Miroslav Karny

The Czech Academy of Sciences | AVCR · Department of Adaptive Systems

The problem of a joint quantification of prior knowledge and structure estimation is solved within the dynamic exponential family of models. The result is elaborated for normal controlled autoregressive models and illustrated on a simulated example. The problem arose as a substantial ingredient of the automatic commission of adaptive controllers, d...

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...

Bayesian decision theory provides a strong theoretical basis for a single-participant decision making under uncertainty, that can be extended to multiple-participant decision making. However, this theory (similarly as others) assumes unlimited abilities of a participant to probabilistically model the participant’s environment and to optimise its de...

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 des...

Ranking of alternatives is a common, difficult and repeatedly addressed problem, especially when it requires negotiation of experts. The celebrated Arrow's impossibility theorem expresses formally its difficulty. In spite of the progress made by adopting soft ranking, the problem is far from being generically solved. The paper provides a, probably...

Axiomatic fully probabilistic design (FPD) of optimal decision rules strictly extends the decision making (DM) theory represented by Markov decision processes (MDP). This means that any MDP task can be approximated by an explicitly found FPD task whereas many FPD tasks have no MDP equivalent. MDP and FPD model the closed loop — the coupling of an a...

Classical decision theory strongly conflicts with observed data from cognitive and descriptive decision-making (DM) research, leading to various paradoxes and inconsistencies. While previous studies have shown the usefulness of quantum models in DM, to the best of the authors’ knowledge none have addressed why these models effectively describe huma...

The poster addresses the problem of the implicit cooperation in multi-agent environment formulated and solved as a decision-making (DM) task. Methodologically agents are modelled as dynamic self-interested independent Bayesian agents that use fully probabilistic design (FPD) [3] to find the optimal DM strategy. The agents cooperate via sharing thei...

Any prescriptive theory of decision-making (DM) has to cope with the common DM agents’ inability to fully specify their preferences dependent on several attributes. The paper provides the needed preference completion and quantification for fully probabilistic design (FPD) of DM strategies. FPD (covering the usual Bayesian DM) probabilistically mode...

This paper deals with user's preferences (wishes). Common users are uneducated in the decision-making (DM) theory and present their preferences incompletely. That is why we elicit them from such a user during the DM. The paper works with the DM theory called fully probabilistic design (FPD). FPD models closed DM loop, made by the user and the syste...

The axiomatic fully probabilistic design (FDP) of decision strategies strictly extends Bayesian decision making (DM) theory. FPD also models the closed decision loop by a joint probability density (pd) of all inspected random variables, referred as behaviour. FPD expresses DM aims via an ideal pd of behaviours, unlike the usual DM. Its optimal stra...

In several hours of a calm meteorological situation, a relatively significant level of radioactivity may accumulate around the source. When the calm situation expires, a wind-induced convective movement of the air immediately begins. Random realisations of the input atmospheric dispersion model parameters for this CALM scenario are generated using...

Accidental discharges of radioactive aerosol into the motionless (calm) atmosphere are examined with aim to quantify ensuing radiological impact on population. This paper offers an advanced methodology that facilitates and accelerates the demanding modelling process in the calm region. The modelling simulates continuous, quite volatile, radioactive...

Bayesian decision making (DM) quantifies information by the probability density (pd) of treated variables. Gradual accumulation of information during acting increases the DM quality reachable by an agent exploiting it. The inspected accumulation way uses a parametric model forecasting observable DM outcomes and updates the posterior pd of its unkno...

A generic decision-making (DM) agent specifies its preferences partially. The studied prescriptiveDMtheory, called f ully probabilistic design (FPD) of decision strategies, has recently addressed this obstacle in a new way. The found preference completion and quantification exploits that: IFPD models the closed DM loop and the agent’s preferences b...

A decision-making (DM) agent models its environment and quantifies its DM preferences. An adaptive agent models them locally nearby the realisation of the behaviour of the closed DM loop. Due to this, a simple tool set often suffices for solving complex dynamic DM tasks. The inspected Bayesian agent relies on a unified learning and optimisation fra...

During several hours of the calm meteorological situation, a relatively significant level of radioactivity can be accumulated around the source. At the second stage, the calm situation is assumed to terminate and convective movement of the air induced by wind immediately starts. Random realisations of the input atmospheric dispersion model paramete...

