords:
unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; global convergence; numerical results
Available in a digital repository NRGL
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey ...
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