Approximate Bayesian Prediction Using State Space Model with Uniform Noise

Jirsa, Ladislav; Pavelková, Lenka; Quinn, Anthony

doi:10.1007/978-3-030-31993-9_27

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…For all these performance quantities, smaller is better. Conversely, the containment probability, p c (41), where evaluable, is a bigger is better quantity. Because of their wide numerical ranges, the quantities ( 38), ( 39) and ( 40) are plotted logarithmically.…”

Section: Evaluation Criteriamentioning

confidence: 98%

“…at an infinite filtering horizon and so cannot be implemented (the curse of dimensionality [35]). In [41,42], approximate Bayesian filtering with the LSU model ( 19) and (20), closed within the UOS class (18), is proposed. This involves a local approximation after each data update (2) and time update (3), as recalled below.…”

Section: Lsu-uos Filtering Task For the Isolated Targetmentioning

confidence: 99%

“…In [41], a local approximation is proposed so that the resulting polytopic support of ( 22) is circumscribed by an orthotope, giving…”

Section: Lsu-uos Data Updatementioning

confidence: 99%

“…The approximate Bayesian sufficient statistics, x t and x t , process d(t) tractably ∀t, yielding an implementable algorithm. The details are provided in [41].…”

Section: Lsu-uos Data Updatementioning

confidence: 99%

“…The resulting pdf does have an orthotopic support, but is not uniform on it. In [41], the following local approximation projects f (x t+1 |d(t)) back into the UOS class, ∀t:…”

Section: Lsu-uos Time Updatementioning

confidence: 99%

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Fully probabilistic design for knowledge fusion between Bayesian filters under uniform disturbances

Pavelková¹,

Jirsa²,

Quinn³

2021

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This paper considers the problem of Bayesian transfer learning-based knowledge fusion between linear state-space processes driven by uniform state and observation noise processes. The target task conditions on probabilistic state predictor(s) supplied by the source filtering task(s) to improve its own state estimate. A joint model of the target and source(s) is not required and is not elicited. The resulting decision-making problem for choosing the optimal conditional target filtering distribution under incomplete modelling is solved via fully probabilistic design (FPD), i.e. via appropriate minimization of Kullback-Leibler divergence (KLD). The resulting FPD-optimal target learner is robust, in the sense that it can reject poor-quality source knowledge. In addition, the fact that this Bayesian transfer learning (BTL) scheme does not depend on a model of interaction between the source and target tasks ensures robustness to the misspecification of such a model. The latter is a problem that affects conventional transfer learning methods. The properties of the proposed BTL scheme are demonstrated via extensive simulations, and in comparison with two contemporary alternatives.

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Section: Evaluation Criteriamentioning

confidence: 98%

Section: Lsu-uos Filtering Task For the Isolated Targetmentioning

confidence: 99%

“…In [41], a local approximation is proposed so that the resulting polytopic support of ( 22) is circumscribed by an orthotope, giving…”

Section: Lsu-uos Data Updatementioning

confidence: 99%

“…The approximate Bayesian sufficient statistics, x t and x t , process d(t) tractably ∀t, yielding an implementable algorithm. The details are provided in [41].…”

Section: Lsu-uos Data Updatementioning

confidence: 99%

“…The resulting pdf does have an orthotopic support, but is not uniform on it. In [41], the following local approximation projects f (x t+1 |d(t)) back into the UOS class, ∀t:…”

Section: Lsu-uos Time Updatementioning

confidence: 99%

See 3 more Smart Citations