The paper proposes the way how to assign a proper prior probability to a new, generally compound, hypothesis. To this purpose, it uses the minimum relative-entropy principle and a forecaster-based knowledge transfer. Methodologically, it opens a way towards enriching the standard Bayesian framework by the possibility to extend the set of models dur...

Any knowledge extraction relies (possibly implicitly) on a hypothesis about the modelled‐data dependence. The extracted knowledge ultimately serves to a decision‐making (DM). DM always faces uncertainty and this makes probabilistic modelling adequate. The inspected black‐box modeling deals with “universal” approximators of the relevant probabilisti...

Approximation, extension, and merging of probability distributions support inductive reasoning. They serve to modeling, knowledge, and preference elicitation as well as to a soft cooperation within various decision-making (DM) scenarios. The theory dubbed as the fully probabilistic design of DM strategies unifies the design of these operations on d...

Fully probabilistic design (FPD) of control strategies models both the closed control loop and control objectives by joint probabilities of involved variables. It selects the optimal strategy as the minimiser of Kullback–Leibler (KL) divergence of the closed-loop model to its ideal counterpart expressing the control objectives. Since its proposal (...

Abstract—Stochastic filtering estimates a timevarying (multivariate) parameter (a hidden variable) from noisy observations. It needs both observation and parameter evolution models. The latter is often missing or makes the estimation too complex. Then, the axiomatic minimum relative entropy (MRE) principle completes the posterior probability densit...

The paper proposes the preference-elicitation support within the framework of fully proba-bilistic design (FPD) of decision strategies. Agent employing FPD uses probability densities to model the closed-loop behaviour, i.e. a collection of all observed, opted and considered random variables. Opted actions are generated by a randomised strategy. The...

The fully probabilistic design (FPD) of decision strategies models the closed decision loop as well as decision aims and constraints by joint probabilities of involved variables. FPD takes the minimiser of cross entropy (CE) of the closed-loop model to its ideal counterpart, expressing the decision aims and constraints, as the optimal strategy. FPD...

The paper presents the stopping rule for random search for Bayesian model-structure estima-tion by maximising the likelihood function. The inspected maximisation uses random restartsto cope with local maxima in discrete space. The stopping rule, suitable for any maximisationof this type, exploits the probability of finding global maximum implied by...

The paper focuses on prescriptive affective decision making in Ultimatum Game (UG). It describes preliminary results on incorporating emotional aspects into normative decision making. One of the players (responder) is modelled via Markov decision process. The responder’s reward function is the weighted combination of two components: economic and em...

Modern prescriptive decision theories try to support the dynamic decision making (DM) in incompletely-known, stochastic, and complex environments. Distributed solutions single out as the only universal and scalable way to cope with DM complexity and with limited DM resources. They require a solid cooperation scheme, which harmonises disparate aims...

Adaptive decision making learns an environment model serving a design of a decision policy. The policygenerated actions influence both the acquired reward and the future knowledge. The optimal policy properly balances exploitation with exploration. The inherent dimensionality curse of decision making under incomplete knowledge prevents the realisat...

Cooperation and negotiation are important elements of human interaction within extensive, flatly organized, mixed human-machine societies. Any sophisticated artificial intelligence cannot be complete without them. Multi-agent system with dynamic locally independent agents, that interact in a distributed way is inevitable in majority of modern appli...

This paper exploits knowledge made available by an external source in the form of a predictive distribution in order to elicit a parameter prior. It uses the terminology of Bayesian transfer learning, one of many domains dealing with reasoning as coherent knowledge processing. An empirical solution of the addressed problem was provided in [19], bas...

The article studies deliberation aspects by modelling a responder in multi-proposers ultimatum game (UG). Compared to the classical UG, deliberative multi-proposers UG suggests that at each round the responder selects the proposer to play with. Any change of the proposer (compared to the previous round) is penalised. The simulation results show tha...

Ultimate Game serves for extensive studies of various aspects of human decision making. The current paper contribute to them by designing proposer optimising its policy using Markov-decision-process (MDP) framework combined with recursive Bayesian learning of responder’s model. Its foreseen use: (i) standardises experimental conditions for studying...

