Miroslav Kárný

Tracking of Slowly Varying Parameters by Directional Forgetting

Abstract The problem of real-time identification of a stochastic (possibly controlled) system with unknown slowly varying parameters is considered. A new technique for parameter tracking is proposed. The basic idea consists in an application of the exponential forgetting only to the marginal (data-conditioned) probability density function on the smallest subspace of parameter space influenced by the current data. Thus, only that piece of information which is substituted by a new one can be for gotten. This idea is applied to the linear normal multivariate regression model and elaborated into algorithmic details. Superiority of the new algorithm, which can be viewed as an improvement of exponentially for gotten least squares, is demonstrated by two simple examples.

Towards fully probabilistic control design

Abstract Control design for stochastic systems is traditionally based on the optimization of the expected value of a suitably chosen loss function. This well elaborated and understood task is practically restricted by the computational complexity of the related dynamic programming equations or its equivalents. For this reason, it is worthwhile to search for an alternative formulation which would lead to a more tractable design. Here, such an alternative is presented which leads to a simpler form of design equations. A way is open to a systematic approximation of the optimizing control design. The controller is designed in such a way that Kullback-Leibler distance between probabilistic description of the closed loop and the required description is minimized. It leads to explicit form of a randomized optimal controller which depends on a solution of a functional equation with a simpler structure than general dynamic programming equations. The basic paradigm is proposed and the resulting algorithm is discussed. For illustration purposes, it is applied to linear Gaussian systems. The desirable result is obtained: the optimal controller is determined by a discrete time Riccati equation. Less trivial applications will be treated elsewhere.

Adaptive cross-direction control of paper basis weight

Abstract The initial setting and maintaining of the desired paper basis weight (in machine direction and cross direction) is to be ensured adaptively for several given paper grades. Technical equipment includes: usual traversing gauge at the output of the paper machine, special traversing robot for shaping the headbox lip (sequential setting of screws), control computer. Adaptive multivariate LQG control with recursive identification generalized to distributed parameter system has been designed with the following features: integral (convolution type) model of the process respecting the continuous nature of all signals and kernels involved (by means of spline approximation), repetitive control synthesis (via Riccati equation with periodical solutions).

Fully probabilistic control design

Abstract Stochastic control design chooses the controller that makes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design describes both the closed loop and its desired behavior in probabilistic terms and uses Kullback–Leibler divergence as their proximity measure. This approach: (i) unifies stochastic control design methodology; (ii) provides explicit minimizer. The paper completes the previous solutions of various particular cases by formulating and solving the fully probabilistic control design in the general, discrete-time, state-space setting.

Computer Intensive Methods in Control and Signal Processing

Fighting dimensionality with linguistic geometry, Boris Stilman Statistical physics and the optimization of autonomous behaviour in complex virtual worlds, Robert W. Penney On merging gradient estimation with mean-tracking techniques for cluster identification, Paul D. Fox et al Computational aspects of graph theoretic methods in control, Katalin M. Hangos, Zsolt Tuza Efficient algorithms for predictive control of systems with bounded inputs, Luigi Chisci et al Applying new numerical algorithms to the solution of discrete-time optimal control problems, Rudiger Franke, Eckhard Arnold System identification using composition networks, Yves Moreau, Joos Vandewalle Recursive nonlinear estimation of non-linear/non-Gaussian dynamic models, Rudolf Kulhavy Monte Carlo approach to Bayesian regression modelling, Jan Smid et al Identification of reality in Bayesian context, Ludek Berec, Miroslav Karny Nonlinear nonnormal dynamic models - state estimation and software, Miroslav Simandl, Miroslav Flidr The EM algorithm - a guided tour, Christophe Couvreur estimation of quasipolynomilas in noise - theoretical algorithmic and implementation aspects, Vytautas Slivinskas, Virginija Simonyte Iterative reconstruction of transmission sinograms with low signal to noise ratio, Johan Nuyts et al Curse of dimensionality - classifying large multi-dimensional images with neural networks, Rudolf Hanka, Thomas P. Harte Dimension-independent rates of approximation by neural networks, Vera Kurkova estimation of human signal detection performance from event-related potentials using feed-forward neural network model, Milos Koska et al Utilizing geometric anomalies of high dimension - when complexity makes computation easier, Paul C. Kainen Approximation using cubic B-splines with improved training speed and accuracy, Julian D. Mason et al.

Axiomatisation of fully probabilistic design

This text provides background of fully probabilistic design (FPD) of decision-making strategies and shows that it is a proper extension of the standard Bayesian decision making. FPD essentially minimises Kullback-Leibler divergence of closed-loop model on its ideal counterpart. The inspection of the background is important as the current motivation for FPD is mostly heuristic one, while the technical development of FPD confirms its far reaching possibilities. FPD unifies and simplifies subtasks and elements of decision making under uncertainty. For instance, (i) both system model and decision preferences are expressed in common probabilistic language; (ii) optimisation is simplified due to existence of explicit minimiser in stochastic dynamic programming; (iii) DM methodology for single and multiple aims is unified; (iv) a way is open to completion and sharing non-probabilistic and probabilistic knowledge and preferences met in knowledge and preference elicitation as well as unsupervised cooperation of decision makers.

Experimental comparison of data transformation procedures for analysis of principal components

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedmans test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

The Reality and Meaning of Physiological Factors

The term “physiological factor” was introduced by Bazin et al. (1979) for a time-activity curve detected above the separate compartment of a radio-pharmaceutical in the body. Considering formally the elementary time-activity curves recorded in dynamic radionuclide study as vectors then the physiological factors can be regarded as a non-orthogonal base of the corresponding vector space. Under certain restrictive conditions this base can be found by the methods of factor analysis.

Approximate Bayesian recursive estimation

Bayesian learning provides a firm theoretical basis of the design and exploitation of algorithms in data-streams processing (preprocessing, change detection, hypothesis testing, clustering, etc.). Primarily, it relies on a recursive parameter estimation of a firmly bounded complexity. As a rule, it has to approximate the exact posterior probability density (pd), which comprises unreduced information about the estimated parameter. In the recursive treatment of the data stream, the latest approximate pd is usually updated using the treated parametric model and the newest data and then approximated. The fact that approximation errors may accumulate over time course is mostly neglected in the estimator design and, at most, checked ex post. The paper inspects the estimator design with respect to the error accumulation and concludes that a sort of forgetting (pd flattening) is an indispensable part of a reliable approximate recursive estimation. The conclusion results from a Bayesian problem formulation complemented by the minimum Kullback-Leibler divergence principle. Claims of the paper are supported by a straightforward analysis, by elaboration of the proposed estimator to widely applicable parametric models and illustrated numerically.

Enhancement of physiological factors in factor analysis of dynamic studies

Factor analysis of dynamic radionuclide studies provides their decomposition into the images and time-activity curves corresponding to the underlying dynamic structures. The method is based on the analysis of study variance and on the subsequent differential imaging of its principal components into a simplified factor space. By changing the amount and the composition of the variance processed in the analysis it is possible to enhance the factors that are important for diagnosis while the less important factors can be suppressed. In our report, a short theoretical review of the problem is given and illustrated by the analysis of dynamic cholescintigraphy. It is shown that a suitable choice of region and/or the temporal interval of interest anables the differential evaluation of such intrahepatic compartments, which could not be observed without enhancement.