|
|
Diffusion Kalman filtering under unknown process and measurement noise covariance matrices
Vlk, T. ; Dedecius, Kamil
The state-of-the-art algorithms for Kalman filtering in agent networks with information diffusion impose the requirement of well-defined state-space models. In particular, they assume that both the process and measurement noise covariance matrices are known and properly set. This is a relatively strong assumption in the signal processing domain. By design, the Kalman filters are rather sensitive to its violation, which may potentially lead to their divergence. In this paper, we propose a novel distributed filtering algorithm with increased robustness under unknown process and measurement noise covariance matrices. It is formulated as a Bayesian variational message passing procedure for simultaneous analytically tractable inference of states and measurement noise covariance matrices.
|
|
|
Distributed Sequential Zero-Inflated Poisson Regression
Žemlička, R. ; Dedecius, Kamil
The zero-inflated Poisson regression model is a generalized linear model (GLM) for non-negative count variables with an excessive number of zeros. This letter proposes its low-cost distributed sequential inference from streaming data in networks with information diffusion. The model is viewed as a probabilistic mixture of a Poisson and a zero-located Dirac component, whose probabilities are estimated using a quasi-Bayesian procedure. The regression coefficients are inferred by means of a weighted Bayesian update. The network nodes share their posterior distributions using the diffusion protocol.\n
|
|
|
Diffusion MCMC for Mixture Estimation
Reichl, Jan ; Dedecius, Kamil
Distributed inference of parameters of mixture models by a network of cooperating nodes (sensors) with computational and communication capabilities still represents a challenging task. In the last decade, several methods were proposed to solve this issue, predominantly formulated within the expectation-maximization framework and with the assumption of mixture components normality. The present paper adopts the Bayesian approach to inference of general (non-normal) mixtures via the Markov chain Monte Carlo simulation from the parameter posterior distribution. By collaborative tuning of node chains, the method allows reliable estimation even at nodes with significantly worse observational conditions, where the components may tend to merge due to high variances. The method runs in the diffusion networks, where the nodes communicate only with their adjacent neighbors within 1 hop distance.
|
|
| |
|
|
Preliminaries of probabilistic hierarchical fault detection
Jirsa, Ladislav ; Pavelková, Lenka ; Dedecius, Kamil
The paper proposes a novel probabilistic fault detection and isolation (FDI) system that enables to evaluate dynamically the industrial system condition (health) at any level of its functional hierarchy. The investigated industrial system is considered as a set of interconnected individual components. Each component acts in its noisy environment as an imperfect participant, more or less dependent on neighbouring components and, in turn, influencing some others. The nature of the problem prevents us from expressing sufficiently hard propositions about the health of the system as a whole at once but we can observe and construct propositions at lower system hierarchies. These propositions (opinions) are combined at higher levels using the rules of probabilistic logic, retaining the ignorance and finally yielding a single opinion on the health of the whole monitored system.
|
|
| |
|
|
Approximate Bayesian Recursive Estimation: On Approximation Errors
Kárný, Miroslav ; Dedecius, Kamil
Adaptive systems rely on recursive estimation of a firmly bounded complex- ity. As a rule, they have to use an approximation of the posterior proba- bility density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then ap- proximated. 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 this problem.
|
|
|
Towards Distributed Bayesian Estimation A Short Note on Selected Aspects
Dedecius, Kamil ; Sečkárová, Vladimíra
The rapid development of ad-hoc wireless networks, sensor networks and similar calls for efficient estimation of common parameters of a linear or nonlinear model used to describe the operating environment. Therefore, the theory of collaborative distributed estimation has attained a very considerable focus in the past decade, however, mostly in the classical deterministic realm. We conjecture, that the consistent and versatile Bayesian decision making framework, whose applications range from the basic probability counting up to the nonlinear estimation theory, can significantly contribute to the distributed estimation theory. The limited extent of the paper allows to address the considered problem only very superficially and shortly. Therefore, we are forced to leave the rigorous approach in favor of a short survey indicating the arising possibilities appealing to the non- Bayesian literature.
|
|
|
Notes on projection based modelling of beta-distributed weights of a two-component mixture
Dedecius, Kamil
This report contains brief notes on estimation of beta-distributed weight of a Gaussian mixture. The results are directly applied in paper Kárný, M.: On approximate Bayesian recursive estimation]. First, we develop a method to update the beta distribution of weights by new data (evidences) and show, that a projection is needed to preserve the low modelling complexity. Then, we show how forgetting may be applied to improve adaptivity. The results can be immediately applied to multicomponent mixtures.
|
|
|
Modelling of Traffic Flow with Bayesian Autoregressive Model with Variable Partial Forgetting
Dedecius, Kamil ; Nagy, Ivan ; Hofman, Radek
Computing the future road traffic intensities in urban and suburban areas is considered inthis paper. The statistical properties of the traffic flow advocate the use of a low-order lin- ear autoregressive models, in which the previous intensities determine the following ones. To achieve adaptivity, the Bayesian modelling framework was chosen. The regression coefficients are considered random, hence they are modelled using a suitable distribution. A significant improvement of the overall modelling performance is further reached with techniques allowing the parameters vary by modification of their distribution. We present the partial forgetting method, allowing to individually track the parameters even in the case of their different variability rate.
|
host ::
RSS.