The minimum cross-entropy principle is an established technique for design of an unknown distribution, processing linear functional constraints on the distribution. More generally, fully probabilistic design (FPD) chooses the distribution—within the knowledge-constrained set of possible distributions— for which the Kullback-Leibler divergence to th...

The traditional use of global and centralised control methods fails for large, complex, noisy and highly connected systems, which typify many real-world industrial and commercial systems. This paper provides an efficient bottom-up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal....

The need for inspecting (ir)rationality in decision making (DM)-the observed discrepancy between real and prescriptive DMs-stems from omnipresence of DM in individuals' and society life. Active approaches try to diminish this discrepancy either by changing behaviour of participants (DM subjects) or modifying prescriptive theories as done in this te...

According to game theory, a human subject playing the ultimatum game should choose more for oneself and offer the least amount possible for co-players (assumption of selfish rationality) (Rubinstein in J Econ Behav Organ 3(4):367– 388, [1]). However, economy, sociology and neurology communities repeatedly claim non-rationality of the human behaviou...

The problem of incorporating user's knowledge – possibly uncertain and/or contradictory – is inspected. Bayesian methodology together with a technique of generating fictitious data are used for computing appropriate initial conditions of recursive least squares for estimating parameters of Gaussian ARX model. Resulting algorithms respect different...

A high-order Markov chain is a universal model of stochastic relations between discrete-valued variables. The exact estimation of its transition probabilities suffers from the curse of dimensionality. It requires an excessive amount of informative observations as well as an extreme memory for storing the corresponding sufficient statistic. The pape...

The paper describes an advanced methodology of automatic knowledge elicitation. It merges fragmental uncer-tain knowledge pieces into the prior distribution of unknown parameter of a probabilistic model of a dynamic system. Careful knowledge elicitation helps in achieving as bump-less start of model-based controllers as possible. It is also importa...

Decision making (DM) is a preferences-driven choice among available actions. Under uncertainty, Savage's axiomatisation singles out Bayesian DM as the adequate normative framework. It constructs strategies generating the optimal actions, while assuming that the decision maker rationally tries to meet her preferences. Descriptive DM theories have o...

This volume focuses on uncovering the fundamental forces underlying dynamic decision making among multiple interacting, imperfect and selfish decision makers. The chapters are written by leading experts from different disciplines, all considering the many sources of imperfection in decision making, and always with an eye to decreasing the myriad dis...

Computational and communication complexities call for distributed, robust, and adaptive control. This paper proposes a promising way of bottom-up design of distributed control in which simple controllers are responsible for individual nodes. The overall behavior of the network can be achieved by interconnecting such controlled loops in cascade cont...

Fully probabilistic design of decision strategies (FPD) extends Bayesian dynamic decision making. The FPD speci�es the decision aim via so-called ideal - a probability density, which assigns high probability values to the desirable behaviours and low values to undesirable ones. The optimal decision strategy minimises the Kullback-Leibler divergence...

SUMMARY Joint parameter and state estimation is proposed for linear state-space model with uniform, entry-wise correlated, state and output noises (LSU model for short). The adopted Bayesian modelling and approximate estimation produce an estimator that (a) provides the maximum a posteriori estimate enriched by information on its precision, (b) res...

An exploitation of prior knowledge in parameter estimation becomes vital whenever measured data is not informative enough. Elicitation of quantified prior knowledge is a well-elaborated art in societal and medical applications but not in the engineering ones. Frequently required involvement of a facilitator is mostly unrealistic due to either facil...

The paper presents a novel concept of the anisotropy-based analysis for the stochastic sequences with nonzero mean. The formulas for the anisotropy of random vector and mean anisotropy of sequence are obtained. Basic types of shaping filter connections are presented.

Decision making (DM) is ubiquitous in both natural and artificial systems. The decisions made often differ from those recommended by the axiomatically well-grounded normative Bayesian decision theory, in a large part due to limited cognitive and computational resources of decision makers (either artificial units or humans). This state of a airs is...

Systems supporting decision making became almost inevitable in the modern complex world. Their efficiency depends on the sophisticated interfaces enabling a user take advantage of the support while respecting the increasing on-line information and incomplete, dynamically changing user's preferences. The best decision making support is useless witho...

