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BSc. Topic: Approximate Recursive Bayesian Estimation with Forgetting (Kárný)

Type of Work: 
ÚTIA AV ČR, v.v.i., oddělení AS, 266052274

1. Learn about Bayesian parameter estimation.
2. Learn about the principle of minimum expected relative entropy.
3. Propose an approximate Bayesian model parameter estimation based on the Taylor expansion of the logarithm of the model.
4. Use Bayesian predictors using a priori and posterior probabilities of parameters to estimate confidence in them. This will serve for the design of a new a priori distribution using the principle of minimum expected entropy.
5. Program the result and, in case of logistic regression, compare its quality with a suitable standard.

Recursive estimation of model parameters is a key part of adaptive systems predicting or influencing their complex random environment. Mostly, the models do not allow the desired exact Bayesian estimation and therefore it is necessary to implement them approximately. In this case, it is necessary to forget the invalid knowledge, because otherwise the behavior of the estimated model and the modeled environment often diverge from each other. The choice of data-dependent forgetting rate is still an open problem despite decades of ongoing research on this issue. The work will be focused on an attempt at an original solution based on the use of: i) the recently derived principle of minimum expected relative entropy and; ii) Bayesian rules for estimating confidence in alternative descriptions of unknown parameters.


Recommended literature (parts selected after agreement with the supervisor)

1. V. Peterka, Bayesian System Identification, in P. Eykhoff "Trends and Progress in System Identification", Pergamon Press, Oxford, 239-304, 1981.
2. R. Kulhavy, M.B. Zarrop, On a General Concept of Forgetting, International Journal of Control 58(4), 905-924, 1993.
3. M. Kárný, Minimum Expected Relative Entropy Principle, Proc. of the 18th European Control Conference, 35-40, 2020.
4. M. Kárný, Approximate Bayesian recursive estimation, Inf. Sciences 285(1), 100-111 2014.

2022-09-15 10:16