Robust Filtering Through Coherent Lower Previsions

Benavoli, Alessio; Zaffalon, Marco; Miranda, Enrique

doi:10.1109/tac.2010.2090707

Cited by 32 publications

(38 citation statements)

References 32 publications

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“…Antonucci et al [34] investigated the use of iHMMs under epistemic irrelevance for tracking tasks. Benavoli et al [8] defined an iHMM over continuous variables aimed at robust filtering. An imprecise version of the Baum-Welch procedure [1], used to estimate the parameters of an HMM when the state sequence is not observable, was developed by Antonucci et al [35], and tested on an activity recognition task.…”

Section: Related Workmentioning

confidence: 99%

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Hidden Markov models with set-valued parameters

2016

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Hidden Markov models (HMMs) are widely used probabilistic models of sequential data. As with other probabilistic models, they require the specification of local conditional probability distributions, whose assessment can be too difficult and error-prone, especially when data are scarce or costly to acquire. The imprecise HMM (iHMM) generalizes HMMs by allowing the quantification to be done by sets of, instead of single, probability distributions. iHMMs have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. In this paper, we consider iHMMs under the strong independence interpretation, for which we develop efficient inference algorithms to address standard HMM usage such as the computation of likelihoods and most probable explanations, as well as performing filtering and predictive inference. Experiments with real data show that iHMMs produce more reliable inferences without compromising the computational efficiency.

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Section: Related Workmentioning

confidence: 99%

“…This is the case, for instance, when data are scarce [5], observations are missing not-at-random [6], and information is conflicting. In such cases, the use of probability distributions to represent uncertainty might be inadequate and lead to overly confident inferences [5,7,8].…”

Section: Introductionmentioning

confidence: 99%

Hidden Markov models with set-valued parameters

2016

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“…Such a state estimate can neither be described by a single probability function nor by a single set. To solve this issue, we make use of the theory of imprecise probabilities [10], from which generalizations of Bayesian state estimation have, for example, been derived in [11,12]. For our purpose of bounding linearization errors within the Kalman filtering framework, sets of probability densities [13,14] will serve as proper characterizations of uncertain quantities.…”

Section: Sets Of Densitiesmentioning

confidence: 99%

“…The covariance of the set of estimated Gaussian densities is still given by the standard equation (11). Because of the linearization, this matrix still can be underestimated, but the set of means, i.e., the bounds for linearization errors, enables us to compute a guaranteed confidence set with respect to the a priori defined probability level P .…”

Section: Filteringmentioning

confidence: 99%

Bounding linearization errors with sets of densities in approximate Kalman filtering

Noack

Klumpp

Petkov

et al. 2010

2010 13th International Conference on Information Fusion

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-Applying the Kalman filtering scheme to linearized system dynamics and observation models does in general not yield optimal state estimates. More precisely, inconsistent state estimates and covariance matrices are caused by neglected linearization errors. This paper introduces a concept for systematically predicting and updating bounds for the linearization errors within the Kalman filtering framework. To achieve this, an uncertain quantity is not characterized by a single probability density anymore, but rather by a set of densities and accordingly, the linear estimation framework is generalized in order to process sets of probability densities. By means of this generalization, the Kalman filter may then not only be applied to stochastic quantities, but also to unknown but bounded quantities. In order to improve the reliability of Kalman filtering results, the last-mentioned quantities are utilized to bound the typically neglected nonlinear parts of a linearized mapping.

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“…Recent work (De Cooman, Hermans, Antonucci, & Zaffalon, 2010) has shown that the use of epistemic irrelevance guarantees that there is an efficient algorithm for updating beliefs about a single target node of a credal tree, that is essentially linear in the number of nodes in the tree. For imprecise-probabilistic hidden Markov models (iHMMs), which are the credal network equivalent of hidden Markov models (HMMs), this efficiency for single target node inferences has been succesfully exploited to develop an imprecise-probabilistic counterpart to the Kalman filter (Benavoli, Zaffalon, & Miranda, 2011).…”

Section: Introductionmentioning

confidence: 99%

An Efficient Algorithm for Estimating State Sequences in Imprecise Hidden Markov Models

Bock

Cooman

2014

jair

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We present an efficient exact algorithm for estimating state sequences from outputs or observations in imprecise hidden Markov models (iHMMs). The uncertainty linking one state to the next, and that linking a state to its output, is represented by a set of probability mass functions instead of a single such mass function. We consider as best estimates for state sequences the maximal sequences for the posterior joint state model conditioned on the observed output sequence, associated with a gain function that is the indicator of the state sequence. This corresponds to and generalises finding the state sequence with the highest posterior probability in (precise-probabilistic) HMMs, thereby making our algorithm a generalisation of the one by Viterbi. We argue that the computational complexity of our algorithm is at worst quadratic in the length of the iHMM, cubic in the number of states, and essentially linear in the number of maximal state sequences. An important feature of our imprecise approach is that there may be more than one maximal sequence, typically in those instances where its precise-probabilistic counterpart is sensitive to the choice of prior. For binary iHMMs, we investigate experimentally how the number of maximal state sequences depends on the model parameters. We also present an application in optical character recognition, demonstrating that our algorithm can be usefully applied to robustify the inferences made by its precise-probabilistic counterpart.

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Robust Filtering Through Coherent Lower Previsions

Cited by 32 publications

References 32 publications

Hidden Markov models with set-valued parameters

Hidden Markov models with set-valued parameters

Bounding linearization errors with sets of densities in approximate Kalman filtering

An Efficient Algorithm for Estimating State Sequences in Imprecise Hidden Markov Models

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