Recursive estimation forms core of adaptive prediction and control. Dynamic exponential family is the only but narrow class of parametric models that allows exact Bayesian estimation. The paper provides an approximate estimation of important autoregressive model with exogenous variables (ARX) and uniform noise. This model reflects well physical nat...

This paper concerns the Bayesian tracking of slowly varying parameters of a linear stochastic regression model. The modelled and predicted system output is assumed to possess time-varying mean value, whereas its dynamics are relatively stable. The proposed estimation method models the system output mean value by time-varying offset. It formulates t...

Prescriptive Bayesian decision making has reached a high level of maturity, supported by efficient, theoretically well-founded algorithms. However experimental data shows that real decision makers choose such Bayes-optimal decisions surprisingly infrequently, often making decisions that are badly sub-optimal. So prevalent is such imperfect decision...

The paper introduces an algorithm for estimation of dynamic mixture models. A new feature of the proposed algorithm is the ability to consider a dynamic form not only for component models but also for the pointer model, which describes the activities of the mixture components in time. The pointer model is represented by a table of transition probab...

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design co...

Any systematic decision-making design selects a decision strategy that makes the resulting closed-loop behaviour close to the desired one. Fully Probabilistic Design (FPD) describes modelled and desired closed-loop behaviours via their distributions. The designed strategy is a minimiser of Kullback-Leibler divergence of these distributions. FPD: i)...

Probabilistic mixtures provide flexible “universal” approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs “naturally” in one-pass mode. This is important in on-line applications and/or extens...

Model-based predictors and controllers frequently depend on efficient recursive estimation of model parameters. Similarly often, there are known hard bounds on parameter values. Adaptive control applied for rolling mills represents a typical example of such case. While common estimation algorithms are elaborated enough to be utilized in industrial...

We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called Dynamic Model Averaging (DMA) in which a state space model for the parameters of each model is combined with a Markov chain model for the correct model. This allows the "correct" model to vary over time. The state s...

Non-symmetric Kullback–Leibler divergence (KLD) measures proximity of probability density functions (pdfs). Bernardo (Ann. Stat. 1979; 7(3):686–690) had shown its unique role in approximation of pdfs. The order of the KLD arguments is also implied by his methodological result. Functional approximation of estimation and stabilized forgetting, servin...

The paper describes an advanced methodology of automatic knowledge elicitation. It merges fragmental uncertain knowledge pieces into the prior distribution of unknown parameter of a probabilistic model of a dynamic system. Careful knowledge elicitation helps in achieving as bump-less start of model-based controllers as possible. It is also importan...

The paper concerns a cooperation problem in multiple participant decision making (DM). A fully scalable cooperation model with individual participants being Bayesian decision makers who use fully probabilistic design of the optimal decision strategy is presented. The solution suggests a flat structure of cooperation, where each participant interact...

The paper proposes a new estimating algorithm for linear parameter varying systems with slowly time-varying parameters when the rate of change of individual parameters is different. It introduces a true probability density function, describing ideally the behaviour of parameters. However, as it is unknown, we search for its best approximation. A co...

Secondary lymphedema of upper limbs, a frequent complication after a breast cancer therapy, can be successfully treated only when diagnosed at an early, ideally latent, stage. Lymphoscintigraphy is a promising candidate to this purpose. A slow lymphatic dynamics of upper limbs allows, however, a routine collection at most three images reflecting it...

The paper provides background of fully probabilistic design of decision-making strategies and finds its position with respect to the standard Bayesian decision making.

This text provides background of fully probabilistic design of decision-making strategies and �nds its position with respect to the standard Bayesian decision making.

The complexity of the problems to be addressed in an e-democracy framework and the variety of involved stakeholders, with different backgrounds, views and access to information sources, lead us to consider the case in which an e-negotiation should be performed among subjects who have partial, sometimes incompatible, information and can hardly gathe...

The problem of evaluation of advisory system quality is studied. Specifically, 18 advisory strategies for op- erators of a cold rolling mill were designed using different modelling assumptions. Since some assumptions may be more appropriate in different working regimes, we also design a new advising strategy based on the on-line merging of advices....

Principal component analysis is a well developed and understood method of multivariate data processing. Performance of PCA depends on the amount and characteristics of the noise in the observed data. In this paper we show how the use of a Bayesian approach, and especially prior information, improves its performance.

The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector (u 1 ,x 1 ,⋯,u T ,x T ) on a sample space of 2T dimensions. One of the distributions is known, the other is known only partially. Namely, onl...

The Dirichlet process prior (DPP) is used to model an unknown probability distribution, F. This eliminates the need for parametric model assumptions, providing robustness in problems where there is significant model uncertainty. Two important parametric techniques for learning are extended to this non-parametric context for the first time. These ar...

Autoregressive model with exogenous inputs (ARX) is a widely-used black-box type model underlying adaptive predictors and controllers. Its innovations, stochastic unobserved stimulus of the model, are white, zero mean with time-invariant variance. Mostly, the innovations are assumed to be normal. It induces least squares as the adequate estimation...

Recursive non-linear Bayesian estimation is addressed using equivalence approach as motivating framework. Its speciflc form { tailored to a model class covering non-normal ARX (auto-regression with exogenous variables) models, models with discrete outputs and continuous-valued regression vectors and their dynamic mixtures { is presented. The result...

Estimation, learning, pattern recognition, diagnostics, fault detection and adaptive control are prominent examples of dynamic decision making under uncertainty. Under rather general conditions, they can be cast into a common theoretical framework labelled as Bayesian decision making. Richness of the practically developed variants stems from: (i) d...

Reliable extrapolation - simulation or prediction - of syste m output is an invaluable departure point for the control system design. For application of model-based techniques, the knowl- edge of the model structure is essential. It can be based purely on the physical point of view or estimated from process data while the system is considered as a...

Estimation, learning, pattern recognition, diagnostics, fault detection and adaptive control are prominent examples of dynamic decision making under uncertainty. Under rather general conditions, they can be cast into a common theoretical framework labelled as Bayesian decision making. Richness of the practically developed variants stems from: (i) d...

This article describes a formal approach to decision making optimization in commodity futures markets. Our aim is to plan optimal decision at a given time, where we could decide to buy or sell a commodity contract or stay out of the market. The decision is made using dynamic programming with loss function equal to negative profit measured in money,...

Linear state-space model with uniformly distributed innovations is considered. Its state and parameters are estimated under hard physical bounds. Off-line maximum a posteriori probability estimation reduces to linear programming. No approximation is required for sole estimation of either model parameters or states. The noise bounds are estimated in...

Any cooperation in multiple-participant decision making (DM) relies on an exchange of individual knowledge pieces and aims. A general methodology of their rational exploitation without calling for an objective mediator is still missing. Desired methodology is proposed for an important particular case, when a participant, performing Bayesian paramet...

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This work summarizes theoretical and algorithmic basis of optimized prob- abilistic advising. It has arisen within a series of targeted research projects supported European Commission and Czech grant bodies. The source text has served as a common communication basis of the research team. When accumulating and re�ning the material we found that the...

The best test of quality of an estimated model is its implementation in real application. However, the use of a bad model is typically too costly. Therefore, model validation is considered as an obligatory step in model learning, and extensive theory has been developed within statistical community. However, the available rules deal almost exclusive...

A mixture-based framework for robust estimation of ARX-type processes is presented. The ARX process is presumed to suffer from an unknown noise and/or distortion. The approach taken here is to model the overall degraded process via a mixture. Each component of this mixture uses the same ARX model but explores a different noise/distortion process. E...

Efficient multiple participant decision-making relies on cooperation of participants. Partially, it is reached by sharing knowledge. A specific but important case of this type is addressed here. Essentially, a participant passes to its partner distribution on common data and partner uses it for correcting its Bayesian parameter estimate.

In nuclear medicine, estimation of doses ab-sorbed in target tissues serves for both medical and radio-hygienical purposes. Dose is proportional to time integral of the target tissue activity. Therefore, a suitable specific model describing ability of the con-sidered tissue to absorb radioactive substance, partic-ularly thyroid gland and 131 I, is...

The paper shares experience gained in application of dynamic Bayesian approach to control problems in the field of metal rolling. The contribution introduces basic notions of theory applied and provides the algorithmic as well as application-oriented solutions developed. Specifically, the consistent use of the approach resulted in an advanced decis...